TSTP Solution File: SWV706-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV706-1 : 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 : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:10:24 EDT 2024

% Result   : Unsatisfiable 27.00s 4.33s
% Output   : Refutation 27.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 2507
% Syntax   : Number of formulae    : 4522 (1453 unt;   0 def)
%            Number of atoms       : 11686 (2139 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 12653 (5489   ~;5840   |;   0   &)
%                                         (1324 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of predicates  : 1396 (1394 usr;1325 prp; 0-6 aty)
%            Number of functors    :   34 (  34 usr;  10 con; 0-5 aty)
%            Number of variables   : 6792 (6792   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f69970,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2020,f2025,f2030,f2035,f2040,f2045,f2050,f2055,f2060,f2065,f2070,f2075,f2080,f2085,f2090,f2095,f2100,f2105,f2110,f2115,f2120,f2125,f2130,f2135,f2140,f2145,f2150,f2155,f2160,f2165,f2170,f2175,f2180,f2185,f2190,f2195,f2200,f2205,f2210,f2215,f2220,f2225,f2230,f2235,f2240,f2245,f2250,f2255,f2260,f2265,f2270,f2275,f2280,f2285,f2290,f2295,f2300,f2305,f2310,f2315,f2320,f2325,f2330,f2335,f2340,f2345,f2350,f2355,f2360,f2365,f2370,f2375,f2380,f2385,f2390,f2395,f2400,f2405,f2410,f2415,f2420,f2425,f2430,f2435,f2440,f2445,f2450,f2455,f2460,f2465,f2470,f2475,f2480,f2485,f2490,f2495,f2500,f2505,f2510,f2515,f2520,f2525,f2530,f2535,f2540,f2545,f2550,f2555,f2560,f2565,f2570,f2575,f2580,f2585,f2590,f2595,f2600,f2605,f2610,f2615,f2620,f2625,f2630,f2635,f2640,f2645,f2650,f2655,f2659,f2664,f2668,f2673,f2677,f2681,f2686,f2690,f2694,f2700,f2704,f2708,f2712,f2718,f2724,f2728,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2794,f2799,f2804,f2810,f2815,f2819,f2823,f2827,f2832,f2836,f2840,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f2873,f2878,f2882,f2886,f2890,f2907,f2918,f2922,f2926,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2967,f2971,f2975,f2979,f2983,f2987,f3024,f3028,f3032,f3036,f3040,f3044,f3048,f3052,f3056,f3057,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3137,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3178,f3182,f3186,f3190,f3194,f3198,f3203,f3209,f3213,f3218,f3222,f3236,f3271,f3288,f3311,f3330,f3334,f3338,f3342,f3346,f3351,f3355,f3359,f3363,f3367,f3371,f3375,f3379,f3383,f3387,f3391,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3433,f3438,f3442,f3446,f3450,f3454,f3458,f3462,f3466,f3470,f3474,f3479,f3483,f3487,f3491,f3495,f3499,f3503,f3507,f3511,f3516,f3521,f3537,f3742,f3924,f3928,f3932,f3937,f3941,f3945,f3949,f3953,f3957,f3961,f3965,f3969,f3973,f3977,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4104,f4109,f4113,f4277,f4416,f4511,f4515,f4519,f4523,f4527,f4537,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4624,f4628,f4632,f4636,f4640,f4645,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4731,f4736,f4740,f4769,f5009,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5265,f5269,f5273,f5277,f5281,f5285,f5289,f5293,f5297,f5301,f5305,f5309,f5313,f5317,f5321,f5325,f5329,f5333,f5338,f5343,f5347,f5352,f5356,f5360,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5392,f5396,f5400,f5404,f5408,f5412,f5416,f5420,f5424,f5428,f5432,f5446,f5450,f5454,f5458,f5462,f5517,f5758,f6085,f6378,f6382,f6386,f6390,f6394,f6398,f6402,f6406,f6410,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6499,f6504,f6508,f6512,f6516,f6520,f6524,f6528,f6532,f6536,f6540,f6544,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6587,f6591,f6596,f6600,f6604,f6608,f6612,f6616,f6620,f6624,f6628,f6632,f6636,f6654,f6658,f6662,f6666,f6670,f6674,f6678,f6682,f6686,f6690,f6695,f6699,f6704,f6928,f6966,f7314,f7755,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8288,f8292,f8296,f8300,f8394,f8813,f9067,f9138,f9142,f9146,f9150,f9154,f9177,f9181,f9185,f9189,f9193,f9197,f9201,f9205,f9209,f9213,f9218,f9222,f9226,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9266,f9270,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9311,f9315,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9347,f9572,f10397,f10525,f10529,f10533,f10537,f10541,f10545,f10549,f10557,f10561,f10565,f10569,f10573,f10577,f10581,f10585,f10589,f10593,f10610,f10614,f10618,f10622,f10626,f10630,f10634,f10638,f10642,f10646,f10650,f10654,f10658,f10662,f10666,f10670,f10674,f10678,f10682,f10686,f10691,f10697,f10701,f10705,f10709,f10713,f10717,f10721,f10725,f10729,f10733,f10753,f10757,f10761,f10765,f10769,f10773,f10777,f10781,f11323,f11712,f12215,f12268,f12272,f12276,f12280,f12284,f12288,f12292,f12296,f12300,f12304,f12308,f12312,f12316,f12320,f12324,f12328,f12332,f12340,f12344,f12348,f12352,f12356,f12360,f12364,f12368,f12372,f12376,f12377,f12381,f12385,f12389,f12393,f12397,f13487,f13491,f13495,f13544,f13548,f13552,f13556,f13560,f13564,f13568,f13572,f13576,f13580,f13585,f13605,f13609,f13613,f13617,f13621,f13628,f13632,f13636,f13640,f13644,f13645,f13651,f13655,f13659,f13663,f13667,f13671,f13675,f13679,f13683,f13687,f13695,f13699,f13703,f13707,f13711,f13715,f13824,f14646,f14650,f14654,f14658,f14662,f14666,f14715,f14719,f14723,f14727,f14731,f14735,f14739,f14743,f14747,f14751,f14755,f14759,f14763,f14767,f14771,f14775,f14779,f14783,f14787,f14791,f14796,f14858,f14862,f14867,f14952,f14956,f14960,f14964,f14968,f14972,f14973,f14981,f14985,f14989,f14993,f14997,f15001,f15005,f15009,f15013,f15017,f15021,f15025,f15029,f15033,f15037,f15698,f17155,f17159,f17163,f17167,f17171,f17175,f17180,f17184,f17188,f17192,f17196,f17200,f17204,f17208,f17212,f17216,f17220,f17351,f17355,f17360,f17409,f17414,f17451,f17455,f17459,f17464,f17468,f17473,f17521,f17866,f17870,f17874,f17878,f17882,f17887,f17896,f17900,f17904,f17908,f17912,f17916,f17920,f17924,f17928,f17932,f17936,f17940,f17944,f17948,f17952,f17956,f17960,f17964,f17968,f17972,f17976,f17980,f17984,f17988,f17992,f17996,f18000,f18004,f18008,f18012,f18016,f18020,f18053,f18057,f18061,f18065,f18069,f18073,f18078,f18102,f18107,f18143,f18147,f18151,f18155,f18159,f18163,f18167,f18171,f18175,f18179,f18183,f18187,f18191,f18195,f18199,f18203,f18207,f18211,f18215,f18219,f18223,f18227,f18231,f18235,f18239,f18243,f18248,f18347,f18759,f19176,f19789,f20245,f20694,f20862,f20866,f20871,f20937,f20941,f20945,f20949,f20954,f21061,f21065,f21069,f21073,f21078,f21145,f21149,f21153,f21157,f21231,f21270,f21274,f21278,f21282,f21286,f21290,f21295,f21380,f21385,f21440,f21445,f21507,f21512,f21582,f21664,f21732,f21737,f21758,f21762,f21766,f21770,f21774,f21863,f23098,f23998,f24235,f24240,f24317,f24321,f24326,f24366,f24464,f24468,f24472,f24476,f24480,f24484,f24488,f24492,f24496,f24500,f24521,f24525,f24529,f24533,f24537,f24541,f24545,f24549,f24553,f24557,f24561,f24565,f24569,f24573,f24766,f25165,f25579,f25583,f25629,f25633,f25637,f25641,f25645,f25649,f25653,f25657,f25661,f25665,f25691,f25695,f25699,f25703,f25707,f25711,f25715,f25719,f25723,f25727,f25731,f25735,f25739,f25743,f25747,f25751,f25755,f25759,f25763,f25767,f25771,f25799,f25803,f25807,f25811,f25815,f25819,f25823,f25827,f25831,f25835,f25881,f25885,f25889,f25893,f25897,f25901,f25905,f25909,f25913,f25917,f25921,f25925,f25929,f25933,f25937,f25941,f25945,f25949,f25953,f26731,f27913,f28828,f28863,f28867,f28871,f28875,f28879,f28883,f28887,f28891,f28895,f28899,f28903,f28907,f28911,f28915,f28919,f28923,f28927,f28931,f28936,f29146,f29150,f29154,f29158,f29167,f29171,f29175,f29179,f29183,f29188,f29452,f29456,f29460,f29464,f29468,f29472,f30867,f30871,f30875,f30879,f30883,f30887,f30891,f30895,f30899,f30933,f31117,f31121,f31126,f31130,f31134,f31138,f31142,f31146,f31150,f32154,f32160,f32215,f32216,f34668,f34673,f34678,f34807,f34811,f34815,f34822,f35314,f35315,f35316,f35825,f35826,f38720,f39253,f41634,f44509,f45903,f46181,f46228,f46232,f47197,f47202,f47220,f47226,f47233,f47240,f47264,f47282,f47287,f47295,f47300,f47328,f47334,f47677,f47833,f47849,f47904,f47911,f47922,f48213,f48266,f48269,f48273,f48318,f49807,f50830,f50889,f51015,f51018,f51026,f51085,f53826,f53861,f55261,f55900,f56815,f56885,f57125,f57676,f58125,f58356,f59645,f59851,f59855,f59859,f59880,f59884,f59888,f59892,f59896,f59900,f59904,f59908,f59912,f59916,f59930,f59934,f59938,f59942,f59946,f59950,f59954,f59958,f59962,f59966,f59967,f59971,f59975,f59979,f60401,f60758,f60762,f60766,f60770,f60774,f60778,f60782,f60786,f60790,f60794,f60798,f60799,f60803,f60807,f60811,f60815,f60819,f61354,f61366,f61370,f61374,f61378,f61382,f61386,f61390,f61394,f61398,f61403,f61407,f61411,f61415,f62032,f62036,f62040,f62044,f62049,f62336,f62340,f62344,f62348,f62352,f62356,f62357,f62365,f62369,f62373,f62377,f62381,f62385,f62389,f63126,f63130,f63134,f63138,f63142,f63146,f63150,f64037,f64041,f64375,f64379,f64383,f64387,f64388,f64478,f64482,f64486,f64490,f64494,f64498,f64855,f64859,f64863,f64867,f65064,f65068,f65072,f65076,f65402,f65416,f65420,f65424,f65428,f65432,f65773,f66023,f66027,f66031,f66383,f66387,f66440,f66444,f66448,f66452,f66456,f66460,f66464,f66468,f66472,f66476,f67946,f68083,f68431,f68435,f68439,f68443,f68447,f68451,f68456,f68460,f68464,f69451,f69811,f69819,f69824,f69828,f69888,f69943,f69953,f69961,f69969]) ).

fof(f69969,plain,
    ( ~ spl0_14
    | ~ spl0_97
    | ~ spl0_163
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | ~ spl0_1208
    | spl0_1324 ),
    inference(avatar_contradiction_clause,[],[f69968]) ).

fof(f69968,plain,
    ( $false
    | ~ spl0_14
    | ~ spl0_97
    | ~ spl0_163
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | ~ spl0_1208
    | spl0_1324 ),
    inference(trivial_inequality_removal,[],[f69967]) ).

fof(f69967,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex)
    | ~ spl0_14
    | ~ spl0_97
    | ~ spl0_163
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | ~ spl0_1208
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69966,f60748]) ).

fof(f60748,plain,
    ( ! [X0] : hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X0),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)) = c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X0,c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))
    | ~ spl0_163
    | ~ spl0_1208 ),
    inference(resolution,[],[f59978,f2809]) ).

fof(f2809,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f2807]) ).

fof(f2807,plain,
    ( spl0_163
  <=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f59978,plain,
    ( ! [X2,X22] :
        ( ~ c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
        | hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X2),X22) = c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X2,X22) )
    | ~ spl0_1208 ),
    inference(avatar_component_clause,[],[f59977]) ).

fof(f59977,plain,
    ( spl0_1208
  <=> ! [X22,X2] :
        ( hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X2),X22) = c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X2,X22)
        | ~ c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f69966,plain,
    ( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex)
    | ~ spl0_14
    | ~ spl0_97
    | ~ spl0_163
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | ~ spl0_1208
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69965,f60748]) ).

fof(f69965,plain,
    ( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex)
    | ~ spl0_14
    | ~ spl0_97
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69964,f8820]) ).

fof(f8820,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_97
    | ~ spl0_594 ),
    inference(resolution,[],[f8239,f2499]) ).

fof(f2499,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f2497]) ).

fof(f2497,plain,
    ( spl0_97
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f8239,plain,
    ( ! [X2,X3,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2) )
    | ~ spl0_594 ),
    inference(avatar_component_clause,[],[f8238]) ).

fof(f8238,plain,
    ( spl0_594
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f69964,plain,
    ( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex)
    | ~ spl0_14
    | ~ spl0_97
    | ~ spl0_300
    | ~ spl0_594
    | ~ spl0_935
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69963,f20704]) ).

fof(f20704,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_14
    | ~ spl0_935 ),
    inference(resolution,[],[f18210,f2084]) ).

fof(f2084,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f2082]) ).

fof(f2082,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f18210,plain,
    ( ! [X0,X19,X17] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) )
    | ~ spl0_935 ),
    inference(avatar_component_clause,[],[f18209]) ).

fof(f18209,plain,
    ( spl0_935
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f69963,plain,
    ( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)))),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat))),tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_300
    | ~ spl0_594
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69962,f3515]) ).

fof(f3515,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_300 ),
    inference(avatar_component_clause,[],[f3513]) ).

fof(f3513,plain,
    ( spl0_300
  <=> 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)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f69962,plain,
    ( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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))),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)),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_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_594
    | spl0_1324 ),
    inference(forward_demodulation,[],[f69960,f8820]) ).

fof(f69960,plain,
    ( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex)
    | spl0_1324 ),
    inference(avatar_component_clause,[],[f69958]) ).

fof(f69958,plain,
    ( spl0_1324
  <=> c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

fof(f69961,plain,
    ~ spl0_1324,
    inference(avatar_split_clause,[],[f1696,f69958]) ).

fof(f1696,axiom,
    c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),c_FFT__Mirabelle_ODFT(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),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),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)),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_HOL_Ominus__class_Ominus(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))),hAPP(c_FFT__Mirabelle_OFFT(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)),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f69953,plain,
    spl0_1323,
    inference(avatar_split_clause,[],[f1142,f69951]) ).

fof(f69951,plain,
    ( spl0_1323
  <=> ! [X2,X19,X0,X3,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),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(X19,X2,X0)),c_HOL_Ominus__class_Ominus(X25,X3,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X19,X2,X0)),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ominus__class_Ominus(X25,X3,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

fof(f1142,axiom,
    ! [X2,X3,X0,X19,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),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(X19,X2,X0)),c_HOL_Ominus__class_Ominus(X25,X3,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X19,X2,X0)),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ominus__class_Ominus(X25,X3,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

fof(f69943,plain,
    spl0_1322,
    inference(avatar_split_clause,[],[f1884,f69941]) ).

fof(f69941,plain,
    ( spl0_1322
  <=> ! [X25,X0,X19] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ominus__class_Ominus(X19,X25,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(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)),X19)),X25),X0)
        | ~ class_Int_Onumber__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f1884,plain,
    ! [X0,X19,X25] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ominus__class_Ominus(X19,X25,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(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)),X19)),X25),X0)
      | ~ class_Int_Onumber__ring(X0) ),
    inference(forward_demodulation,[],[f1575,f1837]) ).

fof(f1837,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)),
    inference(forward_demodulation,[],[f1549,f582]) ).

fof(f582,axiom,
    hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

fof(f1549,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(f1575,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ominus__class_Ominus(X19,X25,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),X19),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),X25),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)),X19)),X25),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__diff_0) ).

fof(f69888,plain,
    spl0_1321,
    inference(avatar_split_clause,[],[f2007,f69886]) ).

fof(f69886,plain,
    ( spl0_1321
  <=> ! [X18] :
        ( c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f2007,plain,
    ! [X18] :
      ( c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))
      | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1453,f1837]) ).

fof(f1453,axiom,
    ! [X18] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__exhaust__less__4_0) ).

fof(f69828,plain,
    spl0_1320,
    inference(avatar_split_clause,[],[f1893,f69826]) ).

fof(f69826,plain,
    ( spl0_1320
  <=> ! [X2,X0,X17] :
        ( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f1893,plain,
    ! [X2,X0,X17] :
      ( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
    inference(forward_demodulation,[],[f1327,f1837]) ).

fof(f1327,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),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)),X17))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),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_comm__monoid__add_Opower__odd__eq_0) ).

fof(f69824,plain,
    spl0_1319,
    inference(avatar_split_clause,[],[f1260,f69822]) ).

fof(f69822,plain,
    ( spl0_1319
  <=> ! [X2,X24,X0,X23,X22] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X23),X0)),X22) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f1260,axiom,
    ! [X2,X0,X24,X22,X23] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X23),X0)),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divides__special_0) ).

fof(f69819,plain,
    spl0_1318,
    inference(avatar_split_clause,[],[f1025,f69817]) ).

fof(f69817,plain,
    ( spl0_1318
  <=> ! [X2,X3,X0,X6,X1,X26] :
        ( ~ class_RealVector_Oreal__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X26),X0),X6,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X26,X0),X6,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X0),X6,X0)),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f1025,axiom,
    ! [X2,X3,X0,X1,X6,X26] :
      ( ~ class_RealVector_Oreal__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X26),X0),X6,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X26,X0),X6,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X0),X6,X0)),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).

fof(f69811,plain,
    spl0_1317,
    inference(avatar_split_clause,[],[f699,f69809]) ).

fof(f69809,plain,
    ( spl0_1317
  <=> ! [X19,X20,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Ozero__class_Ozero(X0) = X27
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X25,X0)),c_HOL_Oinverse__class_Odivide(X20,X27,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f699,axiom,
    ! [X0,X19,X27,X25,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) = X27
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X25,X0)),c_HOL_Oinverse__class_Odivide(X20,X27,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

fof(f69451,plain,
    ( ~ spl0_31
    | spl0_1316
    | ~ spl0_269
    | ~ spl0_1155 ),
    inference(avatar_split_clause,[],[f46195,f38718,f3385,f69449,f2167]) ).

fof(f2167,plain,
    ( spl0_31
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f69449,plain,
    ( spl0_1316
  <=> ! [X0] :
        ( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
        | c_lessequals(X0,v_i____,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f3385,plain,
    ( spl0_269
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X25,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f38718,plain,
    ( spl0_1155
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f46195,plain,
    ( ! [X0] :
        ( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
        | c_lessequals(X0,v_i____,tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_269
    | ~ spl0_1155 ),
    inference(resolution,[],[f38719,f3386]) ).

fof(f3386,plain,
    ( ! [X0,X19,X25] :
        ( c_HOL_Oord__class_Oless(X25,X19,X0)
        | c_lessequals(X19,X25,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f3385]) ).

fof(f38719,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_1155 ),
    inference(avatar_component_clause,[],[f38718]) ).

fof(f68464,plain,
    spl0_1315,
    inference(avatar_split_clause,[],[f1416,f68462]) ).

fof(f68462,plain,
    ( spl0_1315
  <=> ! [X18,X40,X17,X22,X24] :
        ( ~ c_lessequals(X24,X22,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f1416,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).

fof(f68460,plain,
    spl0_1314,
    inference(avatar_split_clause,[],[f1415,f68458]) ).

fof(f68458,plain,
    ( spl0_1314
  <=> ! [X18,X40,X17,X22,X24] :
        ( ~ c_lessequals(X24,X22,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).

fof(f1415,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).

fof(f68456,plain,
    spl0_1313,
    inference(avatar_split_clause,[],[f1414,f68454]) ).

fof(f68454,plain,
    ( spl0_1313
  <=> ! [X17,X40,X18,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f1414,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).

fof(f68451,plain,
    spl0_1312,
    inference(avatar_split_clause,[],[f1413,f68449]) ).

fof(f68449,plain,
    ( spl0_1312
  <=> ! [X17,X40,X18,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | ~ c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f1413,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | ~ c_lessequals(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).

fof(f68447,plain,
    spl0_1311,
    inference(avatar_split_clause,[],[f992,f68445]) ).

fof(f68445,plain,
    ( spl0_1311
  <=> ! [X17,X40,X18,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f992,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).

fof(f68443,plain,
    spl0_1310,
    inference(avatar_split_clause,[],[f991,f68441]) ).

fof(f68441,plain,
    ( spl0_1310
  <=> ! [X17,X40,X18,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).

fof(f991,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).

fof(f68439,plain,
    spl0_1309,
    inference(avatar_split_clause,[],[f990,f68437]) ).

fof(f68437,plain,
    ( spl0_1309
  <=> ! [X18,X40,X17,X22,X24] :
        ( ~ c_lessequals(X24,X22,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).

fof(f990,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

fof(f68435,plain,
    spl0_1308,
    inference(avatar_split_clause,[],[f989,f68433]) ).

fof(f68433,plain,
    ( spl0_1308
  <=> ! [X18,X40,X17,X22,X24] :
        ( ~ c_lessequals(X24,X22,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f989,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).

fof(f68431,plain,
    spl0_1307,
    inference(avatar_split_clause,[],[f5,f68429]) ).

fof(f68429,plain,
    ( spl0_1307
  <=> ! [X3,X0,X6,X2] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X6,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f5,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X6,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).

fof(f68083,plain,
    spl0_1306,
    inference(avatar_split_clause,[],[f1919,f68081]) ).

fof(f68081,plain,
    ( spl0_1306
  <=> ! [X24,X40,X17,X18,X22] :
        ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40),tc_nat),X17,tc_nat)
        | ~ c_lessequals(X24,X22,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f1919,plain,
    ! [X40,X18,X17,X24,X22] :
      ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40),tc_nat),X17,tc_nat)
      | ~ c_lessequals(X24,X22,tc_nat) ),
    inference(forward_demodulation,[],[f1420,f1436]) ).

fof(f1436,axiom,
    ! [X24,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

fof(f1420,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).

fof(f67946,plain,
    ( spl0_848
    | spl0_1305
    | ~ spl0_168
    | ~ spl0_176
    | ~ spl0_243
    | ~ spl0_820 ),
    inference(avatar_split_clause,[],[f14921,f14865,f3188,f2863,f2829,f67943,f17177]) ).

fof(f17177,plain,
    ( spl0_848
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = v_i____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f67943,plain,
    ( spl0_1305
  <=> v_i____ = c_Fact_Ofact__class_Ofact(v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f2829,plain,
    ( spl0_168
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f2863,plain,
    ( spl0_176
  <=> ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X18,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f3188,plain,
    ( spl0_243
  <=> ! [X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f14865,plain,
    ( spl0_820
  <=> ! [X18] :
        ( c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat),tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f14921,plain,
    ( v_i____ = c_Fact_Ofact__class_Ofact(v_i____,tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_168
    | ~ spl0_176
    | ~ spl0_243
    | ~ spl0_820 ),
    inference(forward_demodulation,[],[f14920,f3189]) ).

fof(f3189,plain,
    ( ! [X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)) = X17
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f3188]) ).

fof(f14920,plain,
    ( c_Fact_Ofact__class_Ofact(v_i____,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_168
    | ~ spl0_176
    | ~ spl0_820 ),
    inference(forward_demodulation,[],[f14868,f2831]) ).

fof(f2831,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f2829]) ).

fof(f14868,plain,
    ( c_Fact_Ofact__class_Ofact(v_i____,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))
    | c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_176
    | ~ spl0_820 ),
    inference(superposition,[],[f14866,f2864]) ).

fof(f2864,plain,
    ( ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X18,tc_nat)
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f2863]) ).

fof(f14866,plain,
    ( ! [X18] :
        ( c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat),tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_820 ),
    inference(avatar_component_clause,[],[f14865]) ).

fof(f66476,plain,
    spl0_1304,
    inference(avatar_split_clause,[],[f1892,f66474]) ).

fof(f66474,plain,
    ( spl0_1304
  <=> ! [X2,X0,X17] :
        ( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f1892,plain,
    ! [X2,X0,X17] :
      ( hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
    inference(forward_demodulation,[],[f1103,f1837]) ).

fof(f1103,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),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)),X17)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),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_comm__monoid__add_Opower__even__eq_0) ).

fof(f66472,plain,
    spl0_1303,
    inference(avatar_split_clause,[],[f1422,f66470]) ).

fof(f66470,plain,
    ( spl0_1303
  <=> ! [X18,X40,X17,X22,X24] :
        ( ~ c_lessequals(X24,X22,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18) = X17
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f1422,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X24,X22,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X22,X24,tc_nat)),X40)),X18) = X17
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).

fof(f66468,plain,
    spl0_1302,
    inference(avatar_split_clause,[],[f1390,f66466]) ).

fof(f66466,plain,
    ( spl0_1302
  <=> ! [X1,X48,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f1390,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

fof(f66464,plain,
    spl0_1301,
    inference(avatar_split_clause,[],[f1389,f66462]) ).

fof(f66462,plain,
    ( spl0_1301
  <=> ! [X1,X48,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f1389,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

fof(f66460,plain,
    spl0_1300,
    inference(avatar_split_clause,[],[f1388,f66458]) ).

fof(f66458,plain,
    ( spl0_1300
  <=> ! [X2,X48,X0,X3,X1,X26] :
        ( ~ 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(X2,X3,X0)),X48)),X1),X26,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f1388,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ 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(X2,X3,X0)),X48)),X1),X26,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

fof(f66456,plain,
    spl0_1299,
    inference(avatar_split_clause,[],[f1387,f66454]) ).

fof(f66454,plain,
    ( spl0_1299
  <=> ! [X2,X48,X0,X3,X1,X26] :
        ( ~ 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(X2,X3,X0)),X48)),X1),X26,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f1387,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ 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(X2,X3,X0)),X48)),X1),X26,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

fof(f66452,plain,
    spl0_1298,
    inference(avatar_split_clause,[],[f1030,f66450]) ).

fof(f66450,plain,
    ( spl0_1298
  <=> ! [X2,X48,X0,X3,X1,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X48)),X1),X26,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f1030,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X48)),X1),X26,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

fof(f66448,plain,
    spl0_1297,
    inference(avatar_split_clause,[],[f1029,f66446]) ).

fof(f66446,plain,
    ( spl0_1297
  <=> ! [X2,X48,X0,X3,X1,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X48)),X1),X26,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f1029,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X48)),X1),X26,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

fof(f66444,plain,
    spl0_1296,
    inference(avatar_split_clause,[],[f1028,f66442]) ).

fof(f66442,plain,
    ( spl0_1296
  <=> ! [X1,X48,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f1028,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

fof(f66440,plain,
    spl0_1295,
    inference(avatar_split_clause,[],[f1027,f66438]) ).

fof(f66438,plain,
    ( spl0_1295
  <=> ! [X1,X48,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f1027,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

fof(f66387,plain,
    spl0_1294,
    inference(avatar_split_clause,[],[f1026,f66385]) ).

fof(f66385,plain,
    ( spl0_1294
  <=> ! [X19,X20,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Ozero__class_Ozero(X0) = X27
        | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X19,X25,X0),c_HOL_Oinverse__class_Odivide(X20,X27,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f1026,axiom,
    ! [X0,X19,X27,X25,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) = X27
      | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X19,X25,X0),c_HOL_Oinverse__class_Odivide(X20,X27,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

fof(f66383,plain,
    spl0_1293,
    inference(avatar_split_clause,[],[f872,f66381]) ).

fof(f66381,plain,
    ( spl0_1293
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X2 = X3
        | X1 = X26
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f872,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X2 = X3
      | X1 = X26
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

fof(f66031,plain,
    spl0_1292,
    inference(avatar_split_clause,[],[f1918,f66029]) ).

fof(f66029,plain,
    ( spl0_1292
  <=> ! [X24,X40,X17,X18,X22] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40),tc_nat),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40),tc_nat),X17,tc_nat)
        | ~ c_lessequals(X22,X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f1918,plain,
    ! [X40,X18,X17,X24,X22] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40),tc_nat),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40),tc_nat),X17,tc_nat)
      | ~ c_lessequals(X22,X24,tc_nat) ),
    inference(forward_demodulation,[],[f1917,f1436]) ).

fof(f1917,plain,
    ! [X40,X18,X17,X24,X22] :
      ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40),tc_nat),X17,tc_nat)
      | ~ c_lessequals(X22,X24,tc_nat) ),
    inference(forward_demodulation,[],[f1419,f1436]) ).

fof(f1419,axiom,
    ! [X40,X18,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17),tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).

fof(f66027,plain,
    spl0_1291,
    inference(avatar_split_clause,[],[f514,f66025]) ).

fof(f66025,plain,
    ( spl0_1291
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X3),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f514,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X3),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__mult__distrib_0) ).

fof(f66023,plain,
    spl0_1290,
    inference(avatar_split_clause,[],[f513,f66021]) ).

fof(f66021,plain,
    ( spl0_1290
  <=> ! [X17,X0,X18,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X18)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f513,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X18)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__add_0) ).

fof(f65773,plain,
    ( spl0_1289
    | ~ spl0_286
    | ~ spl0_716 ),
    inference(avatar_split_clause,[],[f13752,f11316,f3456,f65770]) ).

fof(f65770,plain,
    ( spl0_1289
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f3456,plain,
    ( spl0_286
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f11316,plain,
    ( spl0_716
  <=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f13752,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_286
    | ~ spl0_716 ),
    inference(resolution,[],[f11318,f3457]) ).

fof(f3457,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = X18 )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f3456]) ).

fof(f11318,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_716 ),
    inference(avatar_component_clause,[],[f11316]) ).

fof(f65432,plain,
    spl0_1288,
    inference(avatar_split_clause,[],[f1864,f65430]) ).

fof(f65430,plain,
    ( spl0_1288
  <=> ! [X22,X18,X24] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X24)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X18))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X24))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f1864,plain,
    ! [X18,X24,X22] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X24)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X18))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X24))),
    inference(forward_demodulation,[],[f1605,f1837]) ).

fof(f1605,axiom,
    ! [X18,X24,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)),X18))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),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)),X24))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel1_0) ).

fof(f65428,plain,
    spl0_1287,
    inference(avatar_split_clause,[],[f1146,f65426]) ).

fof(f65426,plain,
    ( spl0_1287
  <=> ! [X2,X48,X0,X3,X1,X26] :
        ( ~ 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(X3,X2,X0)),X48)),X26) = X1
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f1146,axiom,
    ! [X2,X3,X48,X0,X1,X26] :
      ( ~ 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(X3,X2,X0)),X48)),X26) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

fof(f65424,plain,
    spl0_1286,
    inference(avatar_split_clause,[],[f302,f65422]) ).

fof(f65422,plain,
    ( spl0_1286
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f302,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).

fof(f65420,plain,
    spl0_1285,
    inference(avatar_split_clause,[],[f301,f65418]) ).

fof(f65418,plain,
    ( spl0_1285
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),c_HOL_Oinverse__class_Oinverse(X2,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f301,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),c_HOL_Oinverse__class_Oinverse(X2,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).

fof(f65416,plain,
    spl0_1284,
    inference(avatar_split_clause,[],[f177,f65414]) ).

fof(f65414,plain,
    ( spl0_1284
  <=> ! [X2,X1,X3] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_Divides_Odiv__class_Odiv(X3,X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),c_Divides_Odiv__class_Omod(X3,X1,tc_nat)),X1,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f177,axiom,
    ! [X2,X3,X1] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_Divides_Odiv__class_Odiv(X3,X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),c_Divides_Odiv__class_Omod(X3,X1,tc_nat)),X1,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).

fof(f65402,plain,
    ( spl0_817
    | ~ spl0_315
    | ~ spl0_716 ),
    inference(avatar_split_clause,[],[f13751,f11316,f3967,f14793]) ).

fof(f14793,plain,
    ( spl0_817
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f3967,plain,
    ( spl0_315
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f13751,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_315
    | ~ spl0_716 ),
    inference(resolution,[],[f11318,f3968]) ).

fof(f3968,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3967]) ).

fof(f65076,plain,
    spl0_1283,
    inference(avatar_split_clause,[],[f1944,f65074]) ).

fof(f65074,plain,
    ( spl0_1283
  <=> ! [X17,X33,X19,X0,X31,X29,X32,X30] :
        ( hAPP(hAPP(X32,X19),hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17))) = hAPP(hAPP(X29,X19),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
        | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f1944,plain,
    ! [X31,X29,X0,X19,X17,X32,X30,X33] :
      ( hAPP(hAPP(X32,X19),hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17))) = hAPP(hAPP(X29,X19),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
      | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ),
    inference(forward_demodulation,[],[f1568,f1837]) ).

fof(f1568,axiom,
    ! [X31,X29,X0,X19,X17,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),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)),X17))) = hAPP(hAPP(X32,X19),hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I37_J_0) ).

fof(f65072,plain,
    spl0_1282,
    inference(avatar_split_clause,[],[f1896,f65070]) ).

fof(f65070,plain,
    ( spl0_1282
  <=> ! [X0,X17,X19] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f1896,plain,
    ! [X0,X19,X17] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
      | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
    inference(forward_demodulation,[],[f1598,f1837]) ).

fof(f1598,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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)),X17))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).

fof(f65068,plain,
    spl0_1281,
    inference(avatar_split_clause,[],[f1865,f65066]) ).

fof(f65066,plain,
    ( spl0_1281
  <=> ! [X2,X1] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)),X1,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f1865,plain,
    ! [X2,X1] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)),X1,tc_nat)),
    inference(forward_demodulation,[],[f519,f582]) ).

fof(f519,axiom,
    ! [X2,X1] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)),X1,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__Suc_0) ).

fof(f65064,plain,
    spl0_1280,
    inference(avatar_split_clause,[],[f1006,f65062]) ).

fof(f65062,plain,
    ( spl0_1280
  <=> ! [X2,X48,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X48)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f1006,axiom,
    ! [X2,X3,X48,X0,X1] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X48)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f64867,plain,
    spl0_1279,
    inference(avatar_split_clause,[],[f1280,f64865]) ).

fof(f64865,plain,
    ( spl0_1279
  <=> ! [X19,X20,X27,X25] :
        ( X19 = X20
        | X25 = X27
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X27)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f1280,axiom,
    ! [X19,X27,X25,X20] :
      ( X19 = X20
      | X25 = X27
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X27)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X20),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

fof(f64863,plain,
    spl0_1278,
    inference(avatar_split_clause,[],[f869,f64861]) ).

fof(f64861,plain,
    ( spl0_1278
  <=> ! [X42,X43,X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
        | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X42),X43),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f869,axiom,
    ! [X2,X3,X0,X1,X42,X43] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
      | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X42),X43),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

fof(f64859,plain,
    spl0_1277,
    inference(avatar_split_clause,[],[f585,f64857]) ).

fof(f64857,plain,
    ( spl0_1277
  <=> ! [X42,X43,X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
        | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X42),X43),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f585,axiom,
    ! [X2,X3,X0,X1,X42,X43] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
      | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X42),X43),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

fof(f64855,plain,
    spl0_1276,
    inference(avatar_split_clause,[],[f312,f64853]) ).

fof(f64853,plain,
    ( spl0_1276
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X2,X3,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f312,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X2,X3,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).

fof(f64498,plain,
    spl0_1275,
    inference(avatar_split_clause,[],[f1890,f64496]) ).

fof(f64496,plain,
    ( spl0_1275
  <=> ! [X2,X0,X17] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
        | ~ class_OrderedGroup_Omonoid__mult(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f1890,plain,
    ! [X2,X0,X17] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
      | ~ class_OrderedGroup_Omonoid__mult(X0) ),
    inference(forward_demodulation,[],[f1611,f1837]) ).

fof(f1611,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),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(f64494,plain,
    spl0_1274,
    inference(avatar_split_clause,[],[f1406,f64492]) ).

fof(f64492,plain,
    ( spl0_1274
  <=> ! [X24,X40,X23,X22] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24)),X40)),X23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f1406,axiom,
    ! [X40,X24,X22,X23] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24)),X40)),X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

fof(f64490,plain,
    spl0_1273,
    inference(avatar_split_clause,[],[f1143,f64488]) ).

fof(f64488,plain,
    ( spl0_1273
  <=> ! [X48,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f1143,axiom,
    ! [X2,X3,X48,X0,X26] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X48)),X26) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X3,X2,X0)),X48)),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

fof(f64486,plain,
    spl0_1272,
    inference(avatar_split_clause,[],[f1141,f64484]) ).

fof(f64484,plain,
    ( spl0_1272
  <=> ! [X34,X0,X3,X2] :
        ( ~ 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),X2),X3)),c_Int_Onumber__class_Onumber__of(X34,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X34,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Int_Onumber__class_Onumber__of(X34,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f1141,axiom,
    ! [X2,X3,X0,X34] :
      ( ~ 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),X2),X3)),c_Int_Onumber__class_Onumber__of(X34,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X34,X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Int_Onumber__class_Onumber__of(X34,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).

fof(f64482,plain,
    spl0_1271,
    inference(avatar_split_clause,[],[f1140,f64480]) ).

fof(f64480,plain,
    ( spl0_1271
  <=> ! [X34,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f1140,axiom,
    ! [X3,X0,X1,X34] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).

fof(f64478,plain,
    spl0_1270,
    inference(avatar_split_clause,[],[f303,f64476]) ).

fof(f64476,plain,
    ( spl0_1270
  <=> ! [X17,X0,X18,X2] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_lessequals(X17,X18,tc_nat)
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0)),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f303,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_lessequals(X17,X18,tc_nat)
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0)),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__rev__if_1) ).

fof(f64388,plain,
    ( spl0_659
    | ~ spl0_316
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f9750,f9304,f3971,f10394]) ).

fof(f10394,plain,
    ( spl0_659
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f3971,plain,
    ( spl0_316
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f9304,plain,
    ( spl0_647
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f9750,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_316
    | ~ spl0_647 ),
    inference(resolution,[],[f9305,f3972]) ).

fof(f3972,plain,
    ( ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3971]) ).

fof(f9305,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f9304]) ).

fof(f64387,plain,
    spl0_1269,
    inference(avatar_split_clause,[],[f1923,f64385]) ).

fof(f64385,plain,
    ( spl0_1269
  <=> ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f1923,plain,
    ! [X17] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)))
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1572,f1837]) ).

fof(f1572,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X17),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_lemma__Suc__Suc__4n__diff__2_0) ).

fof(f64383,plain,
    spl0_1268,
    inference(avatar_split_clause,[],[f1024,f64381]) ).

fof(f64381,plain,
    ( spl0_1268
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X3,X2,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f1024,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X3,X2,X0))),c_HOL_Oinverse__class_Oinverse(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).

fof(f64379,plain,
    spl0_1267,
    inference(avatar_split_clause,[],[f1004,f64377]) ).

fof(f64377,plain,
    ( spl0_1267
  <=> ! [X19,X0,X27,X25] :
        ( ~ 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),X19),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f1004,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ 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),X19),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

fof(f64375,plain,
    spl0_1266,
    inference(avatar_split_clause,[],[f444,f64373]) ).

fof(f64373,plain,
    ( spl0_1266
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X18)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f444,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X18)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__mult_0) ).

fof(f64041,plain,
    spl0_1265,
    inference(avatar_split_clause,[],[f530,f64039]) ).

fof(f64039,plain,
    ( spl0_1265
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26),X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X26,X0),X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f530,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26),X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X26,X0),X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).

fof(f64037,plain,
    spl0_1264,
    inference(avatar_split_clause,[],[f166,f64035]) ).

fof(f64035,plain,
    ( spl0_1264
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_lessequals(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f166,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_lessequals(X18,X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__inverse_0) ).

fof(f63150,plain,
    spl0_1263,
    inference(avatar_split_clause,[],[f1915,f63148]) ).

fof(f63148,plain,
    ( spl0_1263
  <=> ! [X17,X40,X22,X24] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat))),X40)),X17)
        | ~ c_lessequals(X22,X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f1915,plain,
    ! [X40,X17,X24,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat))),X40)),X17)
      | ~ c_lessequals(X22,X24,tc_nat) ),
    inference(forward_demodulation,[],[f1417,f1406]) ).

fof(f1417,axiom,
    ! [X40,X17,X24,X22] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X40)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X40)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X24,X22,tc_nat)),X40)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).

fof(f63146,plain,
    spl0_1262,
    inference(avatar_split_clause,[],[f1657,f63144]) ).

fof(f63144,plain,
    ( spl0_1262
  <=> ! [X38,X0,X36,X35,X37] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),X38)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X37)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X36),X38)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f1657,axiom,
    ! [X38,X0,X36,X37,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),X38)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X37)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X36),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f63142,plain,
    spl0_1261,
    inference(avatar_split_clause,[],[f1032,f63140]) ).

fof(f63140,plain,
    ( spl0_1261
  <=> ! [X42,X43,X0,X3,X2,X1] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
        | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X42,X43,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f1032,axiom,
    ! [X2,X3,X0,X1,X42,X43] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X1,X0) != c_Divides_Odiv__class_Omod(X42,X1,X0)
      | c_Divides_Odiv__class_Omod(X3,X1,X0) != c_Divides_Odiv__class_Omod(X43,X1,X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X42,X43,X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).

fof(f63138,plain,
    spl0_1260,
    inference(avatar_split_clause,[],[f470,f63136]) ).

fof(f63136,plain,
    ( spl0_1260
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | c_Fact_Ofact__class_Ofact(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),c_Fact_Ofact__class_Ofact(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f470,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | c_Fact_Ofact__class_Ofact(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),c_Fact_Ofact__class_Ofact(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__add__num__eq__if2__nat_1) ).

fof(f63134,plain,
    spl0_1259,
    inference(avatar_split_clause,[],[f311,f63132]) ).

fof(f63132,plain,
    ( spl0_1259
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f311,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f63130,plain,
    spl0_1258,
    inference(avatar_split_clause,[],[f45,f63128]) ).

fof(f63128,plain,
    ( spl0_1258
  <=> ! [X2,X1,X3] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X3,X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Omod(X3,X1,tc_nat)),X1,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f45,axiom,
    ! [X2,X3,X1] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X3),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X3,X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Omod(X3,X1,tc_nat)),X1,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).

fof(f63126,plain,
    ( ~ spl0_1257
    | ~ spl0_243
    | ~ spl0_641
    | ~ spl0_946
    | ~ spl0_1160 ),
    inference(avatar_split_clause,[],[f48254,f47224,f18756,f9280,f3188,f63123]) ).

fof(f63123,plain,
    ( spl0_1257
  <=> c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(c_Suc,v_i____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

fof(f9280,plain,
    ( spl0_641
  <=> ! [X19] : c_Fact_Ofact__class_Ofact(hAPP(c_Suc,X19),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X19)),c_Fact_Ofact__class_Ofact(X19,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f18756,plain,
    ( spl0_946
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f47224,plain,
    ( spl0_1160
  <=> ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f48254,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(c_Suc,v_i____)),tc_nat)
    | ~ spl0_243
    | ~ spl0_641
    | ~ spl0_946
    | ~ spl0_1160 ),
    inference(forward_demodulation,[],[f48247,f21056]) ).

fof(f21056,plain,
    ( hAPP(c_Suc,v_i____) = c_Fact_Ofact__class_Ofact(hAPP(c_Suc,v_i____),tc_nat)
    | ~ spl0_243
    | ~ spl0_641
    | ~ spl0_946 ),
    inference(forward_demodulation,[],[f21052,f3189]) ).

fof(f21052,plain,
    ( c_Fact_Ofact__class_Ofact(hAPP(c_Suc,v_i____),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_641
    | ~ spl0_946 ),
    inference(superposition,[],[f9281,f18758]) ).

fof(f18758,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(v_i____,tc_nat)
    | ~ spl0_946 ),
    inference(avatar_component_clause,[],[f18756]) ).

fof(f9281,plain,
    ( ! [X19] : c_Fact_Ofact__class_Ofact(hAPP(c_Suc,X19),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X19)),c_Fact_Ofact__class_Ofact(X19,tc_nat))
    | ~ spl0_641 ),
    inference(avatar_component_clause,[],[f9280]) ).

fof(f48247,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_Fact_Ofact__class_Ofact(hAPP(c_Suc,v_i____),tc_nat)),tc_nat)
    | ~ spl0_641
    | ~ spl0_1160 ),
    inference(superposition,[],[f47225,f9281]) ).

fof(f47225,plain,
    ( ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19)),tc_nat)
    | ~ spl0_1160 ),
    inference(avatar_component_clause,[],[f47224]) ).

fof(f62389,plain,
    spl0_1256,
    inference(avatar_split_clause,[],[f1943,f62387]) ).

fof(f62387,plain,
    ( spl0_1256
  <=> ! [X17,X33,X19,X0,X31,X29,X32,X30] :
        ( hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17)) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
        | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f1943,plain,
    ! [X31,X29,X0,X19,X17,X32,X30,X33] :
      ( hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17)) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
      | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ),
    inference(forward_demodulation,[],[f1562,f1837]) ).

fof(f1562,axiom,
    ! [X31,X29,X0,X19,X17,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),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)),X17)) = hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X17)),hAPP(hAPP(X29,X19),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I36_J_0) ).

fof(f62385,plain,
    spl0_1255,
    inference(avatar_split_clause,[],[f1660,f62383]) ).

fof(f62383,plain,
    ( spl0_1255
  <=> ! [X34,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),c_HOL_Ominus__class_Ominus(X3,X1,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f1660,axiom,
    ! [X3,X0,X1,X34] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),c_HOL_Ominus__class_Ominus(X3,X1,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X34,X0)),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).

fof(f62381,plain,
    spl0_1254,
    inference(avatar_split_clause,[],[f1606,f62379]) ).

fof(f62379,plain,
    ( spl0_1254
  <=> ! [X34,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | ~ class_Int_Onumber(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),c_Int_Onumber__class_Onumber__of(X34,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X34,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Int_Onumber__class_Onumber__of(X34,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f1606,axiom,
    ! [X2,X3,X0,X34] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | ~ class_Int_Onumber(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),c_Int_Onumber__class_Onumber__of(X34,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(X34,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Int_Onumber__class_Onumber__of(X34,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

fof(f62377,plain,
    spl0_1253,
    inference(avatar_split_clause,[],[f807,f62375]) ).

fof(f62375,plain,
    ( spl0_1253
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f807,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

fof(f62373,plain,
    spl0_1252,
    inference(avatar_split_clause,[],[f795,f62371]) ).

fof(f62371,plain,
    ( spl0_1252
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f795,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

fof(f62369,plain,
    spl0_1251,
    inference(avatar_split_clause,[],[f710,f62367]) ).

fof(f62367,plain,
    ( spl0_1251
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_lessequals(X17,X18,tc_nat)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f710,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_lessequals(X17,X18,tc_nat)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__rev__if_0) ).

fof(f62365,plain,
    spl0_1250,
    inference(avatar_split_clause,[],[f679,f62363]) ).

fof(f62363,plain,
    ( spl0_1250
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
        | ~ c_lessequals(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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f679,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
      | ~ c_lessequals(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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

fof(f62357,plain,
    ( spl0_717
    | ~ spl0_171
    | ~ spl0_1235 ),
    inference(avatar_split_clause,[],[f62050,f61400,f2842,f11320]) ).

fof(f11320,plain,
    ( spl0_717
  <=> c_HOL_Oone__class_Oone(tc_nat) = v_i____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f2842,plain,
    ( spl0_171
  <=> hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f61400,plain,
    ( spl0_1235
  <=> hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = v_i____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f62050,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_171
    | ~ spl0_1235 ),
    inference(superposition,[],[f61402,f2844]) ).

fof(f2844,plain,
    ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f2842]) ).

fof(f61402,plain,
    ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = v_i____
    | ~ spl0_1235 ),
    inference(avatar_component_clause,[],[f61400]) ).

fof(f62356,plain,
    spl0_1249,
    inference(avatar_split_clause,[],[f678,f62354]) ).

fof(f62354,plain,
    ( spl0_1249
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_lessequals(X1,X26,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f678,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_lessequals(X1,X26,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

fof(f62352,plain,
    spl0_1248,
    inference(avatar_split_clause,[],[f340,f62350]) ).

fof(f62350,plain,
    ( spl0_1248
  <=> ! [X29,X31,X3,X0,X2,X1,X26,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X3)),hAPP(hAPP(X31,X1),X26)) = hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X1)),hAPP(hAPP(X31,X3),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f340,axiom,
    ! [X31,X2,X3,X29,X0,X1,X26,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X3)),hAPP(hAPP(X31,X1),X26)) = hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X1)),hAPP(hAPP(X31,X3),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).

fof(f62348,plain,
    spl0_1247,
    inference(avatar_split_clause,[],[f333,f62346]) ).

fof(f62346,plain,
    ( spl0_1247
  <=> ! [X31,X38,X29,X0,X36,X37,X35,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X36)),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),hAPP(hAPP(X32,X36),X38)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f333,axiom,
    ! [X31,X38,X29,X0,X36,X37,X35,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X36)),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),hAPP(hAPP(X32,X36),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).

fof(f62344,plain,
    spl0_1246,
    inference(avatar_split_clause,[],[f173,f62342]) ).

fof(f62342,plain,
    ( spl0_1246
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(X1,X26,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f173,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(X1,X26,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

fof(f62340,plain,
    spl0_1245,
    inference(avatar_split_clause,[],[f172,f62338]) ).

fof(f62338,plain,
    ( spl0_1245
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(X1,X26,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f172,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(X1,X26,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

fof(f62336,plain,
    spl0_1244,
    inference(avatar_split_clause,[],[f99,f62334]) ).

fof(f62334,plain,
    ( spl0_1244
  <=> ! [X19,X0,X5,X1,X26] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X1 = X26
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f99,axiom,
    ! [X0,X1,X19,X26,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X1 = X26
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(f62049,plain,
    ( spl0_1243
    | ~ spl0_243
    | ~ spl0_1021
    | ~ spl0_1242 ),
    inference(avatar_split_clause,[],[f62045,f62042,f24563,f3188,f62047]) ).

fof(f62047,plain,
    ( spl0_1243
  <=> ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f24563,plain,
    ( spl0_1021
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f62042,plain,
    ( spl0_1242
  <=> ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f62045,plain,
    ( ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_243
    | ~ spl0_1021
    | ~ spl0_1242 ),
    inference(forward_demodulation,[],[f62043,f25449]) ).

fof(f25449,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),X0,tc_nat)
    | ~ spl0_243
    | ~ spl0_1021 ),
    inference(superposition,[],[f24564,f3189]) ).

fof(f24564,plain,
    ( ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat)
    | ~ spl0_1021 ),
    inference(avatar_component_clause,[],[f24563]) ).

fof(f62043,plain,
    ( ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_1242 ),
    inference(avatar_component_clause,[],[f62042]) ).

fof(f62044,plain,
    spl0_1242,
    inference(avatar_split_clause,[],[f1922,f62042]) ).

fof(f1922,plain,
    ! [X17] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)))
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1573,f1837]) ).

fof(f1573,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | 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)),X17) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(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)),X17),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_Suc__Suc__mult__two__diff__two_0) ).

fof(f62040,plain,
    spl0_1241,
    inference(avatar_split_clause,[],[f1895,f62038]) ).

fof(f62038,plain,
    ( spl0_1241
  <=> ! [X0,X17,X19] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f1895,plain,
    ! [X0,X19,X17] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
      | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
    inference(forward_demodulation,[],[f1685,f1837]) ).

fof(f1685,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).

fof(f62036,plain,
    spl0_1240,
    inference(avatar_split_clause,[],[f1881,f62034]) ).

fof(f62034,plain,
    ( spl0_1240
  <=> ! [X2,X0,X17] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f1881,plain,
    ! [X2,X0,X17] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
      | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
    inference(forward_demodulation,[],[f1570,f1837]) ).

fof(f1570,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,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)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).

fof(f62032,plain,
    spl0_1239,
    inference(avatar_split_clause,[],[f596,f62030]) ).

fof(f62030,plain,
    ( spl0_1239
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X2 = X3
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f596,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X2 = X3
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

fof(f61415,plain,
    spl0_1238,
    inference(avatar_split_clause,[],[f1967,f61413]) ).

fof(f61413,plain,
    ( spl0_1238
  <=> ! [X25,X0,X19] :
        ( 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),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f1967,plain,
    ! [X0,X19,X25] :
      ( 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),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19 ),
    inference(forward_demodulation,[],[f1506,f1837]) ).

fof(f1506,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | 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),X19),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),X25),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(f61411,plain,
    spl0_1237,
    inference(avatar_split_clause,[],[f1966,f61409]) ).

fof(f61409,plain,
    ( spl0_1237
  <=> ! [X25,X0,X19] :
        ( 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),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f1966,plain,
    ! [X0,X19,X25] :
      ( 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),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25 ),
    inference(forward_demodulation,[],[f1507,f1837]) ).

fof(f1507,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | 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),X19),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),X25),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(f61407,plain,
    spl0_1236,
    inference(avatar_split_clause,[],[f1965,f61405]) ).

fof(f61405,plain,
    ( spl0_1236
  <=> ! [X25,X0,X19] :
        ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f1965,plain,
    ! [X0,X19,X25] :
      ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25 ),
    inference(forward_demodulation,[],[f1099,f1837]) ).

fof(f1099,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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),X25),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_sum__power2__le__zero__iff_1) ).

fof(f61403,plain,
    ( spl0_1235
    | ~ spl0_157
    | ~ spl0_176
    | ~ spl0_286
    | ~ spl0_705
    | spl0_867
    | ~ spl0_1165 ),
    inference(avatar_split_clause,[],[f57704,f47285,f17461,f10723,f3456,f2863,f2780,f61400]) ).

fof(f2780,plain,
    ( spl0_157
  <=> ! [X17] : c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f10723,plain,
    ( spl0_705
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f17461,plain,
    ( spl0_867
  <=> c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f47285,plain,
    ( spl0_1165
  <=> ! [X19] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat))) = X19
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f57704,plain,
    ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = v_i____
    | ~ spl0_157
    | ~ spl0_176
    | ~ spl0_286
    | ~ spl0_705
    | spl0_867
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f57703,f2864]) ).

fof(f57703,plain,
    ( v_i____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_i____,v_i____,tc_nat))
    | ~ spl0_157
    | ~ spl0_286
    | ~ spl0_705
    | spl0_867
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f56944,f3761]) ).

fof(f3761,plain,
    ( ! [X0] : c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,X0),tc_nat) = X0
    | ~ spl0_157
    | ~ spl0_286 ),
    inference(resolution,[],[f3457,f2781]) ).

fof(f2781,plain,
    ( ! [X17] : c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X17),tc_nat)
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f2780]) ).

fof(f56944,plain,
    ( v_i____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_i____,c_Divides_Odiv__class_Omod(v_i____,hAPP(c_Suc,v_i____),tc_nat),tc_nat))
    | ~ spl0_705
    | spl0_867
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f56937,f10724]) ).

fof(f10724,plain,
    ( ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat)
    | ~ spl0_705 ),
    inference(avatar_component_clause,[],[f10723]) ).

fof(f56937,plain,
    ( v_i____ = hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Divides_Odiv__class_Odiv(v_i____,hAPP(c_Suc,v_i____),tc_nat)))
    | spl0_867
    | ~ spl0_1165 ),
    inference(resolution,[],[f47286,f17462]) ).

fof(f17462,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | spl0_867 ),
    inference(avatar_component_clause,[],[f17461]) ).

fof(f47286,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat))) = X19 )
    | ~ spl0_1165 ),
    inference(avatar_component_clause,[],[f47285]) ).

fof(f61398,plain,
    spl0_1234,
    inference(avatar_split_clause,[],[f1964,f61396]) ).

fof(f61396,plain,
    ( spl0_1234
  <=> ! [X25,X0,X19] :
        ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f1964,plain,
    ! [X0,X19,X25] :
      ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19 ),
    inference(forward_demodulation,[],[f1098,f1837]) ).

fof(f1098,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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),X25),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_sum__power2__le__zero__iff_0) ).

fof(f61394,plain,
    spl0_1233,
    inference(avatar_split_clause,[],[f1535,f61392]) ).

fof(f61392,plain,
    ( spl0_1233
  <=> ! [X17,X0,X21,X25] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | ~ c_lessequals(X21,X17,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),X21,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),c_HOL_Ominus__class_Ominus(X17,X21,tc_nat))),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f1535,axiom,
    ! [X21,X0,X17,X25] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | ~ c_lessequals(X21,X17,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),X21,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),c_HOL_Ominus__class_Ominus(X17,X21,tc_nat))),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__diff_0) ).

fof(f61390,plain,
    spl0_1232,
    inference(avatar_split_clause,[],[f1207,f61388]) ).

fof(f61388,plain,
    ( spl0_1232
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X2 = X3
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),hAPP(c_Suc,X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f1207,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X2 = X3
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),hAPP(c_Suc,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

fof(f61386,plain,
    spl0_1231,
    inference(avatar_split_clause,[],[f1118,f61384]) ).

fof(f61384,plain,
    ( spl0_1231
  <=> ! [X26,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X0),X26,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f1118,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X0),X26,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).

fof(f61382,plain,
    spl0_1230,
    inference(avatar_split_clause,[],[f960,f61380]) ).

fof(f61380,plain,
    ( spl0_1230
  <=> ! [X19,X20,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Ozero__class_Ozero(X0) = X27
        | c_HOL_Oinverse__class_Odivide(X19,X25,X0) = c_HOL_Oinverse__class_Odivide(X20,X27,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f960,axiom,
    ! [X0,X19,X27,X25,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) = X27
      | c_HOL_Oinverse__class_Odivide(X19,X25,X0) = c_HOL_Oinverse__class_Odivide(X20,X27,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

fof(f61378,plain,
    spl0_1229,
    inference(avatar_split_clause,[],[f959,f61376]) ).

fof(f61376,plain,
    ( spl0_1229
  <=> ! [X19,X20,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Ozero__class_Ozero(X0) = X27
        | c_HOL_Oinverse__class_Odivide(X19,X25,X0) != c_HOL_Oinverse__class_Odivide(X20,X27,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f959,axiom,
    ! [X0,X19,X27,X25,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) = X27
      | c_HOL_Oinverse__class_Odivide(X19,X25,X0) != c_HOL_Oinverse__class_Odivide(X20,X27,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X20),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

fof(f61374,plain,
    spl0_1228,
    inference(avatar_split_clause,[],[f753,f61372]) ).

fof(f61372,plain,
    ( spl0_1228
  <=> ! [X17,X19,X46,X45,X25] :
        ( c_Divides_Odiv__class_Omod(X19,X17,tc_nat) = c_Divides_Odiv__class_Omod(X25,X17,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X45)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X46)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f753,axiom,
    ! [X46,X19,X45,X17,X25] :
      ( c_Divides_Odiv__class_Omod(X19,X17,tc_nat) = c_Divides_Odiv__class_Omod(X25,X17,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X45)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X46)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).

fof(f61370,plain,
    spl0_1227,
    inference(avatar_split_clause,[],[f310,f61368]) ).

fof(f61368,plain,
    ( spl0_1227
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X25)),X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),c_HOL_Oinverse__class_Odivide(X19,X25,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f310,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X25)),X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),c_HOL_Oinverse__class_Odivide(X19,X25,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

fof(f61366,plain,
    spl0_1226,
    inference(avatar_split_clause,[],[f309,f61364]) ).

fof(f61364,plain,
    ( spl0_1226
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X25,X0)),X27) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X25)),X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f309,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X25,X0)),X27) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X25)),X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

fof(f61354,plain,
    ( spl0_1225
    | ~ spl0_190
    | spl0_1114 ),
    inference(avatar_split_clause,[],[f29630,f29164,f2940,f61351]) ).

fof(f61351,plain,
    ( spl0_1225
  <=> c_lessequals(v_i____,c_HOL_Oabs__class_Oabs(v_i____,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f2940,plain,
    ( spl0_190
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | c_lessequals(X17,X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f29164,plain,
    ( spl0_1114
  <=> c_lessequals(c_HOL_Oabs__class_Oabs(v_i____,tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f29630,plain,
    ( c_lessequals(v_i____,c_HOL_Oabs__class_Oabs(v_i____,tc_nat),tc_nat)
    | ~ spl0_190
    | spl0_1114 ),
    inference(resolution,[],[f29165,f2941]) ).

fof(f2941,plain,
    ( ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | c_lessequals(X17,X18,tc_nat) )
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f2940]) ).

fof(f29165,plain,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(v_i____,tc_nat),v_i____,tc_nat)
    | spl0_1114 ),
    inference(avatar_component_clause,[],[f29164]) ).

fof(f60819,plain,
    spl0_1224,
    inference(avatar_split_clause,[],[f1963,f60817]) ).

fof(f60817,plain,
    ( spl0_1224
  <=> ! [X25,X0,X19] :
        ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f1963,plain,
    ! [X0,X19,X25] :
      ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19 ),
    inference(forward_demodulation,[],[f1379,f1837]) ).

fof(f1379,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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),X25),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(f60815,plain,
    spl0_1223,
    inference(avatar_split_clause,[],[f1962,f60813]) ).

fof(f60813,plain,
    ( spl0_1223
  <=> ! [X25,X0,X19] :
        ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f1962,plain,
    ! [X0,X19,X25] :
      ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25 ),
    inference(forward_demodulation,[],[f1380,f1837]) ).

fof(f1380,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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),X25),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(f60811,plain,
    spl0_1222,
    inference(avatar_split_clause,[],[f1933,f60809]) ).

fof(f60809,plain,
    ( spl0_1222
  <=> ! [X18,X17] :
        ( c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f1933,plain,
    ! [X18,X17] :
      ( c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat))
      | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ),
    inference(forward_demodulation,[],[f1540,f1669]) ).

fof(f1669,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

fof(f1540,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat)
      | c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat)),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__diff__Suc_0) ).

fof(f60807,plain,
    spl0_1221,
    inference(avatar_split_clause,[],[f1889,f60805]) ).

fof(f60805,plain,
    ( spl0_1221
  <=> ! [X2,X0,X17] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_OrderedGroup_Omonoid__mult(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f1889,plain,
    ! [X2,X0,X17] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_OrderedGroup_Omonoid__mult(X0) ),
    inference(forward_demodulation,[],[f1612,f1837]) ).

fof(f1612,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),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(f60803,plain,
    spl0_1220,
    inference(avatar_split_clause,[],[f1487,f60801]) ).

fof(f60801,plain,
    ( spl0_1220
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(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),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f1487,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(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),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

fof(f60799,plain,
    ( spl0_848
    | ~ spl0_21
    | ~ spl0_220
    | ~ spl0_870 ),
    inference(avatar_split_clause,[],[f17892,f17518,f3095,f2117,f17177]) ).

fof(f2117,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f3095,plain,
    ( spl0_220
  <=> ! [X0,X27] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | ~ c_Int_Oiszero(X27,X0)
        | c_HOL_Ozero__class_Ozero(X0) = X27 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f17518,plain,
    ( spl0_870
  <=> c_Int_Oiszero(v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f17892,plain,
    ( ~ class_Ring__and__Field_Osemiring__1(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_220
    | ~ spl0_870 ),
    inference(resolution,[],[f17520,f3096]) ).

fof(f3096,plain,
    ( ! [X0,X27] :
        ( ~ c_Int_Oiszero(X27,X0)
        | ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X27 )
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f3095]) ).

fof(f17520,plain,
    ( c_Int_Oiszero(v_i____,tc_nat)
    | ~ spl0_870 ),
    inference(avatar_component_clause,[],[f17518]) ).

fof(f60798,plain,
    spl0_1219,
    inference(avatar_split_clause,[],[f1253,f60796]) ).

fof(f60796,plain,
    ( spl0_1219
  <=> ! [X4,X17,X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = X4
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X4),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,X4)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f1253,axiom,
    ! [X18,X4,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = X4
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X4),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_0) ).

fof(f60794,plain,
    spl0_1218,
    inference(avatar_split_clause,[],[f981,f60792]) ).

fof(f60792,plain,
    ( spl0_1218
  <=> ! [X18,X19,X17,X28] :
        ( ~ hBOOL(hAPP(X28,X19))
        | hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)))
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X19),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,X19)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f981,axiom,
    ! [X28,X18,X19,X17] :
      ( ~ hBOOL(hAPP(X28,X19))
      | hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)))
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X19),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,X19)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_7) ).

fof(f60790,plain,
    spl0_1217,
    inference(avatar_split_clause,[],[f891,f60788]) ).

fof(f60788,plain,
    ( spl0_1217
  <=> ! [X19,X20,X0,X27,X25] :
        ( ~ 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(X19,X25,X0)),c_HOL_Oinverse__class_Odivide(X27,X20,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X20),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f891,axiom,
    ! [X0,X19,X27,X25,X20] :
      ( ~ 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(X19,X25,X0)),c_HOL_Oinverse__class_Odivide(X27,X20,X0)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X20),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

fof(f60786,plain,
    spl0_1216,
    inference(avatar_split_clause,[],[f576,f60784]) ).

fof(f60784,plain,
    ( spl0_1216
  <=> ! [X31,X21,X29,X0,X19,X4,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X21)),hAPP(hAPP(X29,X19),X4)) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f576,axiom,
    ! [X31,X21,X29,X0,X19,X4,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X21)),hAPP(hAPP(X29,X19),X4)) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).

fof(f60782,plain,
    spl0_1215,
    inference(avatar_split_clause,[],[f551,f60780]) ).

fof(f60780,plain,
    ( spl0_1215
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Divides_Odiv__class_Odiv(X2,X3,X0))),c_Divides_Odiv__class_Omod(X2,X3,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f551,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Divides_Odiv__class_Odiv(X2,X3,X0))),c_Divides_Odiv__class_Omod(X2,X3,X0))),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).

fof(f60778,plain,
    spl0_1214,
    inference(avatar_split_clause,[],[f550,f60776]) ).

fof(f60776,plain,
    ( spl0_1214
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = 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_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)),c_Divides_Odiv__class_Omod(X2,X3,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f550,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = 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_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)),c_Divides_Odiv__class_Omod(X2,X3,X0))),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).

fof(f60774,plain,
    spl0_1213,
    inference(avatar_split_clause,[],[f49,f60772]) ).

fof(f60772,plain,
    ( spl0_1213
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f49,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).

fof(f60770,plain,
    spl0_1212,
    inference(avatar_split_clause,[],[f48,f60768]) ).

fof(f60768,plain,
    ( spl0_1212
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f48,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).

fof(f60766,plain,
    spl0_1211,
    inference(avatar_split_clause,[],[f47,f60764]) ).

fof(f60764,plain,
    ( spl0_1211
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f47,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).

fof(f60762,plain,
    spl0_1210,
    inference(avatar_split_clause,[],[f46,f60760]) ).

fof(f60760,plain,
    ( spl0_1210
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f46,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).

fof(f60758,plain,
    spl0_1209,
    inference(avatar_split_clause,[],[f2,f60756]) ).

fof(f60756,plain,
    ( spl0_1209
  <=> ! [X3,X4,X5,X1] :
        ( ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),c_Divides_Odiv__class_Omod(X4,X1,tc_nat))),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f2,axiom,
    ! [X3,X1,X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),c_Divides_Odiv__class_Omod(X4,X1,tc_nat))),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).

fof(f60401,plain,
    ( spl0_764
    | ~ spl0_164
    | ~ spl0_945 ),
    inference(avatar_split_clause,[],[f20856,f18345,f2812,f13582]) ).

fof(f13582,plain,
    ( spl0_764
  <=> c_HOL_Oord__class_Oless(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f2812,plain,
    ( spl0_164
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f18345,plain,
    ( spl0_945
  <=> ! [X0] : c_HOL_Oord__class_Oless(v_i____,c_Fact_Ofact__class_Ofact(X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f20856,plain,
    ( c_HOL_Oord__class_Oless(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_164
    | ~ spl0_945 ),
    inference(superposition,[],[f18346,f2814]) ).

fof(f2814,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f2812]) ).

fof(f18346,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(v_i____,c_Fact_Ofact__class_Ofact(X0,tc_nat),tc_nat)
    | ~ spl0_945 ),
    inference(avatar_component_clause,[],[f18345]) ).

fof(f59979,plain,
    spl0_1208,
    inference(avatar_split_clause,[],[f1957,f59977]) ).

fof(f1957,plain,
    ! [X2,X22] :
      ( hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X2),X22) = c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X2,X22)
      | ~ c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    inference(forward_demodulation,[],[f1956,f1837]) ).

fof(f1956,plain,
    ! [X2,X22] :
      ( ~ c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
      | c_FFT__Mirabelle_ODFT(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____),X2,X22) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X2),X22) ),
    inference(forward_demodulation,[],[f1584,f1837]) ).

fof(f1584,axiom,
    ! [X2,X22] :
      ( ~ c_HOL_Oord__class_Oless(X22,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_ODFT(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____),X2,X22) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X2),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).

fof(f59975,plain,
    spl0_1207,
    inference(avatar_split_clause,[],[f1877,f59973]) ).

fof(f59973,plain,
    ( spl0_1207
  <=> ! [X0] :
        ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f1877,plain,
    ! [X0] :
      ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1097,f1837]) ).

fof(f1097,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(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))),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).

fof(f59971,plain,
    spl0_1206,
    inference(avatar_split_clause,[],[f1876,f59969]) ).

fof(f59969,plain,
    ( spl0_1206
  <=> ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f1876,plain,
    ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1508,f1837]) ).

fof(f1508,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(f59967,plain,
    ( spl0_647
    | ~ spl0_194
    | ~ spl0_716 ),
    inference(avatar_split_clause,[],[f13753,f11316,f2956,f9304]) ).

fof(f2956,plain,
    ( spl0_194
  <=> ! [X25,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | c_lessequals(X19,X25,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f13753,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_194
    | ~ spl0_716 ),
    inference(resolution,[],[f11318,f2957]) ).

fof(f2957,plain,
    ( ! [X19,X25] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | c_lessequals(X19,X25,tc_nat) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f2956]) ).

fof(f59966,plain,
    spl0_1205,
    inference(avatar_split_clause,[],[f1632,f59964]) ).

fof(f59964,plain,
    ( spl0_1205
  <=> ! [X4,X0,X25,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f1632,axiom,
    ! [X0,X19,X4,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

fof(f59962,plain,
    spl0_1204,
    inference(avatar_split_clause,[],[f1631,f59960]) ).

fof(f59960,plain,
    ( spl0_1204
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3)),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f1631,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3)),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

fof(f59958,plain,
    spl0_1203,
    inference(avatar_split_clause,[],[f1541,f59956]) ).

fof(f59956,plain,
    ( spl0_1203
  <=> ! [X17,X23,X26] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X26,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),X26),X17))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X26),X23)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X17)),X23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f1541,axiom,
    ! [X26,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X26,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),X26),X17))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X26),X23)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X17)),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).

fof(f59954,plain,
    spl0_1202,
    inference(avatar_split_clause,[],[f1155,f59952]) ).

fof(f59952,plain,
    ( spl0_1202
  <=> ! [X4,X19,X0,X21] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f1155,axiom,
    ! [X21,X0,X19,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),X19),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).

fof(f59950,plain,
    spl0_1201,
    inference(avatar_split_clause,[],[f1154,f59948]) ).

fof(f59948,plain,
    ( spl0_1201
  <=> ! [X17,X0,X18,X2] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f1154,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).

fof(f59946,plain,
    spl0_1200,
    inference(avatar_split_clause,[],[f1062,f59944]) ).

fof(f59944,plain,
    ( spl0_1200
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f1062,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

fof(f59942,plain,
    spl0_1199,
    inference(avatar_split_clause,[],[f1060,f59940]) ).

fof(f59940,plain,
    ( spl0_1199
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X17) = 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)),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f1060,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X17) = 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)),X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).

fof(f59938,plain,
    spl0_1198,
    inference(avatar_split_clause,[],[f971,f59936]) ).

fof(f59936,plain,
    ( spl0_1198
  <=> ! [X17,X0,X2,X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X17,X39,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f971,axiom,
    ! [X2,X39,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X17,X39,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

fof(f59934,plain,
    spl0_1197,
    inference(avatar_split_clause,[],[f888,f59932]) ).

fof(f59932,plain,
    ( spl0_1197
  <=> ! [X0,X3,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),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f888,axiom,
    ! [X2,X3,X0,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),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f59930,plain,
    spl0_1196,
    inference(avatar_split_clause,[],[f887,f59928]) ).

fof(f59928,plain,
    ( spl0_1196
  <=> ! [X19,X0,X25,X45] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f887,axiom,
    ! [X0,X19,X45,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).

fof(f59916,plain,
    spl0_1195,
    inference(avatar_split_clause,[],[f885,f59914]) ).

fof(f59914,plain,
    ( spl0_1195
  <=> ! [X44,X19,X0,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25)),X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X44)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X44)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f885,axiom,
    ! [X0,X19,X44,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25)),X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X44)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X44)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

fof(f59912,plain,
    spl0_1194,
    inference(avatar_split_clause,[],[f883,f59910]) ).

fof(f59910,plain,
    ( spl0_1194
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f883,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f59908,plain,
    spl0_1193,
    inference(avatar_split_clause,[],[f882,f59906]) ).

fof(f59906,plain,
    ( spl0_1193
  <=> ! [X0,X3,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),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f882,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f59904,plain,
    spl0_1192,
    inference(avatar_split_clause,[],[f780,f59902]) ).

fof(f59902,plain,
    ( spl0_1192
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0)),X17) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f780,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0)),X17) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

fof(f59900,plain,
    spl0_1191,
    inference(avatar_split_clause,[],[f578,f59898]) ).

fof(f59898,plain,
    ( spl0_1191
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Divides_Odiv__class_Odiv(X2,X3,X0)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f578,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Divides_Odiv__class_Odiv(X2,X3,X0)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).

fof(f59896,plain,
    spl0_1190,
    inference(avatar_split_clause,[],[f577,f59894]) ).

fof(f59894,plain,
    ( spl0_1190
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3)),X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Divides_Odiv__class_Odiv(X2,X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f577,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3)),X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_Divides_Odiv__class_Odiv(X2,X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).

fof(f59892,plain,
    spl0_1189,
    inference(avatar_split_clause,[],[f558,f59890]) ).

fof(f59890,plain,
    ( spl0_1189
  <=> ! [X17,X0,X2,X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X17,X39,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f558,axiom,
    ! [X2,X39,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X17,X39,tc_nat)
      | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

fof(f59888,plain,
    spl0_1188,
    inference(avatar_split_clause,[],[f354,f59886]) ).

fof(f59886,plain,
    ( spl0_1188
  <=> ! [X31,X29,X0,X19,X4,X25,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,hAPP(hAPP(X32,X19),X25)),X4) = hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X4)),hAPP(hAPP(X29,X25),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f354,axiom,
    ! [X31,X29,X0,X19,X4,X25,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,hAPP(hAPP(X32,X19),X25)),X4) = hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X4)),hAPP(hAPP(X29,X25),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).

fof(f59884,plain,
    spl0_1187,
    inference(avatar_split_clause,[],[f353,f59882]) ).

fof(f59882,plain,
    ( spl0_1187
  <=> ! [X31,X29,X0,X19,X27,X25,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X19),hAPP(hAPP(X31,X25),X27)) = hAPP(hAPP(X31,hAPP(hAPP(X32,X19),X25)),hAPP(hAPP(X32,X19),X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f353,axiom,
    ! [X31,X29,X0,X19,X27,X25,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X19),hAPP(hAPP(X31,X25),X27)) = hAPP(hAPP(X31,hAPP(hAPP(X32,X19),X25)),hAPP(hAPP(X32,X19),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).

fof(f59880,plain,
    spl0_1186,
    inference(avatar_split_clause,[],[f328,f59878]) ).

fof(f59878,plain,
    ( spl0_1186
  <=> ! [X29,X31,X3,X0,X2,X1,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X3)),X1) = hAPP(hAPP(X31,hAPP(hAPP(X32,X2),X1)),hAPP(hAPP(X32,X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f328,axiom,
    ! [X31,X2,X3,X29,X0,X1,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X3)),X1) = hAPP(hAPP(X31,hAPP(hAPP(X32,X2),X1)),hAPP(hAPP(X32,X3),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).

fof(f59859,plain,
    spl0_1185,
    inference(avatar_split_clause,[],[f279,f59857]) ).

fof(f59857,plain,
    ( spl0_1185
  <=> ! [X2,X0,X17] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f279,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),X17)),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__Suc2_0) ).

fof(f59855,plain,
    spl0_1184,
    inference(avatar_split_clause,[],[f98,f59853]) ).

fof(f59853,plain,
    ( spl0_1184
  <=> ! [X19,X5,X1,X26] :
        ( X1 = X26
        | c_HOL_Ozero__class_Ozero(tc_nat) = X5
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f98,axiom,
    ! [X1,X19,X26,X5] :
      ( X1 = X26
      | c_HOL_Ozero__class_Ozero(tc_nat) = X5
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(f59851,plain,
    spl0_1183,
    inference(avatar_split_clause,[],[f7,f59849]) ).

fof(f59849,plain,
    ( spl0_1183
  <=> ! [X2,X1,X3] : c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),X1,tc_nat))),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f7,axiom,
    ! [X2,X3,X1] : c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),X1,tc_nat))),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).

fof(f59645,plain,
    spl0_1182,
    inference(avatar_split_clause,[],[f1921,f59643]) ).

fof(f59643,plain,
    ( spl0_1182
  <=> ! [X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f1921,plain,
    ! [X17] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1534,f1837]) ).

fof(f1534,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | 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)),X17) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(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)),X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__two__diff__one_0) ).

fof(f58356,plain,
    ( spl0_1181
    | ~ spl0_243
    | ~ spl0_1156 ),
    inference(avatar_split_clause,[],[f56766,f46226,f3188,f58353]) ).

fof(f58353,plain,
    ( spl0_1181
  <=> c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,v_i____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f46226,plain,
    ( spl0_1156
  <=> ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f56766,plain,
    ( c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,v_i____),tc_nat)
    | ~ spl0_243
    | ~ spl0_1156 ),
    inference(superposition,[],[f46227,f3189]) ).

fof(f46227,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19),tc_nat)
    | ~ spl0_1156 ),
    inference(avatar_component_clause,[],[f46226]) ).

fof(f58125,plain,
    ( spl0_898
    | ~ spl0_297
    | ~ spl0_948 ),
    inference(avatar_split_clause,[],[f21350,f19787,f3501,f17978]) ).

fof(f17978,plain,
    ( spl0_898
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f3501,plain,
    ( spl0_297
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f19787,plain,
    ( spl0_948
  <=> ! [X0] : c_HOL_Oord__class_Oless(v_i____,hAPP(c_Suc,X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f21350,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,v_i____,tc_nat)
    | ~ spl0_297
    | ~ spl0_948 ),
    inference(resolution,[],[f19788,f3502]) ).

fof(f3502,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f3501]) ).

fof(f19788,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(v_i____,hAPP(c_Suc,X0),tc_nat)
    | ~ spl0_948 ),
    inference(avatar_component_clause,[],[f19787]) ).

fof(f57676,plain,
    ( spl0_717
    | ~ spl0_197
    | ~ spl0_201
    | ~ spl0_456
    | ~ spl0_595
    | ~ spl0_647
    | ~ spl0_659
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f56191,f23996,f10394,f9304,f8242,f5394,f2985,f2969,f11320]) ).

fof(f2969,plain,
    ( spl0_197
  <=> ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f2985,plain,
    ( spl0_201
  <=> ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f5394,plain,
    ( spl0_456
  <=> ! [X22,X17] :
        ( ~ c_lessequals(X22,X17,tc_nat)
        | c_HOL_Ominus__class_Ominus(X17,c_HOL_Ominus__class_Ominus(X17,X22,tc_nat),tc_nat) = X22 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f8242,plain,
    ( spl0_595
  <=> ! [X22,X24,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X23,tc_nat),X24,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f23996,plain,
    ( spl0_993
  <=> ! [X0] : v_i____ = c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f56191,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_197
    | ~ spl0_201
    | ~ spl0_456
    | ~ spl0_595
    | ~ spl0_647
    | ~ spl0_659
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f9753,f55947]) ).

fof(f55947,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
    | ~ spl0_197
    | ~ spl0_201
    | ~ spl0_595
    | ~ spl0_659
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f55946,f24512]) ).

fof(f24512,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_201
    | ~ spl0_993 ),
    inference(superposition,[],[f2986,f23997]) ).

fof(f23997,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat)
    | ~ spl0_993 ),
    inference(avatar_component_clause,[],[f23996]) ).

fof(f2986,plain,
    ( ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f2985]) ).

fof(f55946,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
    | ~ spl0_197
    | ~ spl0_201
    | ~ spl0_595
    | ~ spl0_659
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f14680,f55945]) ).

fof(f55945,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),v_i____,tc_nat)
    | ~ spl0_197
    | ~ spl0_201
    | ~ spl0_595
    | ~ spl0_659
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f55944,f24512]) ).

fof(f55944,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),v_i____,tc_nat)
    | ~ spl0_197
    | ~ spl0_595
    | ~ spl0_659 ),
    inference(forward_demodulation,[],[f14681,f2970]) ).

fof(f2970,plain,
    ( ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f2969]) ).

fof(f14681,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),v_i____,tc_nat)
    | ~ spl0_595
    | ~ spl0_659 ),
    inference(superposition,[],[f8243,f10396]) ).

fof(f10396,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_659 ),
    inference(avatar_component_clause,[],[f10394]) ).

fof(f8243,plain,
    ( ! [X24,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X23,tc_nat),X24,tc_nat)
    | ~ spl0_595 ),
    inference(avatar_component_clause,[],[f8242]) ).

fof(f14680,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),v_i____,tc_nat)
    | ~ spl0_595
    | ~ spl0_659 ),
    inference(superposition,[],[f8243,f10396]) ).

fof(f9753,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_456
    | ~ spl0_647 ),
    inference(resolution,[],[f9305,f5395]) ).

fof(f5395,plain,
    ( ! [X17,X22] :
        ( ~ c_lessequals(X22,X17,tc_nat)
        | c_HOL_Ominus__class_Ominus(X17,c_HOL_Ominus__class_Ominus(X17,X22,tc_nat),tc_nat) = X22 )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f5394]) ).

fof(f57125,plain,
    ( spl0_867
    | ~ spl0_243
    | ~ spl0_1170 ),
    inference(avatar_split_clause,[],[f56748,f47831,f3188,f17461]) ).

fof(f47831,plain,
    ( spl0_1170
  <=> ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X19),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f56748,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_243
    | ~ spl0_1170 ),
    inference(superposition,[],[f47832,f3189]) ).

fof(f47832,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X19),tc_nat)
    | ~ spl0_1170 ),
    inference(avatar_component_clause,[],[f47831]) ).

fof(f56885,plain,
    ( spl0_867
    | ~ spl0_134
    | ~ spl0_1020 ),
    inference(avatar_split_clause,[],[f25590,f24559,f2679,f17461]) ).

fof(f2679,plain,
    ( spl0_134
  <=> ! [X19] : ~ c_HOL_Oord__class_Oless(X19,X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f24559,plain,
    ( spl0_1020
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f25590,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_134
    | ~ spl0_1020 ),
    inference(resolution,[],[f24560,f2680]) ).

fof(f2680,plain,
    ( ! [X19] : ~ c_HOL_Oord__class_Oless(X19,X19,tc_nat)
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f2679]) ).

fof(f24560,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) )
    | ~ spl0_1020 ),
    inference(avatar_component_clause,[],[f24559]) ).

fof(f56815,plain,
    ( spl0_1180
    | ~ spl0_201
    | ~ spl0_469
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f56065,f23996,f5456,f2985,f56813]) ).

fof(f56813,plain,
    ( spl0_1180
  <=> ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f5456,plain,
    ( spl0_469
  <=> ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f56065,plain,
    ( ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_201
    | ~ spl0_469
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f5457,f24512]) ).

fof(f5457,plain,
    ( ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_469 ),
    inference(avatar_component_clause,[],[f5456]) ).

fof(f55900,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_352
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f55763,f20692,f4413,f2867,f20243]) ).

fof(f20243,plain,
    ( spl0_949
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_i____,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f2867,plain,
    ( spl0_177
  <=> ! [X18] : c_HOL_Ominus__class_Ominus(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f4413,plain,
    ( spl0_352
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f20692,plain,
    ( spl0_950
  <=> ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f55763,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_177
    | ~ spl0_352
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f2868,f21775]) ).

fof(f21775,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_352
    | ~ spl0_950 ),
    inference(superposition,[],[f20693,f4415]) ).

fof(f4415,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f4413]) ).

fof(f20693,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
    | ~ spl0_950 ),
    inference(avatar_component_clause,[],[f20692]) ).

fof(f2868,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X18
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f2867]) ).

fof(f55261,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_202
    | ~ spl0_887 ),
    inference(avatar_split_clause,[],[f54055,f17934,f3022,f2867,f20243]) ).

fof(f3022,plain,
    ( spl0_202
  <=> ! [X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f17934,plain,
    ( spl0_887
  <=> ! [X0] : c_lessequals(v_i____,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f54055,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_177
    | ~ spl0_202
    | ~ spl0_887 ),
    inference(forward_demodulation,[],[f2868,f18032]) ).

fof(f18032,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_202
    | ~ spl0_887 ),
    inference(resolution,[],[f17935,f3023]) ).

fof(f3023,plain,
    ( ! [X17] :
        ( ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f3022]) ).

fof(f17935,plain,
    ( ! [X0] : c_lessequals(v_i____,X0,tc_nat)
    | ~ spl0_887 ),
    inference(avatar_component_clause,[],[f17934]) ).

fof(f53861,plain,
    ( spl0_1154
    | spl0_126
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_705
    | ~ spl0_949
    | ~ spl0_950
    | ~ spl0_1153
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(avatar_split_clause,[],[f51740,f47285,f47195,f34813,f20692,f20243,f10723,f9304,f5394,f2642,f34820]) ).

fof(f34820,plain,
    ( spl0_1154
  <=> ! [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)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),v_i____))
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f2642,plain,
    ( spl0_126
  <=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f34813,plain,
    ( spl0_1153
  <=> ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f47195,plain,
    ( spl0_1157
  <=> ! [X19] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f51740,plain,
    ( ! [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)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),v_i____))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | spl0_126
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_705
    | ~ spl0_949
    | ~ spl0_950
    | ~ spl0_1153
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51739,f34658]) ).

fof(f34658,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f9753,f20693]) ).

fof(f51739,plain,
    ( ! [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_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | spl0_126
    | ~ spl0_705
    | ~ spl0_949
    | ~ spl0_1153
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f34814,f51055]) ).

fof(f51055,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))
    | spl0_126
    | ~ spl0_705
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51054,f20244]) ).

fof(f20244,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_i____,tc_nat) = X0
    | ~ spl0_949 ),
    inference(avatar_component_clause,[],[f20243]) ).

fof(f51054,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat))
    | spl0_126
    | ~ spl0_705
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51053,f47890]) ).

fof(f47890,plain,
    ( v_i____ = c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),hAPP(c_Suc,v_i____),tc_nat)
    | spl0_126
    | ~ spl0_1157 ),
    inference(resolution,[],[f47196,f2644]) ).

fof(f2644,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | spl0_126 ),
    inference(avatar_component_clause,[],[f2642]) ).

fof(f47196,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat) )
    | ~ spl0_1157 ),
    inference(avatar_component_clause,[],[f47195]) ).

fof(f51053,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(c_HOL_Oone__class_Oone(tc_nat),hAPP(c_Suc,v_i____),tc_nat),tc_nat))
    | spl0_126
    | ~ spl0_705
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51034,f10724]) ).

fof(f51034,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Divides_Odiv__class_Odiv(c_HOL_Oone__class_Oone(tc_nat),hAPP(c_Suc,v_i____),tc_nat)))
    | spl0_126
    | ~ spl0_1165 ),
    inference(resolution,[],[f47286,f2644]) ).

fof(f34814,plain,
    ( ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))) )
    | ~ spl0_1153 ),
    inference(avatar_component_clause,[],[f34813]) ).

fof(f53826,plain,
    ( spl0_1179
    | spl0_126
    | ~ spl0_182
    | ~ spl0_467
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_993
    | ~ spl0_1157
    | ~ spl0_1164
    | ~ spl0_1165 ),
    inference(avatar_split_clause,[],[f52806,f47285,f47280,f47195,f23996,f20243,f17461,f15019,f10723,f5448,f2888,f2642,f53824]) ).

fof(f53824,plain,
    ( spl0_1179
  <=> ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f2888,plain,
    ( spl0_182
  <=> ! [X18] : c_Divides_Odiv__class_Odiv(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f5448,plain,
    ( spl0_467
  <=> ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f15019,plain,
    ( spl0_837
  <=> ! [X19] :
        ( c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f47280,plain,
    ( spl0_1164
  <=> ! [X18] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f52806,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat) )
    | spl0_126
    | ~ spl0_182
    | ~ spl0_467
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_993
    | ~ spl0_1157
    | ~ spl0_1164
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f52805,f50937]) ).

fof(f50937,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f50934,f23997]) ).

fof(f50934,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(v_i____,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_467
    | ~ spl0_867 ),
    inference(resolution,[],[f17463,f5449]) ).

fof(f5449,plain,
    ( ! [X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_467 ),
    inference(avatar_component_clause,[],[f5448]) ).

fof(f17463,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_867 ),
    inference(avatar_component_clause,[],[f17461]) ).

fof(f52805,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat) )
    | spl0_126
    | ~ spl0_182
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1164
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f52804,f51115]) ).

fof(f51115,plain,
    ( v_i____ = hAPP(c_Suc,v_i____)
    | spl0_126
    | ~ spl0_182
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51114,f2889]) ).

fof(f2889,plain,
    ( ! [X18] : c_Divides_Odiv__class_Odiv(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X18
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f2888]) ).

fof(f51114,plain,
    ( hAPP(c_Suc,v_i____) = c_Divides_Odiv__class_Odiv(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | spl0_126
    | ~ spl0_182
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f51113,f2889]) ).

fof(f51113,plain,
    ( c_Divides_Odiv__class_Odiv(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,v_i____),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | spl0_126
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f50935,f51055]) ).

fof(f50935,plain,
    ( c_Divides_Odiv__class_Odiv(v_i____,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,v_i____),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_837
    | ~ spl0_867 ),
    inference(resolution,[],[f17463,f15020]) ).

fof(f15020,plain,
    ( ! [X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_837 ),
    inference(avatar_component_clause,[],[f15019]) ).

fof(f52804,plain,
    ( ! [X18] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X18,v_i____,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat) )
    | spl0_126
    | ~ spl0_182
    | ~ spl0_705
    | ~ spl0_837
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_1157
    | ~ spl0_1164
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f47281,f51115]) ).

fof(f47281,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat) )
    | ~ spl0_1164 ),
    inference(avatar_component_clause,[],[f47280]) ).

fof(f51085,plain,
    ( spl0_717
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f48475,f25163,f9304,f5394,f2969,f2702,f11320]) ).

fof(f2702,plain,
    ( spl0_139
  <=> ! [X18] : ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f25163,plain,
    ( spl0_1025
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | v_i____ = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f48475,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f9753,f48319]) ).

fof(f48319,plain,
    ( ! [X17] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X17,tc_nat)
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f2970,f25852]) ).

fof(f25852,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_139
    | ~ spl0_1025 ),
    inference(resolution,[],[f25164,f2703]) ).

fof(f2703,plain,
    ( ! [X18] : ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f2702]) ).

fof(f25164,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | v_i____ = X0 )
    | ~ spl0_1025 ),
    inference(avatar_component_clause,[],[f25163]) ).

fof(f51026,plain,
    ( spl0_1178
    | ~ spl0_949
    | ~ spl0_1168 ),
    inference(avatar_split_clause,[],[f47335,f47326,f20243,f51024]) ).

fof(f51024,plain,
    ( spl0_1178
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(X17,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f47326,plain,
    ( spl0_1168
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f47335,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(X17,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_949
    | ~ spl0_1168 ),
    inference(forward_demodulation,[],[f47327,f20244]) ).

fof(f47327,plain,
    ( ! [X17] :
        ( c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____
        | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),hAPP(c_Suc,v_i____),tc_nat),tc_nat) )
    | ~ spl0_1168 ),
    inference(avatar_component_clause,[],[f47326]) ).

fof(f51018,plain,
    ( spl0_1169
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_949
    | ~ spl0_1025
    | ~ spl0_1087 ),
    inference(avatar_split_clause,[],[f49714,f25951,f25163,f20243,f10711,f9304,f5394,f3180,f2969,f2702,f47332]) ).

fof(f47332,plain,
    ( spl0_1169
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(X17,v_i____,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f3180,plain,
    ( spl0_241
  <=> ! [X17] : c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f10711,plain,
    ( spl0_702
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f25951,plain,
    ( spl0_1087
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f49714,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(X17,v_i____,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_949
    | ~ spl0_1025
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f49713,f20244]) ).

fof(f49713,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),v_i____,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1025
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f49712,f48450]) ).

fof(f48450,plain,
    ( v_i____ = hAPP(c_Suc,v_i____)
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f34631,f48319]) ).

fof(f34631,plain,
    ( v_i____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702 ),
    inference(forward_demodulation,[],[f14111,f3181]) ).

fof(f3181,plain,
    ( ! [X17] : c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X17
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f3180]) ).

fof(f14111,plain,
    ( hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,v_i____),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_647
    | ~ spl0_702 ),
    inference(resolution,[],[f9305,f10712]) ).

fof(f10712,plain,
    ( ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) )
    | ~ spl0_702 ),
    inference(avatar_component_clause,[],[f10711]) ).

fof(f49712,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_1025
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f49711,f48475]) ).

fof(f49711,plain,
    ( ! [X17] :
        ( c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____
        | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat) )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_1025
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f25952,f48475]) ).

fof(f25952,plain,
    ( ! [X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat) )
    | ~ spl0_1087 ),
    inference(avatar_component_clause,[],[f25951]) ).

fof(f51015,plain,
    ( spl0_1177
    | ~ spl0_139
    | ~ spl0_1025
    | ~ spl0_1164 ),
    inference(avatar_split_clause,[],[f47337,f47280,f25163,f2702,f51013]) ).

fof(f51013,plain,
    ( spl0_1177
  <=> ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f47337,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat) )
    | ~ spl0_139
    | ~ spl0_1025
    | ~ spl0_1164 ),
    inference(forward_demodulation,[],[f47281,f25852]) ).

fof(f50889,plain,
    ( spl0_1176
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_469
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f49558,f25163,f10711,f9304,f5456,f5394,f3180,f2969,f2702,f50887]) ).

fof(f50887,plain,
    ( spl0_1176
  <=> ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f49558,plain,
    ( ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_469
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f49557,f25852]) ).

fof(f49557,plain,
    ( ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_241
    | ~ spl0_456
    | ~ spl0_469
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f49556,f48450]) ).

fof(f49556,plain,
    ( ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_456
    | ~ spl0_469
    | ~ spl0_647
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f5457,f48475]) ).

fof(f50830,plain,
    ( spl0_950
    | ~ spl0_197
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f35995,f23996,f17461,f5448,f2969,f20692]) ).

fof(f35995,plain,
    ( ! [X17] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X17,tc_nat)
    | ~ spl0_197
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f2970,f35824]) ).

fof(f35824,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f17819,f23997]) ).

fof(f17819,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(v_i____,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_467
    | ~ spl0_867 ),
    inference(resolution,[],[f17463,f5449]) ).

fof(f49807,plain,
    ( spl0_950
    | ~ spl0_139
    | ~ spl0_197
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f48319,f25163,f2969,f2702,f20692]) ).

fof(f48318,plain,
    ( spl0_1172
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157
    | ~ spl0_1171 ),
    inference(avatar_split_clause,[],[f48280,f47902,f47195,f25163,f11320,f10711,f9304,f8298,f5448,f3211,f3180,f2702,f47909]) ).

fof(f47909,plain,
    ( spl0_1172
  <=> ! [X19] : c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f3211,plain,
    ( spl0_248
  <=> ! [X18,X17] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),hAPP(c_Suc,X18),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f8298,plain,
    ( spl0_607
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f47902,plain,
    ( spl0_1171
  <=> ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f48280,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157
    | ~ spl0_1171 ),
    inference(trivial_inequality_removal,[],[f48279]) ).

fof(f48279,plain,
    ( ! [X19] :
        ( v_i____ != v_i____
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157
    | ~ spl0_1171 ),
    inference(forward_demodulation,[],[f47905,f48067]) ).

fof(f48067,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157 ),
    inference(duplicate_literal_removal,[],[f48066]) ).

fof(f48066,plain,
    ( ! [X0] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157 ),
    inference(forward_demodulation,[],[f48065,f25852]) ).

fof(f48065,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157 ),
    inference(forward_demodulation,[],[f48064,f47717]) ).

fof(f47717,plain,
    ( v_i____ = hAPP(c_Suc,v_i____)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f14120,f47685]) ).

fof(f47685,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
    | ~ spl0_139
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_717
    | ~ spl0_1025 ),
    inference(duplicate_literal_removal,[],[f47684]) ).

fof(f47684,plain,
    ( ! [X0] :
        ( v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
        | v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat) )
    | ~ spl0_139
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_717
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f47683,f25852]) ).

fof(f47683,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
        | v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat) )
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f35380,f11322]) ).

fof(f11322,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_717 ),
    inference(avatar_component_clause,[],[f11320]) ).

fof(f35380,plain,
    ( ! [X0] :
        ( v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) )
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f9130,f11322]) ).

fof(f9130,plain,
    ( ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) )
    | ~ spl0_248
    | ~ spl0_607 ),
    inference(resolution,[],[f8299,f3212]) ).

fof(f3212,plain,
    ( ! [X18,X17] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),hAPP(c_Suc,X18),tc_nat)
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f3211]) ).

fof(f8299,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_607 ),
    inference(avatar_component_clause,[],[f8298]) ).

fof(f14120,plain,
    ( v_i____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702 ),
    inference(forward_demodulation,[],[f14111,f3181]) ).

fof(f48064,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,v_i____),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157 ),
    inference(forward_demodulation,[],[f47891,f11322]) ).

fof(f47891,plain,
    ( ! [X0] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1157 ),
    inference(forward_demodulation,[],[f47881,f47717]) ).

fof(f47881,plain,
    ( ! [X0] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,v_i____),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_467
    | ~ spl0_1157 ),
    inference(resolution,[],[f47196,f5449]) ).

fof(f47905,plain,
    ( ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1171 ),
    inference(forward_demodulation,[],[f47903,f47717]) ).

fof(f47903,plain,
    ( ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_1171 ),
    inference(avatar_component_clause,[],[f47902]) ).

fof(f48273,plain,
    ( spl0_1175
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_717
    | ~ spl0_939
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f48147,f25729,f25163,f18225,f11320,f10727,f10711,f9304,f8298,f3211,f3180,f2702,f48271]) ).

fof(f48271,plain,
    ( spl0_1175
  <=> ! [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)),v_i____)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f10727,plain,
    ( spl0_706
  <=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f18225,plain,
    ( spl0_939
  <=> ! [X0,X17] :
        ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f25729,plain,
    ( spl0_1048
  <=> ! [X0] : v_i____ = c_Divides_Odiv__class_Odiv(v_i____,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f48147,plain,
    ( ! [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)),v_i____)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_717
    | ~ spl0_939
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f48146,f47821]) ).

fof(f47821,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0)
    | ~ spl0_139
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_706
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f25781,f47685]) ).

fof(f25781,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(v_i____,c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0)
    | ~ spl0_706
    | ~ spl0_1048 ),
    inference(superposition,[],[f10728,f25730]) ).

fof(f25730,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Odiv(v_i____,X0,tc_nat)
    | ~ spl0_1048 ),
    inference(avatar_component_clause,[],[f25729]) ).

fof(f10728,plain,
    ( ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X17)
    | ~ spl0_706 ),
    inference(avatar_component_clause,[],[f10727]) ).

fof(f48146,plain,
    ( ! [X0,X17] :
        ( 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),v_i____),X17))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_939
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f48145,f47717]) ).

fof(f48145,plain,
    ( ! [X0,X17] :
        ( 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),hAPP(c_Suc,v_i____)),X17))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_717
    | ~ spl0_939 ),
    inference(forward_demodulation,[],[f18226,f11322]) ).

fof(f18226,plain,
    ( ! [X0,X17] :
        ( ~ 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) )
    | ~ spl0_939 ),
    inference(avatar_component_clause,[],[f18225]) ).

fof(f48269,plain,
    ( spl0_867
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_350
    | ~ spl0_465
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_705
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f48035,f25729,f25163,f11320,f10723,f10711,f9304,f8298,f5430,f4111,f3211,f3180,f2702,f17461]) ).

fof(f4111,plain,
    ( spl0_350
  <=> ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f5430,plain,
    ( spl0_465
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f48035,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_350
    | ~ spl0_465
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_705
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f48034,f47879]) ).

fof(f47879,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____)
    | ~ spl0_139
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_705
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f25780,f47685]) ).

fof(f25780,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(v_i____,c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____)
    | ~ spl0_705
    | ~ spl0_1048 ),
    inference(superposition,[],[f10724,f25730]) ).

fof(f48034,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____),tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_350
    | ~ spl0_465
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f35479,f47717]) ).

fof(f35479,plain,
    ( ! [X0] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(c_Suc,v_i____)),tc_nat)
    | ~ spl0_350
    | ~ spl0_465
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f6336,f11322]) ).

fof(f6336,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_350
    | ~ spl0_465 ),
    inference(superposition,[],[f4112,f5431]) ).

fof(f5431,plain,
    ( ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18)
    | ~ spl0_465 ),
    inference(avatar_component_clause,[],[f5430]) ).

fof(f4112,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19),tc_nat)
    | ~ spl0_350 ),
    inference(avatar_component_clause,[],[f4111]) ).

fof(f48266,plain,
    ( spl0_1174
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_717
    | ~ spl0_865
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f48169,f25729,f25163,f17453,f11320,f10727,f10711,f9304,f8298,f3211,f3180,f2702,f48264]) ).

fof(f48264,plain,
    ( spl0_1174
  <=> ! [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)),v_i____)
        | ~ class_Int_Onumber__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f17453,plain,
    ( spl0_865
  <=> ! [X0,X17] :
        ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
        | ~ class_Int_Onumber__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f48169,plain,
    ( ! [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)),v_i____)
        | ~ class_Int_Onumber__ring(X0) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_717
    | ~ spl0_865
    | ~ spl0_1025
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f48168,f47821]) ).

fof(f48168,plain,
    ( ! [X0,X17] :
        ( 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),v_i____),X17))
        | ~ class_Int_Onumber__ring(X0) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_865
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f48167,f47717]) ).

fof(f48167,plain,
    ( ! [X0,X17] :
        ( 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),hAPP(c_Suc,v_i____)),X17))
        | ~ class_Int_Onumber__ring(X0) )
    | ~ spl0_717
    | ~ spl0_865 ),
    inference(forward_demodulation,[],[f17454,f11322]) ).

fof(f17454,plain,
    ( ! [X0,X17] :
        ( ~ 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)) )
    | ~ spl0_865 ),
    inference(avatar_component_clause,[],[f17453]) ).

fof(f48213,plain,
    ( spl0_1173
    | ~ spl0_14
    | ~ spl0_139
    | ~ spl0_143
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_935
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f48087,f25163,f18209,f11320,f10711,f9304,f8298,f3211,f3180,f2721,f2702,f2082,f48210]) ).

fof(f48210,plain,
    ( spl0_1173
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),v_i____),hAPP(c_Suc,v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f2721,plain,
    ( spl0_143
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f48087,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),v_i____),hAPP(c_Suc,v_ka____)),tc_nat)
    | ~ spl0_14
    | ~ spl0_139
    | ~ spl0_143
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_935
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f48086,f47717]) ).

fof(f48086,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,v_i____)),hAPP(c_Suc,v_ka____)),tc_nat)
    | ~ spl0_14
    | ~ spl0_143
    | ~ spl0_717
    | ~ spl0_935 ),
    inference(forward_demodulation,[],[f48085,f11322]) ).

fof(f48085,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)),tc_nat)
    | ~ spl0_14
    | ~ spl0_143
    | ~ spl0_935 ),
    inference(forward_demodulation,[],[f2723,f20704]) ).

fof(f2723,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f2721]) ).

fof(f47922,plain,
    ( spl0_126
    | ~ spl0_1172 ),
    inference(avatar_contradiction_clause,[],[f47921]) ).

fof(f47921,plain,
    ( $false
    | spl0_126
    | ~ spl0_1172 ),
    inference(resolution,[],[f47910,f2644]) ).

fof(f47910,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
    | ~ spl0_1172 ),
    inference(avatar_component_clause,[],[f47909]) ).

fof(f47911,plain,
    ( spl0_1172
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158
    | ~ spl0_1171 ),
    inference(avatar_split_clause,[],[f47907,f47902,f47200,f25163,f11320,f10711,f9304,f8298,f5448,f3211,f3180,f2702,f47909]) ).

fof(f47200,plain,
    ( spl0_1158
  <=> ! [X19] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f47907,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158
    | ~ spl0_1171 ),
    inference(trivial_inequality_removal,[],[f47906]) ).

fof(f47906,plain,
    ( ! [X19] :
        ( v_i____ != v_i____
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158
    | ~ spl0_1171 ),
    inference(forward_demodulation,[],[f47905,f47848]) ).

fof(f47848,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158 ),
    inference(duplicate_literal_removal,[],[f47847]) ).

fof(f47847,plain,
    ( ! [X0] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158 ),
    inference(forward_demodulation,[],[f47846,f25852]) ).

fof(f47846,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_467
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1158 ),
    inference(forward_demodulation,[],[f47845,f47717]) ).

fof(f47845,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,v_i____),tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat) )
    | ~ spl0_467
    | ~ spl0_717
    | ~ spl0_1158 ),
    inference(forward_demodulation,[],[f47835,f11322]) ).

fof(f47835,plain,
    ( ! [X0] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X0,v_i____,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_467
    | ~ spl0_1158 ),
    inference(resolution,[],[f47201,f5449]) ).

fof(f47201,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | v_i____ = c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat) )
    | ~ spl0_1158 ),
    inference(avatar_component_clause,[],[f47200]) ).

fof(f47904,plain,
    ( spl0_1171
    | ~ spl0_139
    | ~ spl0_1025
    | ~ spl0_1159 ),
    inference(avatar_split_clause,[],[f47341,f47218,f25163,f2702,f47902]) ).

fof(f47218,plain,
    ( spl0_1159
  <=> ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f47341,plain,
    ( ! [X19] :
        ( v_i____ != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_1025
    | ~ spl0_1159 ),
    inference(forward_demodulation,[],[f47219,f25852]) ).

fof(f47219,plain,
    ( ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_1159 ),
    inference(avatar_component_clause,[],[f47218]) ).

fof(f47849,plain,
    ( ~ spl0_718
    | spl0_405
    | ~ spl0_572
    | ~ spl0_1025
    | ~ spl0_1103
    | ~ spl0_1140 ),
    inference(avatar_split_clause,[],[f31741,f31132,f28913,f25163,f8142,f4728,f11709]) ).

fof(f11709,plain,
    ( spl0_718
  <=> c_lessequals(v_i____,v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f4728,plain,
    ( spl0_405
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f8142,plain,
    ( spl0_572
  <=> ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f28913,plain,
    ( spl0_1103
  <=> ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f31132,plain,
    ( spl0_1140
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f31741,plain,
    ( ~ c_lessequals(v_i____,v_i____,tc_nat)
    | spl0_405
    | ~ spl0_572
    | ~ spl0_1025
    | ~ spl0_1103
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31740,f28914]) ).

fof(f28914,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____)
    | ~ spl0_1103 ),
    inference(avatar_component_clause,[],[f28913]) ).

fof(f31740,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),v_i____),v_i____,tc_nat)
    | spl0_405
    | ~ spl0_572
    | ~ spl0_1025
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31531,f25836]) ).

fof(f25836,plain,
    ( v_i____ = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)
    | spl0_405
    | ~ spl0_1025 ),
    inference(resolution,[],[f25164,f4730]) ).

fof(f4730,plain,
    ( ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | spl0_405 ),
    inference(avatar_component_clause,[],[f4728]) ).

fof(f31531,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat)
    | ~ spl0_572
    | ~ spl0_1140 ),
    inference(superposition,[],[f8143,f31133]) ).

fof(f31133,plain,
    ( ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23))
    | ~ spl0_1140 ),
    inference(avatar_component_clause,[],[f31132]) ).

fof(f8143,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat)
    | ~ spl0_572 ),
    inference(avatar_component_clause,[],[f8142]) ).

fof(f47833,plain,
    ( spl0_1170
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1156 ),
    inference(avatar_split_clause,[],[f47780,f46226,f25163,f11320,f10711,f9304,f8298,f3211,f3180,f2702,f47831]) ).

fof(f47780,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X19),tc_nat)
    | ~ spl0_139
    | ~ spl0_241
    | ~ spl0_248
    | ~ spl0_607
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_717
    | ~ spl0_1025
    | ~ spl0_1156 ),
    inference(forward_demodulation,[],[f46227,f47717]) ).

fof(f47677,plain,
    ( spl0_950
    | ~ spl0_197
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f35995,f23996,f17461,f5448,f2969,f20692]) ).

fof(f47334,plain,
    ( spl0_1169
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_949
    | ~ spl0_1024
    | ~ spl0_1168 ),
    inference(avatar_split_clause,[],[f47330,f47326,f24764,f20243,f10711,f9304,f3180,f2871,f47332]) ).

fof(f2871,plain,
    ( spl0_178
  <=> ! [X18,X17] : c_lessequals(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X18,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f24764,plain,
    ( spl0_1024
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | v_i____ = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f47330,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(X17,v_i____,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_949
    | ~ spl0_1024
    | ~ spl0_1168 ),
    inference(forward_demodulation,[],[f47329,f20244]) ).

fof(f47329,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),v_i____,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024
    | ~ spl0_1168 ),
    inference(forward_demodulation,[],[f47327,f45882]) ).

fof(f45882,plain,
    ( v_i____ = hAPP(c_Suc,v_i____)
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f14120,f25669]) ).

fof(f25669,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
    | ~ spl0_178
    | ~ spl0_1024 ),
    inference(resolution,[],[f24765,f2872]) ).

fof(f2872,plain,
    ( ! [X18,X17] : c_lessequals(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X18,tc_nat)
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f2871]) ).

fof(f24765,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | v_i____ = X0 )
    | ~ spl0_1024 ),
    inference(avatar_component_clause,[],[f24764]) ).

fof(f47328,plain,
    ( spl0_1168
    | ~ spl0_717
    | ~ spl0_1087 ),
    inference(avatar_split_clause,[],[f35416,f25951,f11320,f47326]) ).

fof(f35416,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____ )
    | ~ spl0_717
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f35190,f11322]) ).

fof(f35190,plain,
    ( ! [X17] :
        ( c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) != v_i____
        | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat) )
    | ~ spl0_717
    | ~ spl0_1087 ),
    inference(forward_demodulation,[],[f25952,f11322]) ).

fof(f47300,plain,
    ( spl0_1167
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024
    | ~ spl0_1166 ),
    inference(avatar_split_clause,[],[f47296,f47293,f24764,f10711,f9304,f3180,f2871,f47298]) ).

fof(f47298,plain,
    ( spl0_1167
  <=> ! [X19] :
        ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),v_i____,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,v_i____,tc_nat))
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f47293,plain,
    ( spl0_1166
  <=> ! [X19] :
        ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,v_i____),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat))
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f47296,plain,
    ( ! [X19] :
        ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),v_i____,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,v_i____,tc_nat))
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024
    | ~ spl0_1166 ),
    inference(forward_demodulation,[],[f47294,f45882]) ).

fof(f47294,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,v_i____),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat)) )
    | ~ spl0_1166 ),
    inference(avatar_component_clause,[],[f47293]) ).

fof(f47295,plain,
    ( spl0_1166
    | ~ spl0_717
    | ~ spl0_941 ),
    inference(avatar_split_clause,[],[f35519,f18233,f11320,f47293]) ).

fof(f18233,plain,
    ( spl0_941
  <=> ! [X19] :
        ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f35519,plain,
    ( ! [X19] :
        ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,v_i____),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat))
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_717
    | ~ spl0_941 ),
    inference(forward_demodulation,[],[f18234,f11322]) ).

fof(f18234,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) )
    | ~ spl0_941 ),
    inference(avatar_component_clause,[],[f18233]) ).

fof(f47287,plain,
    ( spl0_1165
    | ~ spl0_717
    | ~ spl0_942 ),
    inference(avatar_split_clause,[],[f35517,f18237,f11320,f47285]) ).

fof(f18237,plain,
    ( spl0_942
  <=> ! [X19] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))) = X19
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f35517,plain,
    ( ! [X19] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,v_i____),tc_nat))) = X19
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_717
    | ~ spl0_942 ),
    inference(forward_demodulation,[],[f18238,f11322]) ).

fof(f18238,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))) = X19 )
    | ~ spl0_942 ),
    inference(avatar_component_clause,[],[f18237]) ).

fof(f47282,plain,
    ( spl0_1164
    | ~ spl0_717
    | ~ spl0_868 ),
    inference(avatar_split_clause,[],[f44549,f17466,f11320,f47280]) ).

fof(f17466,plain,
    ( spl0_868
  <=> ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f44549,plain,
    ( ! [X18] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat) )
    | ~ spl0_717
    | ~ spl0_868 ),
    inference(forward_demodulation,[],[f36100,f11322]) ).

fof(f36100,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,v_i____),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_717
    | ~ spl0_868 ),
    inference(forward_demodulation,[],[f17467,f11322]) ).

fof(f17467,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_868 ),
    inference(avatar_component_clause,[],[f17466]) ).

fof(f47264,plain,
    ( spl0_1163
    | ~ spl0_710
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f35558,f11320,f10759,f47262]) ).

fof(f47262,plain,
    ( spl0_1163
  <=> ! [X17] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f10759,plain,
    ( spl0_710
  <=> ! [X17] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f35558,plain,
    ( ! [X17] :
        ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_710
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f10760,f11322]) ).

fof(f10760,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17 )
    | ~ spl0_710 ),
    inference(avatar_component_clause,[],[f10759]) ).

fof(f47240,plain,
    ( spl0_1162
    | ~ spl0_139
    | ~ spl0_650
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f45869,f25163,f9317,f2702,f47238]) ).

fof(f47238,plain,
    ( spl0_1162
  <=> ! [X25,X19] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f9317,plain,
    ( spl0_650
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f45869,plain,
    ( ! [X19,X25] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_139
    | ~ spl0_650
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f9318,f25852]) ).

fof(f9318,plain,
    ( ! [X19,X25] :
        ( c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_650 ),
    inference(avatar_component_clause,[],[f9317]) ).

fof(f47233,plain,
    ( spl0_1161
    | ~ spl0_568
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f34981,f11320,f8126,f47231]) ).

fof(f47231,plain,
    ( spl0_1161
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f8126,plain,
    ( spl0_568
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f34981,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,v_i____,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_568
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f8127,f11322]) ).

fof(f8127,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f8126]) ).

fof(f47226,plain,
    ( spl0_1160
    | ~ spl0_466
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f35625,f11320,f5444,f47224]) ).

fof(f5444,plain,
    ( spl0_466
  <=> ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f35625,plain,
    ( ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19)),tc_nat)
    | ~ spl0_466
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f5445,f11322]) ).

fof(f5445,plain,
    ( ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19)),tc_nat)
    | ~ spl0_466 ),
    inference(avatar_component_clause,[],[f5444]) ).

fof(f47220,plain,
    ( spl0_1159
    | ~ spl0_469
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f35595,f11320,f5456,f47218]) ).

fof(f35595,plain,
    ( ! [X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_469
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f5457,f11322]) ).

fof(f47202,plain,
    ( spl0_1158
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024
    | ~ spl0_1157 ),
    inference(avatar_split_clause,[],[f47198,f47195,f24764,f10711,f9304,f3180,f2871,f47200]) ).

fof(f47198,plain,
    ( ! [X19] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X19,v_i____,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_178
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_1024
    | ~ spl0_1157 ),
    inference(forward_demodulation,[],[f47196,f45882]) ).

fof(f47197,plain,
    ( spl0_1157
    | ~ spl0_470
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f35593,f11320,f5460,f47195]) ).

fof(f5460,plain,
    ( spl0_470
  <=> ! [X19] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f35593,plain,
    ( ! [X19] :
        ( v_i____ = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,v_i____),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_470
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f5461,f11322]) ).

fof(f5461,plain,
    ( ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_470 ),
    inference(avatar_component_clause,[],[f5460]) ).

fof(f46232,plain,
    ( spl0_867
    | ~ spl0_184
    | ~ spl0_898 ),
    inference(avatar_split_clause,[],[f18120,f17978,f2916,f17461]) ).

fof(f2916,plain,
    ( spl0_184
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f18120,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_184
    | ~ spl0_898 ),
    inference(resolution,[],[f17979,f2917]) ).

fof(f2917,plain,
    ( ! [X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f2916]) ).

fof(f17979,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,v_i____,tc_nat)
    | ~ spl0_898 ),
    inference(avatar_component_clause,[],[f17978]) ).

fof(f46228,plain,
    ( spl0_1156
    | ~ spl0_350
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f35477,f11320,f4111,f46226]) ).

fof(f35477,plain,
    ( ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),X19),tc_nat)
    | ~ spl0_350
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f4112,f11322]) ).

fof(f46181,plain,
    ( spl0_1155
    | ~ spl0_139
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_949
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f45988,f25163,f20243,f11320,f8126,f2702,f38718]) ).

fof(f45988,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_139
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_949
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f34983,f25852]) ).

fof(f34983,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) )
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_949 ),
    inference(duplicate_literal_removal,[],[f34982]) ).

fof(f34982,plain,
    ( ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_949 ),
    inference(forward_demodulation,[],[f34981,f20244]) ).

fof(f45903,plain,
    ( spl0_949
    | ~ spl0_139
    | ~ spl0_177
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f45875,f25163,f2867,f2702,f20243]) ).

fof(f45875,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_139
    | ~ spl0_177
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f2868,f25852]) ).

fof(f44509,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_178
    | ~ spl0_316
    | ~ spl0_595
    | ~ spl0_709
    | ~ spl0_992
    | ~ spl0_993
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f41671,f25729,f23996,f23096,f10755,f8242,f3971,f2871,f2867,f20243]) ).

fof(f10755,plain,
    ( spl0_709
  <=> ! [X18,X17] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f23096,plain,
    ( spl0_992
  <=> ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f41671,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_177
    | ~ spl0_178
    | ~ spl0_316
    | ~ spl0_595
    | ~ spl0_709
    | ~ spl0_992
    | ~ spl0_993
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f2868,f41641]) ).

fof(f41641,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_178
    | ~ spl0_316
    | ~ spl0_595
    | ~ spl0_709
    | ~ spl0_992
    | ~ spl0_993
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f41640,f23997]) ).

fof(f41640,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat)
    | ~ spl0_178
    | ~ spl0_316
    | ~ spl0_595
    | ~ spl0_709
    | ~ spl0_992
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f25782,f35876]) ).

fof(f35876,plain,
    ( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,X1,tc_nat)
    | ~ spl0_178
    | ~ spl0_316
    | ~ spl0_595
    | ~ spl0_992 ),
    inference(forward_demodulation,[],[f24389,f4225]) ).

fof(f4225,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
    | ~ spl0_178
    | ~ spl0_316 ),
    inference(resolution,[],[f3972,f2872]) ).

fof(f24389,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,X1,tc_nat)
    | ~ spl0_595
    | ~ spl0_992 ),
    inference(superposition,[],[f8243,f23097]) ).

fof(f23097,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)
    | ~ spl0_992 ),
    inference(avatar_component_clause,[],[f23096]) ).

fof(f25782,plain,
    ( ! [X0] : c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____),tc_nat)
    | ~ spl0_709
    | ~ spl0_1048 ),
    inference(superposition,[],[f10756,f25730]) ).

fof(f10756,plain,
    ( ! [X18,X17] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),tc_nat)
    | ~ spl0_709 ),
    inference(avatar_component_clause,[],[f10755]) ).

fof(f41634,plain,
    ( spl0_950
    | ~ spl0_197
    | ~ spl0_345
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1088 ),
    inference(avatar_split_clause,[],[f41568,f27911,f11320,f10394,f4090,f2969,f20692]) ).

fof(f4090,plain,
    ( spl0_345
  <=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),X17,tc_nat) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f27911,plain,
    ( spl0_1088
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),v_i____) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f41568,plain,
    ( ! [X17] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X17,tc_nat)
    | ~ spl0_197
    | ~ spl0_345
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1088 ),
    inference(forward_demodulation,[],[f2970,f39312]) ).

fof(f39312,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_345
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1088 ),
    inference(forward_demodulation,[],[f39311,f11322]) ).

fof(f39311,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_345
    | ~ spl0_659
    | ~ spl0_1088 ),
    inference(forward_demodulation,[],[f10396,f30125]) ).

fof(f30125,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_i____,tc_nat) = X0
    | ~ spl0_345
    | ~ spl0_1088 ),
    inference(superposition,[],[f4091,f27912]) ).

fof(f27912,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),v_i____) = X0
    | ~ spl0_1088 ),
    inference(avatar_component_clause,[],[f27911]) ).

fof(f4091,plain,
    ( ! [X18,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),X17,tc_nat) = X18
    | ~ spl0_345 ),
    inference(avatar_component_clause,[],[f4090]) ).

fof(f39253,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f35996,f23996,f17461,f5448,f2867,f20243]) ).

fof(f35996,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_177
    | ~ spl0_467
    | ~ spl0_867
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f2868,f35824]) ).

fof(f38720,plain,
    ( spl0_1155
    | ~ spl0_467
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_993 ),
    inference(avatar_split_clause,[],[f36038,f23996,f20243,f17461,f11320,f8126,f5448,f38718]) ).

fof(f36038,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_467
    | ~ spl0_568
    | ~ spl0_717
    | ~ spl0_867
    | ~ spl0_949
    | ~ spl0_993 ),
    inference(forward_demodulation,[],[f34983,f35824]) ).

fof(f35826,plain,
    ( spl0_950
    | ~ spl0_197
    | ~ spl0_1135 ),
    inference(avatar_split_clause,[],[f35379,f30931,f2969,f20692]) ).

fof(f30931,plain,
    ( spl0_1135
  <=> ! [X0] :
        ( v_i____ != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f35379,plain,
    ( ! [X17] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X17,tc_nat)
    | ~ spl0_197
    | ~ spl0_1135 ),
    inference(forward_demodulation,[],[f2970,f31122]) ).

fof(f31122,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_1135 ),
    inference(equality_resolution,[],[f30932]) ).

fof(f30932,plain,
    ( ! [X0] :
        ( v_i____ != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_1135 ),
    inference(avatar_component_clause,[],[f30931]) ).

fof(f35825,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_1135 ),
    inference(avatar_split_clause,[],[f35378,f30931,f2867,f20243]) ).

fof(f35378,plain,
    ( ! [X18] : c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat) = X18
    | ~ spl0_177
    | ~ spl0_1135 ),
    inference(forward_demodulation,[],[f2868,f31122]) ).

fof(f35316,plain,
    ( spl0_867
    | ~ spl0_401
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1135 ),
    inference(avatar_split_clause,[],[f34852,f30931,f11320,f10394,f4712,f17461]) ).

fof(f4712,plain,
    ( spl0_401
  <=> ! [X25,X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f34852,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_401
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1135 ),
    inference(duplicate_literal_removal,[],[f34851]) ).

fof(f34851,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_401
    | ~ spl0_659
    | ~ spl0_717
    | ~ spl0_1135 ),
    inference(forward_demodulation,[],[f34850,f11322]) ).

fof(f34850,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_401
    | ~ spl0_659
    | ~ spl0_1135 ),
    inference(duplicate_literal_removal,[],[f34849]) ).

fof(f34849,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_401
    | ~ spl0_659
    | ~ spl0_1135 ),
    inference(forward_demodulation,[],[f10930,f31122]) ).

fof(f10930,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_401
    | ~ spl0_659 ),
    inference(superposition,[],[f4713,f10396]) ).

fof(f4713,plain,
    ( ! [X19,X25] :
        ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) )
    | ~ spl0_401 ),
    inference(avatar_component_clause,[],[f4712]) ).

fof(f35315,plain,
    ( spl0_1020
    | ~ spl0_184
    | ~ spl0_1135 ),
    inference(avatar_split_clause,[],[f34952,f30931,f2916,f24559]) ).

fof(f34952,plain,
    ( ! [X17] :
        ( c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) )
    | ~ spl0_184
    | ~ spl0_1135 ),
    inference(forward_demodulation,[],[f2917,f31122]) ).

fof(f35314,plain,
    ( ~ spl0_867
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_466
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f34928,f25729,f20692,f10727,f10711,f10684,f10394,f9569,f9337,f9304,f8150,f6697,f5444,f5311,f3180,f3075,f17461]) ).

fof(f3075,plain,
    ( spl0_215
  <=> ! [X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)) = X19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f5311,plain,
    ( spl0_436
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f6697,plain,
    ( spl0_547
  <=> ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X18),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f8150,plain,
    ( spl0_574
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f9337,plain,
    ( spl0_655
  <=> ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X27) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f9569,plain,
    ( spl0_658
  <=> c_lessequals(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f10684,plain,
    ( spl0_696
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(c_Suc,X17)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f34928,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_466
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f5445,f34877]) ).

fof(f34877,plain,
    ( ! [X0] : v_i____ = hAPP(c_Suc,X0)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f34876,f25730]) ).

fof(f34876,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(v_i____,v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f34875,f34860]) ).

fof(f34860,plain,
    ( ! [X0] : v_i____ = hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X0)))
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f34859,f33305]) ).

fof(f33305,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0)
    | ~ spl0_706
    | ~ spl0_950
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f25781,f20693]) ).

fof(f34859,plain,
    ( ! [X0] : hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X0))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),hAPP(c_Suc,X0))
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f11429,f34632]) ).

fof(f34632,plain,
    ( v_i____ = hAPP(c_Suc,v_i____)
    | ~ spl0_241
    | ~ spl0_647
    | ~ spl0_702
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f34631,f20693]) ).

fof(f11429,plain,
    ( ! [X0] : hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X0))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,v_i____)),hAPP(c_Suc,X0))
    | ~ spl0_215
    | ~ spl0_436
    | ~ spl0_574
    | ~ spl0_655
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f11428,f11327]) ).

fof(f11327,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_215
    | ~ spl0_574
    | ~ spl0_658
    | ~ spl0_659 ),
    inference(forward_demodulation,[],[f11326,f3076]) ).

fof(f3076,plain,
    ( ! [X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)) = X19
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f3075]) ).

fof(f11326,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_574
    | ~ spl0_658
    | ~ spl0_659 ),
    inference(forward_demodulation,[],[f10599,f10396]) ).

fof(f10599,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat))
    | ~ spl0_574
    | ~ spl0_658 ),
    inference(resolution,[],[f9571,f8151]) ).

fof(f8151,plain,
    ( ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = X18 )
    | ~ spl0_574 ),
    inference(avatar_component_clause,[],[f8150]) ).

fof(f9571,plain,
    ( c_lessequals(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_658 ),
    inference(avatar_component_clause,[],[f9569]) ).

fof(f11428,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,X0)) = hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X0)))
    | ~ spl0_436
    | ~ spl0_655
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f11427,f10685]) ).

fof(f10685,plain,
    ( ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(c_Suc,X17)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17))
    | ~ spl0_696 ),
    inference(avatar_component_clause,[],[f10684]) ).

fof(f11427,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,X0)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(c_Suc,X0)))
    | ~ spl0_436
    | ~ spl0_655
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f11362,f5312]) ).

fof(f5312,plain,
    ( ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18)
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f5311]) ).

fof(f11362,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,X0)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X0)),X0))
    | ~ spl0_655
    | ~ spl0_696 ),
    inference(superposition,[],[f10685,f9338]) ).

fof(f9338,plain,
    ( ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X27)
    | ~ spl0_655 ),
    inference(avatar_component_clause,[],[f9337]) ).

fof(f34875,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X0))),v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f34874,f10685]) ).

fof(f34874,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(c_Suc,X0))),v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_436
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f34873,f5312]) ).

fof(f34873,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X0)),X0)),v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_241
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_647
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696
    | ~ spl0_702
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f11439,f34632]) ).

fof(f11439,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X0)),X0)),hAPP(c_Suc,v_i____),tc_nat)
    | ~ spl0_215
    | ~ spl0_547
    | ~ spl0_574
    | ~ spl0_658
    | ~ spl0_659
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f11372,f11327]) ).

fof(f11372,plain,
    ( ! [X0] : hAPP(c_Suc,X0) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X0)),X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_547
    | ~ spl0_696 ),
    inference(superposition,[],[f6698,f10685]) ).

fof(f6698,plain,
    ( ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X18),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = X18
    | ~ spl0_547 ),
    inference(avatar_component_clause,[],[f6697]) ).

fof(f34822,plain,
    ( spl0_1154
    | ~ spl0_717
    | ~ spl0_947
    | ~ spl0_1153 ),
    inference(avatar_split_clause,[],[f34818,f34813,f19173,f11320,f34820]) ).

fof(f19173,plain,
    ( spl0_947
  <=> c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,v_i____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f34818,plain,
    ( ! [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)),v_i____)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),v_i____))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_717
    | ~ spl0_947
    | ~ spl0_1153 ),
    inference(forward_demodulation,[],[f34817,f11322]) ).

fof(f34817,plain,
    ( ! [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_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_717
    | ~ spl0_947
    | ~ spl0_1153 ),
    inference(forward_demodulation,[],[f34816,f19175]) ).

fof(f19175,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,v_i____)
    | ~ spl0_947 ),
    inference(avatar_component_clause,[],[f19173]) ).

fof(f34816,plain,
    ( ! [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)),hAPP(c_Suc,v_i____))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,v_i____)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_717
    | ~ spl0_1153 ),
    inference(forward_demodulation,[],[f34814,f11322]) ).

fof(f34815,plain,
    spl0_1153,
    inference(avatar_split_clause,[],[f1875,f34813]) ).

fof(f1875,plain,
    ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))))
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1382,f1837]) ).

fof(f1382,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(f34811,plain,
    spl0_1152,
    inference(avatar_split_clause,[],[f1206,f34809]) ).

fof(f34809,plain,
    ( spl0_1152
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),hAPP(c_Suc,X17)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f1206,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),hAPP(c_Suc,X17)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

fof(f34807,plain,
    spl0_1151,
    inference(avatar_split_clause,[],[f1050,f34805]) ).

fof(f34805,plain,
    ( spl0_1151
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),c_HOL_Ominus__class_Ominus(X1,X26,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f1050,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),c_HOL_Ominus__class_Ominus(X1,X26,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

fof(f34678,plain,
    ( spl0_1150
    | ~ spl0_1135
    | ~ spl0_1149 ),
    inference(avatar_split_clause,[],[f34674,f34671,f30931,f34676]) ).

fof(f34676,plain,
    ( spl0_1150
  <=> ! [X28,X24,X23,X22] :
        ( v_i____ = X23
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | hBOOL(hAPP(X28,X22))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f34671,plain,
    ( spl0_1149
  <=> ! [X28,X24,X23,X22] :
        ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X22))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f34674,plain,
    ( ! [X28,X24,X22,X23] :
        ( v_i____ = X23
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | hBOOL(hAPP(X28,X22))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) )
    | ~ spl0_1135
    | ~ spl0_1149 ),
    inference(forward_demodulation,[],[f34672,f31122]) ).

fof(f34672,plain,
    ( ! [X28,X24,X22,X23] :
        ( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat)))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X22))
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat) )
    | ~ spl0_1149 ),
    inference(avatar_component_clause,[],[f34671]) ).

fof(f34673,plain,
    spl0_1149,
    inference(avatar_split_clause,[],[f590,f34671]) ).

fof(f590,axiom,
    ! [X28,X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X23
      | hBOOL(hAPP(X28,X22))
      | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_1) ).

fof(f34668,plain,
    ( spl0_1148
    | ~ spl0_465
    | ~ spl0_755
    | ~ spl0_1145 ),
    inference(avatar_split_clause,[],[f32234,f32152,f13546,f5430,f34666]) ).

fof(f34666,plain,
    ( spl0_1148
  <=> ! [X24,X28,X23] :
        ( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X24,X23,tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X24)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f13546,plain,
    ( spl0_755
  <=> ! [X18,X17,X23] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),X18),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f32152,plain,
    ( spl0_1145
  <=> ! [X28,X24,X23,X22] :
        ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X24))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f32234,plain,
    ( ! [X28,X24,X23] :
        ( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X24,X23,tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X24)) )
    | ~ spl0_465
    | ~ spl0_755
    | ~ spl0_1145 ),
    inference(forward_demodulation,[],[f32153,f13770]) ).

fof(f13770,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),X2),X1,tc_nat)
    | ~ spl0_465
    | ~ spl0_755 ),
    inference(superposition,[],[f13547,f5431]) ).

fof(f13547,plain,
    ( ! [X18,X17,X23] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),X18),X17,tc_nat)
    | ~ spl0_755 ),
    inference(avatar_component_clause,[],[f13546]) ).

fof(f32153,plain,
    ( ! [X28,X24,X22,X23] :
        ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hBOOL(hAPP(X28,X24))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) )
    | ~ spl0_1145 ),
    inference(avatar_component_clause,[],[f32152]) ).

fof(f32216,plain,
    ( ~ spl0_718
    | spl0_405
    | ~ spl0_465
    | ~ spl0_561
    | ~ spl0_598
    | ~ spl0_1025
    | ~ spl0_1092
    | ~ spl0_1140 ),
    inference(avatar_split_clause,[],[f31716,f31132,f28869,f25163,f8254,f8098,f5430,f4728,f11709]) ).

fof(f8098,plain,
    ( spl0_561
  <=> ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),X0),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f8254,plain,
    ( spl0_598
  <=> ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f28869,plain,
    ( spl0_1092
  <=> ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f31716,plain,
    ( ~ c_lessequals(v_i____,v_i____,tc_nat)
    | spl0_405
    | ~ spl0_465
    | ~ spl0_561
    | ~ spl0_598
    | ~ spl0_1025
    | ~ spl0_1092
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31715,f28870]) ).

fof(f28870,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0)
    | ~ spl0_1092 ),
    inference(avatar_component_clause,[],[f28869]) ).

fof(f31715,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),hAPP(c_Suc,hAPP(c_Suc,X0))),v_i____,tc_nat)
    | spl0_405
    | ~ spl0_465
    | ~ spl0_561
    | ~ spl0_598
    | ~ spl0_1025
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31714,f25836]) ).

fof(f31714,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),hAPP(c_Suc,hAPP(c_Suc,X0))),v_i____,tc_nat)
    | ~ spl0_465
    | ~ spl0_561
    | ~ spl0_598
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31713,f8255]) ).

fof(f8255,plain,
    ( ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)
    | ~ spl0_598 ),
    inference(avatar_component_clause,[],[f8254]) ).

fof(f31713,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)),v_i____,tc_nat)
    | ~ spl0_465
    | ~ spl0_561
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f31518,f5431]) ).

fof(f31518,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat)
    | ~ spl0_561
    | ~ spl0_1140 ),
    inference(superposition,[],[f8099,f31133]) ).

fof(f8099,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),X0),v_i____,tc_nat)
    | ~ spl0_561 ),
    inference(avatar_component_clause,[],[f8098]) ).

fof(f32215,plain,
    spl0_1147,
    inference(avatar_split_clause,[],[f380,f32213]) ).

fof(f32213,plain,
    ( spl0_1147
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X3,X0)),c_HOL_Oinverse__class_Oinverse(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f380,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X3,X0)),c_HOL_Oinverse__class_Oinverse(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

fof(f32160,plain,
    ( spl0_1146
    | ~ spl0_465
    | ~ spl0_755
    | ~ spl0_848
    | ~ spl0_1145 ),
    inference(avatar_split_clause,[],[f32156,f32152,f17177,f13546,f5430,f32158]) ).

fof(f32158,plain,
    ( spl0_1146
  <=> ! [X24,X28,X23] :
        ( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X24,X23,tc_nat)))
        | v_i____ = X23
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | hBOOL(hAPP(X28,X24)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f32156,plain,
    ( ! [X28,X24,X23] :
        ( ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X24,X23,tc_nat)))
        | v_i____ = X23
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | hBOOL(hAPP(X28,X24)) )
    | ~ spl0_465
    | ~ spl0_755
    | ~ spl0_848
    | ~ spl0_1145 ),
    inference(forward_demodulation,[],[f32155,f13770]) ).

fof(f32155,plain,
    ( ! [X28,X24,X22,X23] :
        ( v_i____ = X23
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | hBOOL(hAPP(X28,X24))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) )
    | ~ spl0_848
    | ~ spl0_1145 ),
    inference(forward_demodulation,[],[f32153,f17179]) ).

fof(f17179,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_848 ),
    inference(avatar_component_clause,[],[f17177]) ).

fof(f32154,plain,
    spl0_1145,
    inference(avatar_split_clause,[],[f147,f32152]) ).

fof(f147,axiom,
    ! [X28,X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X23
      | hBOOL(hAPP(X28,X24))
      | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X22)),X24),X23,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).

fof(f31150,plain,
    spl0_1144,
    inference(avatar_split_clause,[],[f1958,f31148]) ).

fof(f31148,plain,
    ( spl0_1144
  <=> ! [X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f1958,plain,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1451,f1837]) ).

fof(f1451,axiom,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__odd__mod__4__div__2_0) ).

fof(f31146,plain,
    spl0_1143,
    inference(avatar_split_clause,[],[f1874,f31144]) ).

fof(f31144,plain,
    ( spl0_1143
  <=> ! [X25,X0,X19] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f1874,plain,
    ! [X0,X19,X25] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1096,f1837]) ).

fof(f1096,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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),X25),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__ge__zero_0) ).

fof(f31142,plain,
    spl0_1142,
    inference(avatar_split_clause,[],[f1873,f31140]) ).

fof(f31140,plain,
    ( spl0_1142
  <=> ! [X25,X0,X19] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f1873,plain,
    ! [X0,X19,X25] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1505,f1837]) ).

fof(f1505,axiom,
    ! [X0,X19,X25] :
      ( ~ 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),X19),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),X25),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(f31138,plain,
    spl0_1141,
    inference(avatar_split_clause,[],[f1291,f31136]) ).

fof(f31136,plain,
    ( spl0_1141
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f1291,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

fof(f31134,plain,
    spl0_1140,
    inference(avatar_split_clause,[],[f1290,f31132]) ).

fof(f1290,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

fof(f31130,plain,
    spl0_1139,
    inference(avatar_split_clause,[],[f1245,f31128]) ).

fof(f31128,plain,
    ( spl0_1139
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f1245,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower3__eq__cube_0) ).

fof(f31126,plain,
    spl0_1138,
    inference(avatar_split_clause,[],[f1214,f31124]) ).

fof(f31124,plain,
    ( spl0_1138
  <=> ! [X17,X0,X3,X2] :
        ( ~ 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(X2,X3,X0)),X17) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f1214,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ 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(X2,X3,X0)),X17) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).

fof(f31121,plain,
    spl0_1137,
    inference(avatar_split_clause,[],[f1010,f31119]) ).

fof(f31119,plain,
    ( spl0_1137
  <=> ! [X20,X0,X3,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Int_Onumber__class_Onumber__of(X20,X0) != c_HOL_Oinverse__class_Odivide(X3,X1,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X20,X0)),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f1010,axiom,
    ! [X3,X0,X1,X20] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_Int_Onumber__class_Onumber__of(X20,X0) != c_HOL_Oinverse__class_Odivide(X3,X1,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(X20,X0)),X1) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

fof(f31117,plain,
    spl0_1136,
    inference(avatar_split_clause,[],[f503,f31115]) ).

fof(f31115,plain,
    ( spl0_1136
  <=> ! [X40,X0,X27,X25,X19] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27) = X40
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X40) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f503,axiom,
    ! [X40,X0,X19,X27,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27) = X40
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

fof(f30933,plain,
    ( spl0_1135
    | ~ spl0_362
    | ~ spl0_1089 ),
    inference(avatar_split_clause,[],[f30694,f28826,f4551,f30931]) ).

fof(f4551,plain,
    ( spl0_362
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) != X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f28826,plain,
    ( spl0_1089
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f30694,plain,
    ( ! [X0] :
        ( v_i____ != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_362
    | ~ spl0_1089 ),
    inference(superposition,[],[f4552,f28827]) ).

fof(f28827,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),X0) = X0
    | ~ spl0_1089 ),
    inference(avatar_component_clause,[],[f28826]) ).

fof(f4552,plain,
    ( ! [X18,X17] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) != X18
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f4551]) ).

fof(f30899,plain,
    spl0_1134,
    inference(avatar_split_clause,[],[f1969,f30897]) ).

fof(f30897,plain,
    ( spl0_1134
  <=> ! [X2,X0,X17] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f1969,plain,
    ! [X2,X0,X17] :
      ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    inference(forward_demodulation,[],[f1532,f1837]) ).

fof(f1532,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).

fof(f30895,plain,
    spl0_1133,
    inference(avatar_split_clause,[],[f1968,f30893]) ).

fof(f30893,plain,
    ( spl0_1133
  <=> ! [X2,X0,X17] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f1968,plain,
    ! [X2,X0,X17] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    inference(forward_demodulation,[],[f1576,f1837]) ).

fof(f1576,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17))),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).

fof(f30891,plain,
    spl0_1132,
    inference(avatar_split_clause,[],[f1287,f30889]) ).

fof(f30889,plain,
    ( spl0_1132
  <=> ! [X31,X21,X29,X0,X19,X4,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,hAPP(hAPP(X29,X19),X21)),X4) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f1287,axiom,
    ! [X31,X21,X29,X0,X19,X4,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,hAPP(hAPP(X29,X19),X21)),X4) = hAPP(hAPP(X29,X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).

fof(f30887,plain,
    spl0_1131,
    inference(avatar_split_clause,[],[f873,f30885]) ).

fof(f30885,plain,
    ( spl0_1131
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f873,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

fof(f30883,plain,
    spl0_1130,
    inference(avatar_split_clause,[],[f826,f30881]) ).

fof(f30881,plain,
    ( spl0_1130
  <=> ! [X19,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X5,X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f826,axiom,
    ! [X2,X0,X19,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X5,X0),X19,X0)
      | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).

fof(f30879,plain,
    spl0_1129,
    inference(avatar_split_clause,[],[f599,f30877]) ).

fof(f30877,plain,
    ( spl0_1129
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f599,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

fof(f30875,plain,
    spl0_1128,
    inference(avatar_split_clause,[],[f598,f30873]) ).

fof(f30873,plain,
    ( spl0_1128
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f598,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

fof(f30871,plain,
    spl0_1127,
    inference(avatar_split_clause,[],[f283,f30869]) ).

fof(f30869,plain,
    ( spl0_1127
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f283,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

fof(f30867,plain,
    spl0_1126,
    inference(avatar_split_clause,[],[f60,f30865]) ).

fof(f30865,plain,
    ( spl0_1126
  <=> ! [X17,X19,X0,X25] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X19,X0),c_HOL_Oabs__class_Oabs(X25,X0),X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f60,axiom,
    ! [X0,X19,X17,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X19,X0),c_HOL_Oabs__class_Oabs(X25,X0),X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__even_0) ).

fof(f29472,plain,
    spl0_1125,
    inference(avatar_split_clause,[],[f1880,f29470]) ).

fof(f29470,plain,
    ( spl0_1125
  <=> ! [X0,X17] :
        ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f1880,plain,
    ! [X0,X17] :
      ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
      | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
    inference(forward_demodulation,[],[f1533,f1837]) ).

fof(f1533,axiom,
    ! [X0,X17] :
      ( ~ 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)),X17))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).

fof(f29468,plain,
    spl0_1124,
    inference(avatar_split_clause,[],[f1683,f29466]) ).

fof(f29466,plain,
    ( spl0_1124
  <=> ! [X44,X19,X0,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X19,X25,X0)),X44) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X44),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f1683,axiom,
    ! [X0,X19,X44,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ominus__class_Ominus(X19,X25,X0)),X44) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X44),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).

fof(f29464,plain,
    spl0_1123,
    inference(avatar_split_clause,[],[f1678,f29462]) ).

fof(f29462,plain,
    ( spl0_1123
  <=> ! [X19,X0,X25,X45] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),c_HOL_Ominus__class_Ominus(X19,X25,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X25),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f1678,axiom,
    ! [X0,X19,X45,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),c_HOL_Ominus__class_Ominus(X19,X25,X0)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X25),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).

fof(f29460,plain,
    spl0_1122,
    inference(avatar_split_clause,[],[f1392,f29458]) ).

fof(f29458,plain,
    ( spl0_1122
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ 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),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f1392,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ 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),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

fof(f29456,plain,
    spl0_1121,
    inference(avatar_split_clause,[],[f1127,f29454]) ).

fof(f29454,plain,
    ( spl0_1121
  <=> ! [X0,X3,X2,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f1127,axiom,
    ! [X2,X3,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

fof(f29452,plain,
    spl0_1120,
    inference(avatar_split_clause,[],[f1126,f29450]) ).

fof(f29450,plain,
    ( spl0_1120
  <=> ! [X0,X3,X2,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f1126,axiom,
    ! [X2,X3,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

fof(f29188,plain,
    ( spl0_1119
    | ~ spl0_848
    | ~ spl0_1118 ),
    inference(avatar_split_clause,[],[f29184,f29181,f17177,f29186]) ).

fof(f29186,plain,
    ( spl0_1119
  <=> ! [X18,X21] :
        ( v_i____ = X18
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f29181,plain,
    ( spl0_1118
  <=> ! [X18,X21] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f29184,plain,
    ( ! [X21,X18] :
        ( v_i____ = X18
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_848
    | ~ spl0_1118 ),
    inference(forward_demodulation,[],[f29182,f17179]) ).

fof(f29182,plain,
    ( ! [X21,X18] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_1118 ),
    inference(avatar_component_clause,[],[f29181]) ).

fof(f29183,plain,
    spl0_1118,
    inference(avatar_split_clause,[],[f993,f29181]) ).

fof(f993,axiom,
    ! [X21,X18] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__if_1) ).

fof(f29179,plain,
    spl0_1117,
    inference(avatar_split_clause,[],[f856,f29177]) ).

fof(f29177,plain,
    ( spl0_1117
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Divides_Odiv__class_Omod(X2,X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f856,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_Divides_Odiv__class_Omod(X2,X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

fof(f29175,plain,
    spl0_1116,
    inference(avatar_split_clause,[],[f855,f29173]) ).

fof(f29173,plain,
    ( spl0_1116
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X3,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f855,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X3,X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

fof(f29171,plain,
    spl0_1115,
    inference(avatar_split_clause,[],[f815,f29169]) ).

fof(f29169,plain,
    ( spl0_1115
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f815,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

fof(f29167,plain,
    ( ~ spl0_1113
    | spl0_1114
    | ~ spl0_259
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17273,f17177,f3344,f29164,f29160]) ).

fof(f29160,plain,
    ( spl0_1113
  <=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f3344,plain,
    ( spl0_259
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f17273,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(v_i____,tc_nat),v_i____,tc_nat)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat)
    | ~ spl0_259
    | ~ spl0_848 ),
    inference(superposition,[],[f3345,f17179]) ).

fof(f3345,plain,
    ( ! [X0] :
        ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
    | ~ spl0_259 ),
    inference(avatar_component_clause,[],[f3344]) ).

fof(f29158,plain,
    spl0_1112,
    inference(avatar_split_clause,[],[f814,f29156]) ).

fof(f29156,plain,
    ( spl0_1112
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f814,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

fof(f29154,plain,
    spl0_1111,
    inference(avatar_split_clause,[],[f794,f29152]) ).

fof(f29152,plain,
    ( spl0_1111
  <=> ! [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_1111])]) ).

fof(f794,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(f29150,plain,
    spl0_1110,
    inference(avatar_split_clause,[],[f705,f29148]) ).

fof(f29148,plain,
    ( spl0_1110
  <=> ! [X18,X0,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f705,axiom,
    ! [X2,X0,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(f29146,plain,
    spl0_1109,
    inference(avatar_split_clause,[],[f704,f29144]) ).

fof(f29144,plain,
    ( spl0_1109
  <=> ! [X18,X0,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X18)),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f704,axiom,
    ! [X2,X0,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X18)),X18) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(f28936,plain,
    ( spl0_1108
    | ~ spl0_848
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28932,f28929,f17177,f28934]) ).

fof(f28934,plain,
    ( spl0_1108
  <=> ! [X18,X17] :
        ( v_i____ = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f28929,plain,
    ( spl0_1107
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f28932,plain,
    ( ! [X18,X17] :
        ( v_i____ = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) )
    | ~ spl0_848
    | ~ spl0_1107 ),
    inference(forward_demodulation,[],[f28930,f17179]) ).

fof(f28930,plain,
    ( ! [X18,X17] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_1107 ),
    inference(avatar_component_clause,[],[f28929]) ).

fof(f28931,plain,
    spl0_1107,
    inference(avatar_split_clause,[],[f506,f28929]) ).

fof(f506,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__if_1) ).

fof(f28927,plain,
    spl0_1106,
    inference(avatar_split_clause,[],[f434,f28925]) ).

fof(f28925,plain,
    ( spl0_1106
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f434,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

fof(f28923,plain,
    spl0_1105,
    inference(avatar_split_clause,[],[f433,f28921]) ).

fof(f28921,plain,
    ( spl0_1105
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f433,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

fof(f28919,plain,
    spl0_1104,
    inference(avatar_split_clause,[],[f358,f28917]) ).

fof(f28917,plain,
    ( spl0_1104
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_lessequals(X25,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f358,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_lessequals(X25,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

fof(f28915,plain,
    ( spl0_1103
    | ~ spl0_290
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17242,f17177,f3472,f28913]) ).

fof(f3472,plain,
    ( spl0_290
  <=> ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f17242,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),v_i____)
    | ~ spl0_290
    | ~ spl0_848 ),
    inference(superposition,[],[f3473,f17179]) ).

fof(f3473,plain,
    ( ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f3472]) ).

fof(f28911,plain,
    spl0_1102,
    inference(avatar_split_clause,[],[f357,f28909]) ).

fof(f28909,plain,
    ( spl0_1102
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_lessequals(X25,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X19),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f357,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_lessequals(X25,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X19),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

fof(f28907,plain,
    spl0_1101,
    inference(avatar_split_clause,[],[f347,f28905]) ).

fof(f28905,plain,
    ( spl0_1101
  <=> ! [X31,X29,X0,X19,X27,X25,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X19),hAPP(hAPP(X31,X25),X27)) = hAPP(hAPP(X31,hAPP(hAPP(X31,X19),X25)),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f347,axiom,
    ! [X31,X29,X0,X19,X27,X25,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X19),hAPP(hAPP(X31,X25),X27)) = hAPP(hAPP(X31,hAPP(hAPP(X31,X19),X25)),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).

fof(f28903,plain,
    spl0_1100,
    inference(avatar_split_clause,[],[f343,f28901]) ).

fof(f28901,plain,
    ( spl0_1100
  <=> ! [X29,X31,X3,X0,X2,X1,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X3)),X1) = hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X1)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f343,axiom,
    ! [X31,X2,X3,X29,X0,X1,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X3)),X1) = hAPP(hAPP(X31,hAPP(hAPP(X31,X2),X1)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).

fof(f28899,plain,
    spl0_1099,
    inference(avatar_split_clause,[],[f342,f28897]) ).

fof(f28897,plain,
    ( spl0_1099
  <=> ! [X29,X31,X2,X0,X1,X26,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X2),hAPP(hAPP(X31,X1),X26)) = hAPP(hAPP(X31,X1),hAPP(hAPP(X31,X2),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f342,axiom,
    ! [X31,X2,X29,X0,X1,X26,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X2),hAPP(hAPP(X31,X1),X26)) = hAPP(hAPP(X31,X1),hAPP(hAPP(X31,X2),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).

fof(f28895,plain,
    spl0_1098,
    inference(avatar_split_clause,[],[f339,f28893]) ).

fof(f28893,plain,
    ( spl0_1098
  <=> ! [X31,X38,X29,X0,X37,X35,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X35),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,X37),hAPP(hAPP(X32,X35),X38)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f339,axiom,
    ! [X31,X38,X29,X0,X37,X35,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X35),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,X37),hAPP(hAPP(X32,X35),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).

fof(f28891,plain,
    spl0_1097,
    inference(avatar_split_clause,[],[f338,f28889]) ).

fof(f28889,plain,
    ( spl0_1097
  <=> ! [X31,X38,X29,X0,X37,X35,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X35),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),X38) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f338,axiom,
    ! [X31,X38,X29,X0,X37,X35,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X35),hAPP(hAPP(X32,X37),X38)) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).

fof(f28887,plain,
    spl0_1096,
    inference(avatar_split_clause,[],[f336,f28885]) ).

fof(f28885,plain,
    ( spl0_1096
  <=> ! [X31,X29,X0,X36,X37,X35,X32,X30,X33] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X36)),X37) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f336,axiom,
    ! [X31,X29,X0,X36,X37,X35,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X36)),X37) = hAPP(hAPP(X32,hAPP(hAPP(X32,X35),X37)),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).

fof(f28883,plain,
    spl0_1095,
    inference(avatar_split_clause,[],[f323,f28881]) ).

fof(f28881,plain,
    ( spl0_1095
  <=> ! [X2,X31,X33,X0,X18,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X30)),X18) = hAPP(hAPP(X31,X18),hAPP(hAPP(X32,X2),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f323,axiom,
    ! [X31,X2,X29,X0,X18,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X30)),X18) = hAPP(hAPP(X31,X18),hAPP(hAPP(X32,X2),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).

fof(f28879,plain,
    spl0_1094,
    inference(avatar_split_clause,[],[f322,f28877]) ).

fof(f28877,plain,
    ( spl0_1094
  <=> ! [X2,X31,X33,X0,X18,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,hAPP(hAPP(X32,X2),X18)),X18) = hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X30)),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f322,axiom,
    ! [X31,X2,X29,X0,X18,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,hAPP(hAPP(X32,X2),X18)),X18) = hAPP(hAPP(X32,hAPP(hAPP(X31,X2),X30)),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).

fof(f28875,plain,
    spl0_1093,
    inference(avatar_split_clause,[],[f165,f28873]) ).

fof(f28873,plain,
    ( spl0_1093
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),c_HOL_Oone__class_Oone(X0)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f165,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),c_HOL_Oone__class_Oone(X0)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).

fof(f28871,plain,
    ( spl0_1092
    | ~ spl0_289
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17241,f17177,f3468,f28869]) ).

fof(f3468,plain,
    ( spl0_289
  <=> ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f17241,plain,
    ( ! [X0] : v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i____),X0)
    | ~ spl0_289
    | ~ spl0_848 ),
    inference(superposition,[],[f3469,f17179]) ).

fof(f3469,plain,
    ( ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17)
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f3468]) ).

fof(f28867,plain,
    spl0_1091,
    inference(avatar_split_clause,[],[f164,f28865]) ).

fof(f28865,plain,
    ( spl0_1091
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2),X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),c_HOL_Oone__class_Oone(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f164,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2),X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),c_HOL_Oone__class_Oone(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).

fof(f28863,plain,
    spl0_1090,
    inference(avatar_split_clause,[],[f86,f28861]) ).

fof(f28861,plain,
    ( spl0_1090
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(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))),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f86,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(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))),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

fof(f28828,plain,
    ( spl0_1089
    | ~ spl0_216
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17237,f17177,f3079,f28826]) ).

fof(f3079,plain,
    ( spl0_216
  <=> ! [X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f17237,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),X0) = X0
    | ~ spl0_216
    | ~ spl0_848 ),
    inference(superposition,[],[f3080,f17179]) ).

fof(f3080,plain,
    ( ! [X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17) = X17
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f3079]) ).

fof(f27913,plain,
    ( spl0_1088
    | ~ spl0_215
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17236,f17177,f3075,f27911]) ).

fof(f17236,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),v_i____) = X0
    | ~ spl0_215
    | ~ spl0_848 ),
    inference(superposition,[],[f3076,f17179]) ).

fof(f26731,plain,
    ( spl0_697
    | ~ spl0_316
    | ~ spl0_658 ),
    inference(avatar_split_clause,[],[f10595,f9569,f3971,f10688]) ).

fof(f10688,plain,
    ( spl0_697
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f10595,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_316
    | ~ spl0_658 ),
    inference(resolution,[],[f9571,f3972]) ).

fof(f25953,plain,
    spl0_1087,
    inference(avatar_split_clause,[],[f1955,f25951]) ).

fof(f1955,plain,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1452,f1837]) ).

fof(f1452,axiom,
    ! [X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__even__mod__4__div__2_0) ).

fof(f25949,plain,
    spl0_1086,
    inference(avatar_split_clause,[],[f1663,f25947]) ).

fof(f25947,plain,
    ( spl0_1086
  <=> ! [X4,X19,X0,X21] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X21)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f1663,axiom,
    ! [X21,X0,X19,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),X19),X21)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X21),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

fof(f25945,plain,
    spl0_1085,
    inference(avatar_split_clause,[],[f1629,f25943]) ).

fof(f25943,plain,
    ( spl0_1085
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f1629,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f25941,plain,
    spl0_1084,
    inference(avatar_split_clause,[],[f1628,f25939]) ).

fof(f25939,plain,
    ( spl0_1084
  <=> ! [X37,X0,X36,X35] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X36)),X37) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X37)),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f1628,axiom,
    ! [X0,X36,X37,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X36)),X37) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X37)),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f25937,plain,
    spl0_1083,
    inference(avatar_split_clause,[],[f1625,f25935]) ).

fof(f25935,plain,
    ( spl0_1083
  <=> ! [X38,X0,X35,X37] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),X38)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X38)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f1625,axiom,
    ! [X38,X0,X37,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),X38)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X37),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X35),X38)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f25933,plain,
    spl0_1082,
    inference(avatar_split_clause,[],[f1623,f25931]) ).

fof(f25931,plain,
    ( spl0_1082
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f1623,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X27)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X25)),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

fof(f25929,plain,
    spl0_1081,
    inference(avatar_split_clause,[],[f1601,f25927]) ).

fof(f25927,plain,
    ( spl0_1081
  <=> ! [X2,X0,X17] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f1601,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

fof(f25925,plain,
    spl0_1080,
    inference(avatar_split_clause,[],[f1589,f25923]) ).

fof(f25923,plain,
    ( spl0_1080
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f1589,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).

fof(f25921,plain,
    ( spl0_1079
    | ~ spl0_317
    | ~ spl0_848
    | ~ spl0_949 ),
    inference(avatar_split_clause,[],[f21650,f20243,f17177,f3975,f25919]) ).

fof(f25919,plain,
    ( spl0_1079
  <=> ! [X0] :
        ( v_i____ != X0
        | c_lessequals(X0,v_i____,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f3975,plain,
    ( spl0_317
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f21650,plain,
    ( ! [X0] :
        ( v_i____ != X0
        | c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_317
    | ~ spl0_848
    | ~ spl0_949 ),
    inference(forward_demodulation,[],[f21595,f17179]) ).

fof(f21595,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X0
        | c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_317
    | ~ spl0_949 ),
    inference(superposition,[],[f3976,f20244]) ).

fof(f3976,plain,
    ( ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)
        | c_lessequals(X18,X17,tc_nat) )
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f3975]) ).

fof(f25917,plain,
    spl0_1078,
    inference(avatar_split_clause,[],[f1497,f25915]) ).

fof(f25915,plain,
    ( spl0_1078
  <=> ! [X19,X0,X3,X25] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X25),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f1497,axiom,
    ! [X3,X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X25),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

fof(f25913,plain,
    spl0_1077,
    inference(avatar_split_clause,[],[f1494,f25911]) ).

fof(f25911,plain,
    ( spl0_1077
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X18,X17,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),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f1494,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X18,X17,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),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

fof(f25909,plain,
    spl0_1076,
    inference(avatar_split_clause,[],[f1271,f25907]) ).

fof(f25907,plain,
    ( spl0_1076
  <=> ! [X18,X24,X23] :
        ( ~ c_lessequals(X23,X24,tc_nat)
        | c_HOL_Ominus__class_Ominus(X18,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),hAPP(c_Suc,X24),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f1271,axiom,
    ! [X18,X24,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(X18,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),hAPP(c_Suc,X24),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

fof(f25905,plain,
    spl0_1075,
    inference(avatar_split_clause,[],[f1132,f25903]) ).

fof(f25903,plain,
    ( spl0_1075
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f1132,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

fof(f25901,plain,
    spl0_1074,
    inference(avatar_split_clause,[],[f1131,f25899]) ).

fof(f25899,plain,
    ( spl0_1074
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X3,X2,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f1131,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X3,X2,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

fof(f25897,plain,
    spl0_1073,
    inference(avatar_split_clause,[],[f1130,f25895]) ).

fof(f25895,plain,
    ( spl0_1073
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f1130,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

fof(f25893,plain,
    spl0_1072,
    inference(avatar_split_clause,[],[f1129,f25891]) ).

fof(f25891,plain,
    ( spl0_1072
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X3,X2,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f1129,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X3,X2,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

fof(f25889,plain,
    spl0_1071,
    inference(avatar_split_clause,[],[f1117,f25887]) ).

fof(f25887,plain,
    ( spl0_1071
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f1117,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

fof(f25885,plain,
    spl0_1070,
    inference(avatar_split_clause,[],[f1115,f25883]) ).

fof(f25883,plain,
    ( spl0_1070
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f1115,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

fof(f25881,plain,
    spl0_1069,
    inference(avatar_split_clause,[],[f1114,f25879]) ).

fof(f25879,plain,
    ( spl0_1069
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f1114,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,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),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

fof(f25835,plain,
    spl0_1068,
    inference(avatar_split_clause,[],[f1113,f25833]) ).

fof(f25833,plain,
    ( spl0_1068
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f1113,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

fof(f25831,plain,
    spl0_1067,
    inference(avatar_split_clause,[],[f1111,f25829]) ).

fof(f25829,plain,
    ( spl0_1067
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f1111,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

fof(f25827,plain,
    spl0_1066,
    inference(avatar_split_clause,[],[f1110,f25825]) ).

fof(f25825,plain,
    ( spl0_1066
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f1110,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

fof(f25823,plain,
    spl0_1065,
    inference(avatar_split_clause,[],[f1107,f25821]) ).

fof(f25821,plain,
    ( spl0_1065
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f1107,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

fof(f25819,plain,
    spl0_1064,
    inference(avatar_split_clause,[],[f1106,f25817]) ).

fof(f25817,plain,
    ( spl0_1064
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f1106,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

fof(f25815,plain,
    spl0_1063,
    inference(avatar_split_clause,[],[f1105,f25813]) ).

fof(f25813,plain,
    ( spl0_1063
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f1105,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

fof(f25811,plain,
    spl0_1062,
    inference(avatar_split_clause,[],[f1057,f25809]) ).

fof(f25809,plain,
    ( spl0_1062
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f1057,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

fof(f25807,plain,
    spl0_1061,
    inference(avatar_split_clause,[],[f948,f25805]) ).

fof(f25805,plain,
    ( spl0_1061
  <=> ! [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_1061])]) ).

fof(f948,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(f25803,plain,
    spl0_1060,
    inference(avatar_split_clause,[],[f813,f25801]) ).

fof(f25801,plain,
    ( spl0_1060
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f813,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

fof(f25799,plain,
    spl0_1059,
    inference(avatar_split_clause,[],[f812,f25797]) ).

fof(f25797,plain,
    ( spl0_1059
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f812,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

fof(f25771,plain,
    spl0_1058,
    inference(avatar_split_clause,[],[f811,f25769]) ).

fof(f25769,plain,
    ( spl0_1058
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f811,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

fof(f25767,plain,
    spl0_1057,
    inference(avatar_split_clause,[],[f810,f25765]) ).

fof(f25765,plain,
    ( spl0_1057
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f810,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

fof(f25763,plain,
    spl0_1056,
    inference(avatar_split_clause,[],[f809,f25761]) ).

fof(f25761,plain,
    ( spl0_1056
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f809,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

fof(f25759,plain,
    spl0_1055,
    inference(avatar_split_clause,[],[f808,f25757]) ).

fof(f25757,plain,
    ( spl0_1055
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f808,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

fof(f25755,plain,
    spl0_1054,
    inference(avatar_split_clause,[],[f806,f25753]) ).

fof(f25753,plain,
    ( spl0_1054
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f806,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

fof(f25751,plain,
    spl0_1053,
    inference(avatar_split_clause,[],[f805,f25749]) ).

fof(f25749,plain,
    ( spl0_1053
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f805,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

fof(f25747,plain,
    spl0_1052,
    inference(avatar_split_clause,[],[f804,f25745]) ).

fof(f25745,plain,
    ( spl0_1052
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f804,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

fof(f25743,plain,
    spl0_1051,
    inference(avatar_split_clause,[],[f803,f25741]) ).

fof(f25741,plain,
    ( spl0_1051
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f803,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

fof(f25739,plain,
    spl0_1050,
    inference(avatar_split_clause,[],[f782,f25737]) ).

fof(f25737,plain,
    ( spl0_1050
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f782,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).

fof(f25735,plain,
    spl0_1049,
    inference(avatar_split_clause,[],[f494,f25733]) ).

fof(f25733,plain,
    ( spl0_1049
  <=> ! [X17,X0,X2,X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X17,X39,tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f494,axiom,
    ! [X2,X39,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X17,X39,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X39),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).

fof(f25731,plain,
    ( spl0_1048
    | ~ spl0_166
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f25670,f24764,f2821,f25729]) ).

fof(f2821,plain,
    ( spl0_166
  <=> ! [X18,X17] : c_lessequals(c_Divides_Odiv__class_Odiv(X18,X17,tc_nat),X18,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f25670,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Odiv(v_i____,X0,tc_nat)
    | ~ spl0_166
    | ~ spl0_1024 ),
    inference(resolution,[],[f24765,f2822]) ).

fof(f2822,plain,
    ( ! [X18,X17] : c_lessequals(c_Divides_Odiv__class_Odiv(X18,X17,tc_nat),X18,tc_nat)
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f2821]) ).

fof(f25727,plain,
    spl0_1047,
    inference(avatar_split_clause,[],[f417,f25725]) ).

fof(f25725,plain,
    ( spl0_1047
  <=> ! [X17,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f417,axiom,
    ! [X2,X3,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

fof(f25723,plain,
    spl0_1046,
    inference(avatar_split_clause,[],[f395,f25721]) ).

fof(f25721,plain,
    ( spl0_1046
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f395,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(f25719,plain,
    spl0_1045,
    inference(avatar_split_clause,[],[f394,f25717]) ).

fof(f25717,plain,
    ( spl0_1045
  <=> ! [X26,X0,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f394,axiom,
    ! [X2,X0,X1,X26] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f25715,plain,
    spl0_1044,
    inference(avatar_split_clause,[],[f293,f25713]) ).

fof(f25713,plain,
    ( spl0_1044
  <=> ! [X0,X3,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),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f293,axiom,
    ! [X2,X3,X0,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),X2),X3)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f25711,plain,
    spl0_1043,
    inference(avatar_split_clause,[],[f291,f25709]) ).

fof(f25709,plain,
    ( spl0_1043
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f291,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f25707,plain,
    spl0_1042,
    inference(avatar_split_clause,[],[f288,f25705]) ).

fof(f25705,plain,
    ( spl0_1042
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f288,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

fof(f25703,plain,
    spl0_1041,
    inference(avatar_split_clause,[],[f286,f25701]) ).

fof(f25701,plain,
    ( spl0_1041
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f286,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f25699,plain,
    spl0_1040,
    inference(avatar_split_clause,[],[f285,f25697]) ).

fof(f25697,plain,
    ( spl0_1040
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f285,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f25695,plain,
    spl0_1039,
    inference(avatar_split_clause,[],[f265,f25693]) ).

fof(f25693,plain,
    ( spl0_1039
  <=> ! [X2,X0,X17] :
        ( ~ 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),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f265,axiom,
    ! [X2,X0,X17] :
      ( ~ 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),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).

fof(f25691,plain,
    spl0_1038,
    inference(avatar_split_clause,[],[f214,f25689]) ).

fof(f25689,plain,
    ( spl0_1038
  <=> ! [X25,X0,X19] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f214,axiom,
    ! [X0,X19,X25] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

fof(f25665,plain,
    spl0_1037,
    inference(avatar_split_clause,[],[f213,f25663]) ).

fof(f25663,plain,
    ( spl0_1037
  <=> ! [X25,X0,X19] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f213,axiom,
    ! [X0,X19,X25] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X25,X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

fof(f25661,plain,
    spl0_1036,
    inference(avatar_split_clause,[],[f175,f25659]) ).

fof(f25659,plain,
    ( spl0_1036
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Divides_Odiv__class_Odiv(X2,X3,X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f175,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_Divides_Odiv__class_Odiv(X2,X3,X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).

fof(f25657,plain,
    spl0_1035,
    inference(avatar_split_clause,[],[f174,f25655]) ).

fof(f25655,plain,
    ( spl0_1035
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Divides_Odiv__class_Odiv(X2,X3,X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f174,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_Divides_Odiv__class_Odiv(X2,X3,X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).

fof(f25653,plain,
    spl0_1034,
    inference(avatar_split_clause,[],[f152,f25651]) ).

fof(f25651,plain,
    ( spl0_1034
  <=> ! [X19,X0,X3,X25] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X19,X25,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X25),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f152,axiom,
    ! [X3,X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X19,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X3),X25),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

fof(f25649,plain,
    spl0_1033,
    inference(avatar_split_clause,[],[f150,f25647]) ).

fof(f25647,plain,
    ( spl0_1033
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f150,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).

fof(f25645,plain,
    spl0_1032,
    inference(avatar_split_clause,[],[f101,f25643]) ).

fof(f25643,plain,
    ( spl0_1032
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f101,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

fof(f25641,plain,
    spl0_1031,
    inference(avatar_split_clause,[],[f100,f25639]) ).

fof(f25639,plain,
    ( spl0_1031
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f100,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

fof(f25637,plain,
    spl0_1030,
    inference(avatar_split_clause,[],[f97,f25635]) ).

fof(f25635,plain,
    ( spl0_1030
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(X3,X2,X0)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f97,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(X3,X2,X0)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

fof(f25633,plain,
    spl0_1029,
    inference(avatar_split_clause,[],[f96,f25631]) ).

fof(f25631,plain,
    ( spl0_1029
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(X3,X2,X0)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f96,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(X3,X2,X0)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

fof(f25629,plain,
    spl0_1028,
    inference(avatar_split_clause,[],[f95,f25627]) ).

fof(f25627,plain,
    ( spl0_1028
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Omult__mono(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f95,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Omult__mono(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

fof(f25583,plain,
    spl0_1027,
    inference(avatar_split_clause,[],[f94,f25581]) ).

fof(f25581,plain,
    ( spl0_1027
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Omult__mono(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f94,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Omult__mono(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

fof(f25579,plain,
    spl0_1026,
    inference(avatar_split_clause,[],[f1,f25577]) ).

fof(f25577,plain,
    ( spl0_1026
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Omult__mono1(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Omult__mono1(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

fof(f25165,plain,
    ( spl0_1025
    | ~ spl0_240
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17238,f17177,f3176,f25163]) ).

fof(f3176,plain,
    ( spl0_240
  <=> ! [X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f17238,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | v_i____ = X0 )
    | ~ spl0_240
    | ~ spl0_848 ),
    inference(superposition,[],[f3177,f17179]) ).

fof(f3177,plain,
    ( ! [X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f3176]) ).

fof(f24766,plain,
    ( spl0_1024
    | ~ spl0_202
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17235,f17177,f3022,f24764]) ).

fof(f17235,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | v_i____ = X0 )
    | ~ spl0_202
    | ~ spl0_848 ),
    inference(superposition,[],[f3023,f17179]) ).

fof(f24573,plain,
    spl0_1023,
    inference(avatar_split_clause,[],[f1961,f24571]) ).

fof(f24571,plain,
    ( spl0_1023
  <=> ! [X2,X0,X23] :
        ( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X23)),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f1961,plain,
    ! [X2,X0,X23] :
      ( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X23)),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2 ),
    inference(forward_demodulation,[],[f1519,f1837]) ).

fof(f1519,axiom,
    ! [X2,X0,X23] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X23)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).

fof(f24569,plain,
    spl0_1022,
    inference(avatar_split_clause,[],[f1883,f24567]) ).

fof(f24567,plain,
    ( spl0_1022
  <=> ! [X0,X17] :
        ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
        | ~ class_Int_Onumber__ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f1883,plain,
    ! [X0,X17] :
      ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)))
      | ~ class_Int_Onumber__ring(X0) ),
    inference(forward_demodulation,[],[f1577,f1837]) ).

fof(f1577,axiom,
    ! [X0,X17] :
      ( ~ 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)),X17))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).

fof(f24565,plain,
    spl0_1021,
    inference(avatar_split_clause,[],[f1681,f24563]) ).

fof(f1681,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

fof(f24561,plain,
    ( spl0_1020
    | ~ spl0_184
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17232,f17177,f2916,f24559]) ).

fof(f17232,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(v_i____,X0,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) )
    | ~ spl0_184
    | ~ spl0_848 ),
    inference(superposition,[],[f2917,f17179]) ).

fof(f24557,plain,
    spl0_1019,
    inference(avatar_split_clause,[],[f1680,f24555]) ).

fof(f24555,plain,
    ( spl0_1019
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)),X23) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f1680,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)),X23) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

fof(f24553,plain,
    spl0_1018,
    inference(avatar_split_clause,[],[f1676,f24551]) ).

fof(f24551,plain,
    ( spl0_1018
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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),X2),X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f1676,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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),X2),X2)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).

fof(f24549,plain,
    spl0_1017,
    inference(avatar_split_clause,[],[f1616,f24547]) ).

fof(f24547,plain,
    ( spl0_1017
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f1616,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

fof(f24545,plain,
    spl0_1016,
    inference(avatar_split_clause,[],[f1615,f24543]) ).

fof(f24543,plain,
    ( spl0_1016
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f1615,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

fof(f24541,plain,
    spl0_1015,
    inference(avatar_split_clause,[],[f1493,f24539]) ).

fof(f24539,plain,
    ( spl0_1015
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f1493,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

fof(f24537,plain,
    spl0_1014,
    inference(avatar_split_clause,[],[f1410,f24535]) ).

fof(f24535,plain,
    ( spl0_1014
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f1410,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).

fof(f24533,plain,
    spl0_1013,
    inference(avatar_split_clause,[],[f1409,f24531]) ).

fof(f24531,plain,
    ( spl0_1013
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(X18,X17,tc_nat)),X23) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f1409,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(X18,X17,tc_nat)),X23) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).

fof(f24529,plain,
    spl0_1012,
    inference(avatar_split_clause,[],[f1093,f24527]) ).

fof(f24527,plain,
    ( spl0_1012
  <=> ! [X31,X33,X19,X0,X4,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,X19),hAPP(c_Suc,X4)) = hAPP(hAPP(X32,X19),hAPP(hAPP(X29,X19),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f1093,axiom,
    ! [X31,X29,X0,X19,X4,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),hAPP(c_Suc,X4)) = hAPP(hAPP(X32,X19),hAPP(hAPP(X29,X19),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).

fof(f24525,plain,
    spl0_1011,
    inference(avatar_split_clause,[],[f1092,f24523]) ).

fof(f24523,plain,
    ( spl0_1011
  <=> ! [X31,X33,X19,X0,X4,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,X19),hAPP(c_Suc,X4)) = hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X4)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f1092,axiom,
    ! [X31,X29,X0,X19,X4,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),hAPP(c_Suc,X4)) = hAPP(hAPP(X32,hAPP(hAPP(X29,X19),X4)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).

fof(f24521,plain,
    spl0_1010,
    inference(avatar_split_clause,[],[f1007,f24519]) ).

fof(f24519,plain,
    ( spl0_1010
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f1007,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).

fof(f24500,plain,
    spl0_1009,
    inference(avatar_split_clause,[],[f997,f24498]) ).

fof(f24498,plain,
    ( spl0_1009
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),X3),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f997,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),X3),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).

fof(f24496,plain,
    spl0_1008,
    inference(avatar_split_clause,[],[f935,f24494]) ).

fof(f24494,plain,
    ( spl0_1008
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X1,X26,X0)
        | ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0)
        | c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f935,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X1,X26,X0)
      | ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0)
      | c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

fof(f24492,plain,
    spl0_1007,
    inference(avatar_split_clause,[],[f714,f24490]) ).

fof(f24490,plain,
    ( spl0_1007
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X25,X0)),X19) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f714,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X25,X0)),X19) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).

fof(f24488,plain,
    spl0_1006,
    inference(avatar_split_clause,[],[f653,f24486]) ).

fof(f24486,plain,
    ( spl0_1006
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f653,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f24484,plain,
    spl0_1005,
    inference(avatar_split_clause,[],[f636,f24482]) ).

fof(f24482,plain,
    ( spl0_1005
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f636,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X26,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

fof(f24480,plain,
    spl0_1004,
    inference(avatar_split_clause,[],[f635,f24478]) ).

fof(f24478,plain,
    ( spl0_1004
  <=> ! [X2,X0,X3,X1,X26] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_lessequals(X1,X26,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f635,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_lessequals(X1,X26,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

fof(f24476,plain,
    spl0_1003,
    inference(avatar_split_clause,[],[f628,f24474]) ).

fof(f24474,plain,
    ( spl0_1003
  <=> ! [X44,X19,X0,X25] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25),X44,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X44,X0)),c_HOL_Oinverse__class_Odivide(X25,X44,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f628,axiom,
    ! [X0,X19,X44,X25] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25),X44,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X19,X44,X0)),c_HOL_Oinverse__class_Odivide(X25,X44,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

fof(f24472,plain,
    spl0_1002,
    inference(avatar_split_clause,[],[f627,f24470]) ).

fof(f24470,plain,
    ( spl0_1002
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X2,X1,X0)),c_HOL_Oinverse__class_Odivide(X3,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f627,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oinverse__class_Odivide(X2,X1,X0)),c_HOL_Oinverse__class_Odivide(X3,X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

fof(f24468,plain,
    spl0_1001,
    inference(avatar_split_clause,[],[f575,f24466]) ).

fof(f24466,plain,
    ( spl0_1001
  <=> ! [X42,X0,X3,X2] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X3,X0) != c_Divides_Odiv__class_Omod(X42,X3,X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X42,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f575,axiom,
    ! [X2,X3,X0,X42] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X3,X0) != c_Divides_Odiv__class_Omod(X42,X3,X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X42,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).

fof(f24464,plain,
    spl0_1000,
    inference(avatar_split_clause,[],[f516,f24462]) ).

fof(f24462,plain,
    ( spl0_1000
  <=> ! [X1,X0,X3,X2,X26] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(X1,X26,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f516,axiom,
    ! [X2,X3,X0,X1,X26] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(X1,X26,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X26),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

fof(f24366,plain,
    spl0_999,
    inference(avatar_split_clause,[],[f409,f24364]) ).

fof(f24364,plain,
    ( spl0_999
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f409,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).

fof(f24326,plain,
    ( spl0_998
    | ~ spl0_848
    | ~ spl0_997 ),
    inference(avatar_split_clause,[],[f24322,f24319,f17177,f24324]) ).

fof(f24324,plain,
    ( spl0_998
  <=> ! [X0,X17,X19] :
        ( v_i____ = X17
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f24319,plain,
    ( spl0_997
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f24322,plain,
    ( ! [X0,X19,X17] :
        ( v_i____ = X17
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) )
    | ~ spl0_848
    | ~ spl0_997 ),
    inference(forward_demodulation,[],[f24320,f17179]) ).

fof(f24320,plain,
    ( ! [X0,X19,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_997 ),
    inference(avatar_component_clause,[],[f24319]) ).

fof(f24321,plain,
    spl0_997,
    inference(avatar_split_clause,[],[f261,f24319]) ).

fof(f261,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).

fof(f24317,plain,
    spl0_996,
    inference(avatar_split_clause,[],[f122,f24315]) ).

fof(f24315,plain,
    ( spl0_996
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),X3),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f122,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X1,X0)),X3),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).

fof(f24240,plain,
    ( spl0_995
    | ~ spl0_848
    | ~ spl0_994 ),
    inference(avatar_split_clause,[],[f24236,f24233,f17177,f24238]) ).

fof(f24238,plain,
    ( spl0_995
  <=> ! [X0,X17,X19] :
        ( v_i____ = X17
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f24233,plain,
    ( spl0_994
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f24236,plain,
    ( ! [X0,X19,X17] :
        ( v_i____ = X17
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_848
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f24234,f17179]) ).

fof(f24234,plain,
    ( ! [X0,X19,X17] :
        ( c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_994 ),
    inference(avatar_component_clause,[],[f24233]) ).

fof(f24235,plain,
    spl0_994,
    inference(avatar_split_clause,[],[f104,f24233]) ).

fof(f104,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).

fof(f23998,plain,
    ( spl0_993
    | ~ spl0_709
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f21779,f20692,f10755,f23996]) ).

fof(f21779,plain,
    ( ! [X0] : v_i____ = c_Divides_Odiv__class_Omod(v_i____,X0,tc_nat)
    | ~ spl0_709
    | ~ spl0_950 ),
    inference(superposition,[],[f20693,f10756]) ).

fof(f23098,plain,
    ( spl0_992
    | ~ spl0_177
    | ~ spl0_456
    | ~ spl0_848
    | ~ spl0_887 ),
    inference(avatar_split_clause,[],[f18045,f17934,f17177,f5394,f2867,f23096]) ).

fof(f18045,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat)
    | ~ spl0_177
    | ~ spl0_456
    | ~ spl0_848
    | ~ spl0_887 ),
    inference(forward_demodulation,[],[f18025,f17230]) ).

fof(f17230,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_i____,tc_nat) = X0
    | ~ spl0_177
    | ~ spl0_848 ),
    inference(superposition,[],[f2868,f17179]) ).

fof(f18025,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,v_i____,tc_nat),tc_nat)
    | ~ spl0_456
    | ~ spl0_887 ),
    inference(resolution,[],[f17935,f5395]) ).

fof(f21863,plain,
    spl0_991,
    inference(avatar_split_clause,[],[f1914,f21861]) ).

fof(f21861,plain,
    ( spl0_991
  <=> ! [X24,X18,X23] :
        ( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X18,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X24),X23,tc_nat),X18,tc_nat)
        | ~ c_lessequals(X23,X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f1914,plain,
    ! [X18,X24,X23] :
      ( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X18,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X24),X23,tc_nat),X18,tc_nat)
      | ~ c_lessequals(X23,X24,tc_nat) ),
    inference(forward_demodulation,[],[f1272,f1436]) ).

fof(f1272,axiom,
    ! [X18,X24,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X18,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

fof(f21774,plain,
    spl0_990,
    inference(avatar_split_clause,[],[f1879,f21772]) ).

fof(f21772,plain,
    ( spl0_990
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f1879,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
    inference(forward_demodulation,[],[f1551,f1837]) ).

fof(f1551,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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_Ouminus__class_Ouminus(X2,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_power2__minus_0) ).

fof(f21770,plain,
    spl0_989,
    inference(avatar_split_clause,[],[f1872,f21768]) ).

fof(f21768,plain,
    ( spl0_989
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f1872,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1553,f1837]) ).

fof(f1553,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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_Oabs__class_Oabs(X2,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_power2__abs_0) ).

fof(f21766,plain,
    spl0_988,
    inference(avatar_split_clause,[],[f1871,f21764]) ).

fof(f21764,plain,
    ( spl0_988
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f1871,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1550,f1837]) ).

fof(f1550,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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_abs__power2_0) ).

fof(f21762,plain,
    spl0_987,
    inference(avatar_split_clause,[],[f1624,f21760]) ).

fof(f21760,plain,
    ( spl0_987
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f1624,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

fof(f21758,plain,
    spl0_986,
    inference(avatar_split_clause,[],[f1442,f21756]) ).

fof(f21756,plain,
    ( spl0_986
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X23,X18,tc_nat)
        | ~ c_lessequals(X23,X17,tc_nat)
        | c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f1442,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X23,X18,tc_nat)
      | ~ c_lessequals(X23,X17,tc_nat)
      | c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

fof(f21737,plain,
    ( spl0_985
    | ~ spl0_848
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f21733,f21730,f17177,f21735]) ).

fof(f21735,plain,
    ( spl0_985
  <=> ! [X22,X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X22,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f21730,plain,
    ( spl0_984
  <=> ! [X22,X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f21733,plain,
    ( ! [X18,X17,X22] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X22,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) )
    | ~ spl0_848
    | ~ spl0_984 ),
    inference(forward_demodulation,[],[f21731,f17179]) ).

fof(f21731,plain,
    ( ! [X18,X17,X22] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
    | ~ spl0_984 ),
    inference(avatar_component_clause,[],[f21730]) ).

fof(f21732,plain,
    spl0_984,
    inference(avatar_split_clause,[],[f1370,f21730]) ).

fof(f1370,axiom,
    ! [X18,X17,X22] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X18),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).

fof(f21664,plain,
    ( spl0_983
    | ~ spl0_848
    | ~ spl0_982 ),
    inference(avatar_split_clause,[],[f21583,f21580,f17177,f21662]) ).

fof(f21662,plain,
    ( spl0_983
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f21580,plain,
    ( spl0_982
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f21583,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) )
    | ~ spl0_848
    | ~ spl0_982 ),
    inference(forward_demodulation,[],[f21581,f17179]) ).

fof(f21581,plain,
    ( ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
    | ~ spl0_982 ),
    inference(avatar_component_clause,[],[f21580]) ).

fof(f21582,plain,
    spl0_982,
    inference(avatar_split_clause,[],[f1342,f21580]) ).

fof(f1342,axiom,
    ! [X18,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

fof(f21512,plain,
    ( spl0_981
    | ~ spl0_848
    | ~ spl0_980 ),
    inference(avatar_split_clause,[],[f21508,f21505,f17177,f21510]) ).

fof(f21510,plain,
    ( spl0_981
  <=> ! [X24,X22,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f21505,plain,
    ( spl0_980
  <=> ! [X22,X24,X23] :
        ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f21508,plain,
    ( ! [X24,X22,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X23),tc_nat) )
    | ~ spl0_848
    | ~ spl0_980 ),
    inference(forward_demodulation,[],[f21506,f17179]) ).

fof(f21506,plain,
    ( ! [X24,X22,X23] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X23),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat) )
    | ~ spl0_980 ),
    inference(avatar_component_clause,[],[f21505]) ).

fof(f21507,plain,
    spl0_980,
    inference(avatar_split_clause,[],[f1340,f21505]) ).

fof(f1340,axiom,
    ! [X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

fof(f21445,plain,
    ( spl0_979
    | ~ spl0_848
    | ~ spl0_978 ),
    inference(avatar_split_clause,[],[f21441,f21438,f17177,f21443]) ).

fof(f21443,plain,
    ( spl0_979
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | ~ c_lessequals(X17,X18,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f21438,plain,
    ( spl0_978
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f21441,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | ~ c_lessequals(X17,X18,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) )
    | ~ spl0_848
    | ~ spl0_978 ),
    inference(forward_demodulation,[],[f21439,f17179]) ).

fof(f21439,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_lessequals(X17,X18,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) )
    | ~ spl0_978 ),
    inference(avatar_component_clause,[],[f21438]) ).

fof(f21440,plain,
    spl0_978,
    inference(avatar_split_clause,[],[f1270,f21438]) ).

fof(f1270,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X17,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__div__geq_0) ).

fof(f21385,plain,
    ( spl0_977
    | ~ spl0_848
    | ~ spl0_976 ),
    inference(avatar_split_clause,[],[f21381,f21378,f17177,f21383]) ).

fof(f21383,plain,
    ( spl0_977
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f21378,plain,
    ( spl0_976
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f21381,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) )
    | ~ spl0_848
    | ~ spl0_976 ),
    inference(forward_demodulation,[],[f21379,f17179]) ).

fof(f21379,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat) )
    | ~ spl0_976 ),
    inference(avatar_component_clause,[],[f21378]) ).

fof(f21380,plain,
    spl0_976,
    inference(avatar_split_clause,[],[f1269,f21378]) ).

fof(f1269,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

fof(f21295,plain,
    ( spl0_975
    | ~ spl0_848
    | ~ spl0_974 ),
    inference(avatar_split_clause,[],[f21291,f21288,f17177,f21293]) ).

fof(f21293,plain,
    ( spl0_975
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f21288,plain,
    ( spl0_974
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f21291,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) )
    | ~ spl0_848
    | ~ spl0_974 ),
    inference(forward_demodulation,[],[f21289,f17179]) ).

fof(f21289,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_lessequals(X18,X17,tc_nat) )
    | ~ spl0_974 ),
    inference(avatar_component_clause,[],[f21288]) ).

fof(f21290,plain,
    spl0_974,
    inference(avatar_split_clause,[],[f1268,f21288]) ).

fof(f1268,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).

fof(f21286,plain,
    spl0_973,
    inference(avatar_split_clause,[],[f1255,f21284]) ).

fof(f21284,plain,
    ( spl0_973
  <=> ! [X18,X17,X23] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),X18)),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f1255,axiom,
    ! [X18,X17,X23] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),X18)),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).

fof(f21282,plain,
    spl0_972,
    inference(avatar_split_clause,[],[f1149,f21280]) ).

fof(f21280,plain,
    ( spl0_972
  <=> ! [X18,X0,X17,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X17 = X18
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

fof(f1149,axiom,
    ! [X2,X0,X18,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X17 = X18
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X18) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

fof(f21278,plain,
    spl0_971,
    inference(avatar_split_clause,[],[f1085,f21276]) ).

fof(f21276,plain,
    ( spl0_971
  <=> ! [X15,X17,X0,X14,X2] : hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(X15,X2),hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f1085,axiom,
    ! [X2,X0,X14,X17,X15] : hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(X15,X2),hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power_Opower_Opower__Suc_0) ).

fof(f21274,plain,
    spl0_970,
    inference(avatar_split_clause,[],[f1068,f21272]) ).

fof(f21272,plain,
    ( spl0_970
  <=> ! [X20,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),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(X20,X0))),c_Int_Onumber__class_Onumber__of(X20,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f1068,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),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(X20,X0))),c_Int_Onumber__class_Onumber__of(X20,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).

fof(f21270,plain,
    spl0_969,
    inference(avatar_split_clause,[],[f1063,f21268]) ).

fof(f21268,plain,
    ( spl0_969
  <=> ! [X20,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X20),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(X20,X0))),c_Int_Onumber__class_Onumber__of(X20,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f1063,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X20),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(X20,X0))),c_Int_Onumber__class_Onumber__of(X20,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).

fof(f21231,plain,
    ( spl0_968
    | ~ spl0_848
    | ~ spl0_967 ),
    inference(avatar_split_clause,[],[f21158,f21155,f17177,f21229]) ).

fof(f21229,plain,
    ( spl0_968
  <=> ! [X0,X17] :
        ( v_i____ = X17
        | ~ 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)
        | ~ 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)),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f21155,plain,
    ( spl0_967
  <=> ! [X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | 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)),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f21158,plain,
    ( ! [X0,X17] :
        ( v_i____ = X17
        | ~ 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)
        | ~ 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)),X17),X0) )
    | ~ spl0_848
    | ~ spl0_967 ),
    inference(forward_demodulation,[],[f21156,f17179]) ).

fof(f21156,plain,
    ( ! [X0,X17] :
        ( ~ 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)),X17),X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_967 ),
    inference(avatar_component_clause,[],[f21155]) ).

fof(f21157,plain,
    spl0_967,
    inference(avatar_split_clause,[],[f1059,f21155]) ).

fof(f1059,axiom,
    ! [X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | 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)),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).

fof(f21153,plain,
    spl0_966,
    inference(avatar_split_clause,[],[f1035,f21151]) ).

fof(f21151,plain,
    ( spl0_966
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X1,X0),c_Divides_Odiv__class_Omod(X3,X1,X0),X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f1035,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X1,X0),c_Divides_Odiv__class_Omod(X3,X1,X0),X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).

fof(f21149,plain,
    spl0_965,
    inference(avatar_split_clause,[],[f1009,f21147]) ).

fof(f21147,plain,
    ( spl0_965
  <=> ! [X19,X0,X27,X25] :
        ( ~ 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(X19,X25,X0)),X27) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f1009,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ 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(X19,X25,X0)),X27) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X27),X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

fof(f21145,plain,
    spl0_964,
    inference(avatar_split_clause,[],[f996,f21143]) ).

fof(f21143,plain,
    ( spl0_964
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | X2 = X3
        | c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f996,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | X2 = X3
      | c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

fof(f21078,plain,
    ( spl0_963
    | ~ spl0_848
    | ~ spl0_962 ),
    inference(avatar_split_clause,[],[f21074,f21071,f17177,f21076]) ).

fof(f21076,plain,
    ( spl0_963
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f21071,plain,
    ( spl0_962
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f21074,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) )
    | ~ spl0_848
    | ~ spl0_962 ),
    inference(forward_demodulation,[],[f21072,f17179]) ).

fof(f21072,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) )
    | ~ spl0_962 ),
    inference(avatar_component_clause,[],[f21071]) ).

fof(f21073,plain,
    spl0_962,
    inference(avatar_split_clause,[],[f986,f21071]) ).

fof(f986,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_1) ).

fof(f21069,plain,
    spl0_961,
    inference(avatar_split_clause,[],[f874,f21067]) ).

fof(f21067,plain,
    ( spl0_961
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f874,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),c_HOL_Oinverse__class_Oinverse(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).

fof(f21065,plain,
    spl0_960,
    inference(avatar_split_clause,[],[f750,f21063]) ).

fof(f21063,plain,
    ( spl0_960
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X23,X24,tc_nat)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X23,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f750,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X23,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

fof(f21061,plain,
    spl0_959,
    inference(avatar_split_clause,[],[f749,f21059]) ).

fof(f21059,plain,
    ( spl0_959
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X23,X24,tc_nat)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X22),X23,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X22) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f749,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X22),X23,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X24,X23,tc_nat)),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

fof(f20954,plain,
    ( spl0_958
    | ~ spl0_848
    | ~ spl0_957 ),
    inference(avatar_split_clause,[],[f20950,f20947,f17177,f20952]) ).

fof(f20952,plain,
    ( spl0_958
  <=> ! [X18,X17] :
        ( v_i____ = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f20947,plain,
    ( spl0_957
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f20950,plain,
    ( ! [X18,X17] :
        ( v_i____ = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) )
    | ~ spl0_848
    | ~ spl0_957 ),
    inference(forward_demodulation,[],[f20948,f17179]) ).

fof(f20948,plain,
    ( ! [X18,X17] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_957 ),
    inference(avatar_component_clause,[],[f20947]) ).

fof(f20949,plain,
    spl0_957,
    inference(avatar_split_clause,[],[f711,f20947]) ).

fof(f711,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

fof(f20945,plain,
    spl0_956,
    inference(avatar_split_clause,[],[f695,f20943]) ).

fof(f20943,plain,
    ( spl0_956
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f695,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).

fof(f20941,plain,
    spl0_955,
    inference(avatar_split_clause,[],[f290,f20939]) ).

fof(f20939,plain,
    ( spl0_955
  <=> ! [X25,X27,X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X27)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f290,axiom,
    ! [X19,X27,X25] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X27)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

fof(f20937,plain,
    spl0_954,
    inference(avatar_split_clause,[],[f289,f20935]) ).

fof(f20935,plain,
    ( spl0_954
  <=> ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f289,axiom,
    ! [X18,X17,X23] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

fof(f20871,plain,
    ( spl0_953
    | ~ spl0_848
    | ~ spl0_952 ),
    inference(avatar_split_clause,[],[f20867,f20864,f17177,f20869]) ).

fof(f20869,plain,
    ( spl0_953
  <=> ! [X18,X17,X23] :
        ( v_i____ = X23
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f20864,plain,
    ( spl0_952
  <=> ! [X18,X17,X23] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f20867,plain,
    ( ! [X18,X17,X23] :
        ( v_i____ = X23
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) )
    | ~ spl0_848
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f20865,f17179]) ).

fof(f20865,plain,
    ( ! [X18,X17,X23] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) )
    | ~ spl0_952 ),
    inference(avatar_component_clause,[],[f20864]) ).

fof(f20866,plain,
    spl0_952,
    inference(avatar_split_clause,[],[f176,f20864]) ).

fof(f176,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X23
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).

fof(f20862,plain,
    spl0_951,
    inference(avatar_split_clause,[],[f116,f20860]) ).

fof(f20860,plain,
    ( spl0_951
  <=> ! [X17,X19,X0,X25] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_lessequals(X19,X25,X0)
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f116,axiom,
    ! [X0,X19,X17,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_lessequals(X19,X25,X0)
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X25),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).

fof(f20694,plain,
    ( spl0_950
    | ~ spl0_197
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17234,f17177,f2969,f20692]) ).

fof(f17234,plain,
    ( ! [X0] : v_i____ = c_HOL_Ominus__class_Ominus(v_i____,X0,tc_nat)
    | ~ spl0_197
    | ~ spl0_848 ),
    inference(superposition,[],[f2970,f17179]) ).

fof(f20245,plain,
    ( spl0_949
    | ~ spl0_177
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17230,f17177,f2867,f20243]) ).

fof(f19789,plain,
    ( spl0_948
    | ~ spl0_175
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17229,f17177,f2859,f19787]) ).

fof(f2859,plain,
    ( spl0_175
  <=> ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f17229,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(v_i____,hAPP(c_Suc,X0),tc_nat)
    | ~ spl0_175
    | ~ spl0_848 ),
    inference(superposition,[],[f2860,f17179]) ).

fof(f2860,plain,
    ( ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X17),tc_nat)
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f2859]) ).

fof(f19176,plain,
    ( spl0_947
    | ~ spl0_171
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17228,f17177,f2842,f19173]) ).

fof(f17228,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,v_i____)
    | ~ spl0_171
    | ~ spl0_848 ),
    inference(superposition,[],[f2844,f17179]) ).

fof(f18759,plain,
    ( spl0_946
    | ~ spl0_168
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17227,f17177,f2829,f18756]) ).

fof(f17227,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(v_i____,tc_nat)
    | ~ spl0_168
    | ~ spl0_848 ),
    inference(superposition,[],[f2831,f17179]) ).

fof(f18347,plain,
    ( spl0_945
    | ~ spl0_165
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17226,f17177,f2817,f18345]) ).

fof(f2817,plain,
    ( spl0_165
  <=> ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f17226,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(v_i____,c_Fact_Ofact__class_Ofact(X0,tc_nat),tc_nat)
    | ~ spl0_165
    | ~ spl0_848 ),
    inference(superposition,[],[f2818,f17179]) ).

fof(f2818,plain,
    ( ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat)
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f2817]) ).

fof(f18248,plain,
    ( spl0_944
    | ~ spl0_848
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f18244,f18241,f17177,f18246]) ).

fof(f18246,plain,
    ( spl0_944
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),X23,tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f18241,plain,
    ( spl0_943
  <=> ! [X18,X17,X23] :
        ( c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),X23,tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f18244,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),X23,tc_nat),X17,tc_nat) )
    | ~ spl0_848
    | ~ spl0_943 ),
    inference(forward_demodulation,[],[f18242,f17179]) ).

fof(f18242,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),X23,tc_nat),X17,tc_nat) )
    | ~ spl0_943 ),
    inference(avatar_component_clause,[],[f18241]) ).

fof(f18243,plain,
    spl0_943,
    inference(avatar_split_clause,[],[f1930,f18241]) ).

fof(f1930,plain,
    ! [X18,X17,X23] :
      ( c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),X23,tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat) ),
    inference(forward_demodulation,[],[f1263,f1277]) ).

fof(f1277,axiom,
    ! [X2,X3,X1] : c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).

fof(f1263,axiom,
    ! [X18,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).

fof(f18239,plain,
    spl0_942,
    inference(avatar_split_clause,[],[f1907,f18237]) ).

fof(f1907,plain,
    ! [X19] :
      ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))) = X19
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f504,f582]) ).

fof(f504,axiom,
    ! [X19] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_0) ).

fof(f18235,plain,
    spl0_941,
    inference(avatar_split_clause,[],[f1906,f18233]) ).

fof(f1906,plain,
    ! [X19] :
      ( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f294,f582]) ).

fof(f294,axiom,
    ! [X19] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__plus__one__div__two_0) ).

fof(f18231,plain,
    spl0_940,
    inference(avatar_split_clause,[],[f1891,f18229]) ).

fof(f18229,plain,
    ( spl0_940
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f1891,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
    inference(forward_demodulation,[],[f1454,f1837]) ).

fof(f1454,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),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_comm__monoid__add_Opower2__eq__square_0) ).

fof(f18227,plain,
    spl0_939,
    inference(avatar_split_clause,[],[f1878,f18225]) ).

fof(f1878,plain,
    ! [X0,X17] :
      ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
      | ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
    inference(forward_demodulation,[],[f1521,f1837]) ).

fof(f1521,axiom,
    ! [X0,X17] :
      ( ~ 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)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).

fof(f18223,plain,
    spl0_938,
    inference(avatar_split_clause,[],[f1687,f18221]) ).

fof(f18221,plain,
    ( spl0_938
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f1687,axiom,
    ! [X18,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

fof(f18219,plain,
    spl0_937,
    inference(avatar_split_clause,[],[f1666,f18217]) ).

fof(f18217,plain,
    ( spl0_937
  <=> ! [X2,X0,X17] :
        ( ~ class_Power_Opower(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f1666,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Power_Opower(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).

fof(f18215,plain,
    spl0_936,
    inference(avatar_split_clause,[],[f1665,f18213]) ).

fof(f18213,plain,
    ( spl0_936
  <=> ! [X2,X0,X17] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f1665,axiom,
    ! [X2,X0,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

fof(f18211,plain,
    spl0_935,
    inference(avatar_split_clause,[],[f1664,f18209]) ).

fof(f1664,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

fof(f18207,plain,
    spl0_934,
    inference(avatar_split_clause,[],[f1587,f18205]) ).

fof(f18205,plain,
    ( spl0_934
  <=> ! [X4,X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f1587,axiom,
    ! [X0,X19,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X4)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

fof(f18203,plain,
    spl0_933,
    inference(avatar_split_clause,[],[f1492,f18201]) ).

fof(f18201,plain,
    ( spl0_933
  <=> ! [X20,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),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(X20,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f1492,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),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(X20,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).

fof(f18199,plain,
    spl0_932,
    inference(avatar_split_clause,[],[f1432,f18197]) ).

fof(f18197,plain,
    ( spl0_932
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X23,X18,tc_nat)
        | ~ c_lessequals(X23,X17,tc_nat)
        | c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f1432,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X23,X18,tc_nat)
      | ~ c_lessequals(X23,X17,tc_nat)
      | c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

fof(f18195,plain,
    spl0_931,
    inference(avatar_split_clause,[],[f1391,f18193]) ).

fof(f18193,plain,
    ( spl0_931
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f1391,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

fof(f18191,plain,
    spl0_930,
    inference(avatar_split_clause,[],[f1358,f18189]) ).

fof(f18189,plain,
    ( spl0_930
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X23,X18,tc_nat)
        | ~ c_lessequals(X23,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f1358,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X23,X18,tc_nat)
      | ~ c_lessequals(X23,X17,tc_nat)
      | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X23,tc_nat),c_HOL_Ominus__class_Ominus(X17,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

fof(f18187,plain,
    spl0_929,
    inference(avatar_split_clause,[],[f1329,f18185]) ).

fof(f18185,plain,
    ( spl0_929
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f1329,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

fof(f18183,plain,
    spl0_928,
    inference(avatar_split_clause,[],[f1289,f18181]) ).

fof(f18181,plain,
    ( spl0_928
  <=> ! [X41,X23,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | ~ c_lessequals(X23,X41,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X41),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f1289,axiom,
    ! [X41,X24,X22,X23] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | ~ c_lessequals(X23,X41,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X24),X41),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

fof(f18179,plain,
    ( spl0_927
    | ~ spl0_151
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17224,f17177,f2755,f18177]) ).

fof(f18177,plain,
    ( spl0_927
  <=> ! [X0] : c_FFT__Mirabelle_OFFT(v_i____,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f2755,plain,
    ( spl0_151
  <=> ! [X2] : c_FFT__Mirabelle_OFFT(c_HOL_Ozero__class_Ozero(tc_nat),X2) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f17224,plain,
    ( ! [X0] : c_FFT__Mirabelle_OFFT(v_i____,X0) = X0
    | ~ spl0_151
    | ~ spl0_848 ),
    inference(superposition,[],[f2756,f17179]) ).

fof(f2756,plain,
    ( ! [X2] : c_FFT__Mirabelle_OFFT(c_HOL_Ozero__class_Ozero(tc_nat),X2) = X2
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f2755]) ).

fof(f18175,plain,
    spl0_926,
    inference(avatar_split_clause,[],[f1246,f18173]) ).

fof(f18173,plain,
    ( spl0_926
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X47,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
        | c_Int_Onumber__class_Onumber__of(X34,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f1246,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X47,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
      | c_Int_Onumber__class_Onumber__of(X34,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nat__number__of_1) ).

fof(f18171,plain,
    spl0_925,
    inference(avatar_split_clause,[],[f1225,f18169]) ).

fof(f18169,plain,
    ( spl0_925
  <=> ! [X41,X23,X22,X24] :
        ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X23,X41,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X41),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f1225,axiom,
    ! [X41,X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X23,X41,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X41),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

fof(f18167,plain,
    spl0_924,
    inference(avatar_split_clause,[],[f1125,f18165]) ).

fof(f18165,plain,
    ( spl0_924
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X3,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),X3),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f1125,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X3,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),X3),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

fof(f18163,plain,
    spl0_923,
    inference(avatar_split_clause,[],[f1124,f18161]) ).

fof(f18161,plain,
    ( spl0_923
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X3,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),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f1124,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X3,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),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

fof(f18159,plain,
    spl0_922,
    inference(avatar_split_clause,[],[f1122,f18157]) ).

fof(f18157,plain,
    ( spl0_922
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f1122,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

fof(f18155,plain,
    spl0_921,
    inference(avatar_split_clause,[],[f1121,f18153]) ).

fof(f18153,plain,
    ( spl0_921
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f1121,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

fof(f18151,plain,
    spl0_920,
    inference(avatar_split_clause,[],[f1120,f18149]) ).

fof(f18149,plain,
    ( spl0_920
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f1120,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

fof(f18147,plain,
    spl0_919,
    inference(avatar_split_clause,[],[f1119,f18145]) ).

fof(f18145,plain,
    ( spl0_919
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X3,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),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f1119,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X3,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),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

fof(f18143,plain,
    spl0_918,
    inference(avatar_split_clause,[],[f1104,f18141]) ).

fof(f18141,plain,
    ( spl0_918
  <=> ! [X18,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X18,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X17,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f1104,axiom,
    ! [X0,X18,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X18,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X17,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X18),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

fof(f18107,plain,
    ( spl0_917
    | ~ spl0_848
    | ~ spl0_916 ),
    inference(avatar_split_clause,[],[f18103,f18100,f17177,f18105]) ).

fof(f18105,plain,
    ( spl0_917
  <=> ! [X34,X23,X47] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat)),X23)) = v_i____
        | ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f18100,plain,
    ( spl0_916
  <=> ! [X34,X23,X47] :
        ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat)),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f18103,plain,
    ( ! [X47,X34,X23] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat)),X23)) = v_i____
        | ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint) )
    | ~ spl0_848
    | ~ spl0_916 ),
    inference(forward_demodulation,[],[f18101,f17179]) ).

fof(f18101,plain,
    ( ! [X47,X34,X23] :
        ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat)),X23)) )
    | ~ spl0_916 ),
    inference(avatar_component_clause,[],[f18100]) ).

fof(f18102,plain,
    spl0_916,
    inference(avatar_split_clause,[],[f984,f18100]) ).

fof(f984,axiom,
    ! [X47,X34,X23] :
      ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat)),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__mult__left_0) ).

fof(f18078,plain,
    ( spl0_915
    | ~ spl0_848
    | ~ spl0_914 ),
    inference(avatar_split_clause,[],[f18074,f18071,f17177,f18076]) ).

fof(f18076,plain,
    ( spl0_915
  <=> ! [X2,X0,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f18071,plain,
    ( spl0_914
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f18074,plain,
    ( ! [X2,X0,X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) )
    | ~ spl0_848
    | ~ spl0_914 ),
    inference(forward_demodulation,[],[f18072,f17179]) ).

fof(f18072,plain,
    ( ! [X2,X0,X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_914 ),
    inference(avatar_component_clause,[],[f18071]) ).

fof(f18073,plain,
    spl0_914,
    inference(avatar_split_clause,[],[f970,f18071]) ).

fof(f970,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

fof(f18069,plain,
    spl0_913,
    inference(avatar_split_clause,[],[f937,f18067]) ).

fof(f18067,plain,
    ( spl0_913
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f937,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

fof(f18065,plain,
    spl0_912,
    inference(avatar_split_clause,[],[f802,f18063]) ).

fof(f18063,plain,
    ( spl0_912
  <=> ! [X25,X0,X19] :
        ( ~ 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f802,axiom,
    ! [X0,X19,X25] :
      ( ~ 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),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

fof(f18061,plain,
    spl0_911,
    inference(avatar_split_clause,[],[f761,f18059]) ).

fof(f18059,plain,
    ( spl0_911
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X19,X0)),X17) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f761,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X19,X0)),X17) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_1) ).

fof(f18057,plain,
    spl0_910,
    inference(avatar_split_clause,[],[f719,f18055]) ).

fof(f18055,plain,
    ( spl0_910
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(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),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f719,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(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),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f18053,plain,
    spl0_909,
    inference(avatar_split_clause,[],[f580,f18051]) ).

fof(f18051,plain,
    ( spl0_909
  <=> ! [X18,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) = 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))),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f580,axiom,
    ! [X0,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X18),X18) = 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))),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(f18020,plain,
    spl0_908,
    inference(avatar_split_clause,[],[f531,f18018]) ).

fof(f18018,plain,
    ( spl0_908
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_lessequals(X3,X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f531,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_lessequals(X3,X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

fof(f18016,plain,
    spl0_907,
    inference(avatar_split_clause,[],[f515,f18014]) ).

fof(f18014,plain,
    ( spl0_907
  <=> ! [X41,X23,X22,X24] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | ~ c_lessequals(X23,X41,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X41),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f515,axiom,
    ! [X41,X24,X22,X23] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | ~ c_lessequals(X23,X41,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X41),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

fof(f18012,plain,
    spl0_906,
    inference(avatar_split_clause,[],[f512,f18010]) ).

fof(f18010,plain,
    ( spl0_906
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f512,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

fof(f18008,plain,
    spl0_905,
    inference(avatar_split_clause,[],[f432,f18006]) ).

fof(f18006,plain,
    ( spl0_905
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f432,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f18004,plain,
    spl0_904,
    inference(avatar_split_clause,[],[f415,f18002]) ).

fof(f18002,plain,
    ( spl0_904
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X1,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f415,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X1,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

fof(f18000,plain,
    spl0_903,
    inference(avatar_split_clause,[],[f399,f17998]) ).

fof(f17998,plain,
    ( spl0_903
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f399,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).

fof(f17996,plain,
    spl0_902,
    inference(avatar_split_clause,[],[f383,f17994]) ).

fof(f17994,plain,
    ( spl0_902
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,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),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f383,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,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),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

fof(f17992,plain,
    spl0_901,
    inference(avatar_split_clause,[],[f382,f17990]) ).

fof(f17990,plain,
    ( spl0_901
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f382,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

fof(f17988,plain,
    spl0_900,
    inference(avatar_split_clause,[],[f378,f17986]) ).

fof(f17986,plain,
    ( spl0_900
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f378,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

fof(f17984,plain,
    spl0_899,
    inference(avatar_split_clause,[],[f377,f17982]) ).

fof(f17982,plain,
    ( spl0_899
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f377,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

fof(f17980,plain,
    ( spl0_898
    | ~ spl0_139
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17223,f17177,f2702,f17978]) ).

fof(f17223,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,v_i____,tc_nat)
    | ~ spl0_139
    | ~ spl0_848 ),
    inference(superposition,[],[f2703,f17179]) ).

fof(f17976,plain,
    spl0_897,
    inference(avatar_split_clause,[],[f374,f17974]) ).

fof(f17974,plain,
    ( spl0_897
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f374,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

fof(f17972,plain,
    spl0_896,
    inference(avatar_split_clause,[],[f373,f17970]) ).

fof(f17970,plain,
    ( spl0_896
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f373,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

fof(f17968,plain,
    spl0_895,
    inference(avatar_split_clause,[],[f324,f17966]) ).

fof(f17966,plain,
    ( spl0_895
  <=> ! [X31,X33,X0,X18,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X18),X18) = hAPP(hAPP(X32,hAPP(hAPP(X31,X30),X30)),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f324,axiom,
    ! [X31,X29,X0,X18,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X18),X18) = hAPP(hAPP(X32,hAPP(hAPP(X31,X30),X30)),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).

fof(f17964,plain,
    spl0_894,
    inference(avatar_split_clause,[],[f269,f17962]) ).

fof(f17962,plain,
    ( spl0_894
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X19,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X19,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f269,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X19,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X19,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_0) ).

fof(f17960,plain,
    spl0_893,
    inference(avatar_split_clause,[],[f252,f17958]) ).

fof(f17958,plain,
    ( spl0_893
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Olordered__ring(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f252,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Olordered__ring(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).

fof(f17956,plain,
    spl0_892,
    inference(avatar_split_clause,[],[f244,f17954]) ).

fof(f17954,plain,
    ( spl0_892
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_lessequals(X3,X1,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f244,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_lessequals(X3,X1,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

fof(f17952,plain,
    spl0_891,
    inference(avatar_split_clause,[],[f243,f17950]) ).

fof(f17950,plain,
    ( spl0_891
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_lessequals(X3,X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f243,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_lessequals(X3,X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

fof(f17948,plain,
    spl0_890,
    inference(avatar_split_clause,[],[f238,f17946]) ).

fof(f17946,plain,
    ( spl0_890
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f238,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X25),X25)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

fof(f17944,plain,
    spl0_889,
    inference(avatar_split_clause,[],[f158,f17942]) ).

fof(f17942,plain,
    ( spl0_889
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f158,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

fof(f17940,plain,
    spl0_888,
    inference(avatar_split_clause,[],[f157,f17938]) ).

fof(f17938,plain,
    ( spl0_888
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f157,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

fof(f17936,plain,
    ( spl0_887
    | ~ spl0_138
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17222,f17177,f2698,f17934]) ).

fof(f2698,plain,
    ( spl0_138
  <=> ! [X17] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f17222,plain,
    ( ! [X0] : c_lessequals(v_i____,X0,tc_nat)
    | ~ spl0_138
    | ~ spl0_848 ),
    inference(superposition,[],[f2699,f17179]) ).

fof(f2699,plain,
    ( ! [X17] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f2698]) ).

fof(f17932,plain,
    spl0_886,
    inference(avatar_split_clause,[],[f156,f17930]) ).

fof(f17930,plain,
    ( spl0_886
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f156,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

fof(f17928,plain,
    spl0_885,
    inference(avatar_split_clause,[],[f155,f17926]) ).

fof(f17926,plain,
    ( spl0_885
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f155,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

fof(f17924,plain,
    spl0_884,
    inference(avatar_split_clause,[],[f137,f17922]) ).

fof(f17922,plain,
    ( spl0_884
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f137,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

fof(f17920,plain,
    spl0_883,
    inference(avatar_split_clause,[],[f136,f17918]) ).

fof(f17918,plain,
    ( spl0_883
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f136,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

fof(f17916,plain,
    spl0_882,
    inference(avatar_split_clause,[],[f135,f17914]) ).

fof(f17914,plain,
    ( spl0_882
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f135,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

fof(f17912,plain,
    spl0_881,
    inference(avatar_split_clause,[],[f133,f17910]) ).

fof(f17910,plain,
    ( spl0_881
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f133,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

fof(f17908,plain,
    spl0_880,
    inference(avatar_split_clause,[],[f131,f17906]) ).

fof(f17906,plain,
    ( spl0_880
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Opordered__ring(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f131,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Opordered__ring(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

fof(f17904,plain,
    spl0_879,
    inference(avatar_split_clause,[],[f90,f17902]) ).

fof(f17902,plain,
    ( spl0_879
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X3,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),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f90,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X3,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),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

fof(f17900,plain,
    spl0_878,
    inference(avatar_split_clause,[],[f89,f17898]) ).

fof(f17898,plain,
    ( spl0_878
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f89,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

fof(f17896,plain,
    spl0_877,
    inference(avatar_split_clause,[],[f73,f17894]) ).

fof(f17894,plain,
    ( spl0_877
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0)
        | c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f73,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X1,X0)
      | c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).

fof(f17887,plain,
    ( spl0_876
    | ~ spl0_848
    | ~ spl0_875 ),
    inference(avatar_split_clause,[],[f17883,f17880,f17177,f17885]) ).

fof(f17885,plain,
    ( spl0_876
  <=> ! [X0,X17] :
        ( v_i____ = X17
        | ~ 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),c_HOL_Ozero__class_Ozero(X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f17880,plain,
    ( spl0_875
  <=> ! [X0,X17] :
        ( ~ 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) = X17
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f17883,plain,
    ( ! [X0,X17] :
        ( v_i____ = X17
        | ~ 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),c_HOL_Ozero__class_Ozero(X0)),X17) )
    | ~ spl0_848
    | ~ spl0_875 ),
    inference(forward_demodulation,[],[f17881,f17179]) ).

fof(f17881,plain,
    ( ! [X0,X17] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17) )
    | ~ spl0_875 ),
    inference(avatar_component_clause,[],[f17880]) ).

fof(f17882,plain,
    spl0_875,
    inference(avatar_split_clause,[],[f27,f17880]) ).

fof(f27,axiom,
    ! [X0,X17] :
      ( ~ 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) = X17
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

fof(f17878,plain,
    spl0_874,
    inference(avatar_split_clause,[],[f17,f17876]) ).

fof(f17876,plain,
    ( spl0_874
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f17,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

fof(f17874,plain,
    spl0_873,
    inference(avatar_split_clause,[],[f16,f17872]) ).

fof(f17872,plain,
    ( spl0_873
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f16,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

fof(f17870,plain,
    spl0_872,
    inference(avatar_split_clause,[],[f15,f17868]) ).

fof(f17868,plain,
    ( spl0_872
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f15,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

fof(f17866,plain,
    spl0_871,
    inference(avatar_split_clause,[],[f14,f17864]) ).

fof(f17864,plain,
    ( spl0_871
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f14,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

fof(f17521,plain,
    ( spl0_870
    | ~ spl0_196
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17233,f17177,f2964,f17518]) ).

fof(f2964,plain,
    ( spl0_196
  <=> c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f17233,plain,
    ( c_Int_Oiszero(v_i____,tc_nat)
    | ~ spl0_196
    | ~ spl0_848 ),
    inference(superposition,[],[f2965,f17179]) ).

fof(f2965,plain,
    ( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f2964]) ).

fof(f17473,plain,
    ( spl0_869
    | ~ spl0_848
    | ~ spl0_868 ),
    inference(avatar_split_clause,[],[f17469,f17466,f17177,f17471]) ).

fof(f17471,plain,
    ( spl0_869
  <=> ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f17469,plain,
    ( ! [X18] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_848
    | ~ spl0_868 ),
    inference(forward_demodulation,[],[f17467,f17179]) ).

fof(f17468,plain,
    spl0_868,
    inference(avatar_split_clause,[],[f1954,f17466]) ).

fof(f1954,plain,
    ! [X18] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(forward_demodulation,[],[f1953,f1837]) ).

fof(f1953,plain,
    ! [X18] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1102,f1837]) ).

fof(f1102,axiom,
    ! [X18] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod2__gr__0_0) ).

fof(f17464,plain,
    ( spl0_867
    | ~ spl0_128
    | ~ spl0_848 ),
    inference(avatar_split_clause,[],[f17221,f17177,f2652,f17461]) ).

fof(f2652,plain,
    ( spl0_128
  <=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f17221,plain,
    ( c_Parity_Oeven__odd__class_Oeven(v_i____,tc_nat)
    | ~ spl0_128
    | ~ spl0_848 ),
    inference(superposition,[],[f2654,f17179]) ).

fof(f2654,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f2652]) ).

fof(f17459,plain,
    spl0_866,
    inference(avatar_split_clause,[],[f1942,f17457]) ).

fof(f17457,plain,
    ( spl0_866
  <=> ! [X31,X33,X19,X0,X29,X32,X30] :
        ( hAPP(hAPP(X32,X19),X19) = hAPP(hAPP(X29,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f1942,plain,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( hAPP(hAPP(X32,X19),X19) = hAPP(hAPP(X29,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0) ),
    inference(forward_demodulation,[],[f1539,f1837]) ).

fof(f1539,axiom,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X19),X19) = hAPP(hAPP(X29,X19),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(f17455,plain,
    spl0_865,
    inference(avatar_split_clause,[],[f1882,f17453]) ).

fof(f1882,plain,
    ! [X0,X17] :
      ( 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),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17))
      | ~ class_Int_Onumber__ring(X0) ),
    inference(forward_demodulation,[],[f1531,f1837]) ).

fof(f1531,axiom,
    ! [X0,X17] :
      ( ~ 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)),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__even_0) ).

fof(f17451,plain,
    spl0_864,
    inference(avatar_split_clause,[],[f1862,f17449]) ).

fof(f17449,plain,
    ( spl0_864
  <=> ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,X18)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f1862,plain,
    ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,X18)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),
    inference(forward_demodulation,[],[f1548,f1837]) ).

fof(f1548,axiom,
    ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,X18)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X18,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_div2__Suc__Suc_0) ).

fof(f17414,plain,
    ( spl0_863
    | ~ spl0_848
    | ~ spl0_862 ),
    inference(avatar_split_clause,[],[f17410,f17407,f17177,f17412]) ).

fof(f17412,plain,
    ( spl0_863
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | X17 = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f17407,plain,
    ( spl0_862
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f17410,plain,
    ( ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X23,tc_nat)
        | X17 = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) )
    | ~ spl0_848
    | ~ spl0_862 ),
    inference(forward_demodulation,[],[f17408,f17179]) ).

fof(f17408,plain,
    ( ! [X18,X17,X23] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | X17 = X18 )
    | ~ spl0_862 ),
    inference(avatar_component_clause,[],[f17407]) ).

fof(f17409,plain,
    spl0_862,
    inference(avatar_split_clause,[],[f1347,f17407]) ).

fof(f1347,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

fof(f17360,plain,
    ( spl0_861
    | ~ spl0_848
    | ~ spl0_860 ),
    inference(avatar_split_clause,[],[f17356,f17353,f17177,f17358]) ).

fof(f17358,plain,
    ( spl0_861
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Fact_Ofact__class_Ofact(X17,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f17353,plain,
    ( spl0_860
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Fact_Ofact__class_Ofact(X17,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f17356,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(v_i____,X17,tc_nat)
        | c_Fact_Ofact__class_Ofact(X17,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) )
    | ~ spl0_848
    | ~ spl0_860 ),
    inference(forward_demodulation,[],[f17354,f17179]) ).

fof(f17354,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Fact_Ofact__class_Ofact(X17,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) )
    | ~ spl0_860 ),
    inference(avatar_component_clause,[],[f17353]) ).

fof(f17355,plain,
    spl0_860,
    inference(avatar_split_clause,[],[f1273,f17353]) ).

fof(f1273,axiom,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Fact_Ofact__class_Ofact(X17,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__reduce__nat_0) ).

fof(f17351,plain,
    spl0_859,
    inference(avatar_split_clause,[],[f1226,f17349]) ).

fof(f17349,plain,
    ( spl0_859
  <=> ! [X41,X17,X18,X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f1226,axiom,
    ! [X41,X18,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_nat)
      | c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

fof(f17220,plain,
    spl0_858,
    inference(avatar_split_clause,[],[f1213,f17218]) ).

fof(f17218,plain,
    ( spl0_858
  <=> ! [X2,X0,X17] :
        ( ~ 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) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f1213,axiom,
    ! [X2,X0,X17] :
      ( ~ 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) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

fof(f17216,plain,
    spl0_857,
    inference(avatar_split_clause,[],[f1211,f17214]) ).

fof(f17214,plain,
    ( spl0_857
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f1211,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).

fof(f17212,plain,
    spl0_856,
    inference(avatar_split_clause,[],[f1197,f17210]) ).

fof(f17210,plain,
    ( spl0_856
  <=> ! [X18,X17] :
        ( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = X17
        | hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f1197,axiom,
    ! [X18,X17] :
      ( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = X17
      | hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

fof(f17208,plain,
    spl0_855,
    inference(avatar_split_clause,[],[f967,f17206]) ).

fof(f17206,plain,
    ( spl0_855
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f967,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

fof(f17204,plain,
    spl0_854,
    inference(avatar_split_clause,[],[f966,f17202]) ).

fof(f17202,plain,
    ( spl0_854
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X3,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f966,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X3,X0)),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).

fof(f17200,plain,
    spl0_853,
    inference(avatar_split_clause,[],[f947,f17198]) ).

fof(f17198,plain,
    ( spl0_853
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X3,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f947,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Divides_Odiv__class_Omod(X2,X3,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).

fof(f17196,plain,
    spl0_852,
    inference(avatar_split_clause,[],[f892,f17194]) ).

fof(f17194,plain,
    ( spl0_852
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f892,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).

fof(f17192,plain,
    spl0_851,
    inference(avatar_split_clause,[],[f706,f17190]) ).

fof(f17190,plain,
    ( spl0_851
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X23,X24,tc_nat)
        | c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f706,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

fof(f17188,plain,
    spl0_850,
    inference(avatar_split_clause,[],[f703,f17186]) ).

fof(f17186,plain,
    ( spl0_850
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X17),X0) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f703,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X17),X0) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).

fof(f17184,plain,
    spl0_849,
    inference(avatar_split_clause,[],[f607,f17182]) ).

fof(f17182,plain,
    ( spl0_849
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3)),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f607,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X3)),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

fof(f17180,plain,
    ( spl0_848
    | ~ spl0_250
    | ~ spl0_764 ),
    inference(avatar_split_clause,[],[f16940,f13582,f3220,f17177]) ).

fof(f3220,plain,
    ( spl0_250
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f16940,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = v_i____
    | ~ spl0_250
    | ~ spl0_764 ),
    inference(resolution,[],[f13584,f3221]) ).

fof(f3221,plain,
    ( ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 )
    | ~ spl0_250 ),
    inference(avatar_component_clause,[],[f3220]) ).

fof(f13584,plain,
    ( c_HOL_Oord__class_Oless(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_764 ),
    inference(avatar_component_clause,[],[f13582]) ).

fof(f17175,plain,
    spl0_847,
    inference(avatar_split_clause,[],[f606,f17173]) ).

fof(f17173,plain,
    ( spl0_847
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f606,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X1)),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

fof(f17171,plain,
    spl0_846,
    inference(avatar_split_clause,[],[f420,f17169]) ).

fof(f17169,plain,
    ( spl0_846
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f420,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).

fof(f17167,plain,
    spl0_845,
    inference(avatar_split_clause,[],[f218,f17165]) ).

fof(f17165,plain,
    ( spl0_845
  <=> ! [X20,X0,X3] :
        ( ~ 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(X20,X0)
        | c_Int_Onumber__class_Onumber__of(X20,X0) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f218,axiom,
    ! [X3,X0,X20] :
      ( ~ 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(X20,X0)
      | c_Int_Onumber__class_Onumber__of(X20,X0) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

fof(f17163,plain,
    spl0_844,
    inference(avatar_split_clause,[],[f127,f17161]) ).

fof(f17161,plain,
    ( spl0_844
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Divides_Odiv__class_Odiv(X2,X3,X0))),c_Divides_Odiv__class_Omod(X2,X3,X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f127,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),c_Divides_Odiv__class_Odiv(X2,X3,X0))),c_Divides_Odiv__class_Omod(X2,X3,X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).

fof(f17159,plain,
    spl0_843,
    inference(avatar_split_clause,[],[f125,f17157]) ).

fof(f17157,plain,
    ( spl0_843
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)),c_Divides_Odiv__class_Omod(X2,X3,X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f125,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Divides_Odiv__class_Odiv(X2,X3,X0)),X3)),c_Divides_Odiv__class_Omod(X2,X3,X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).

fof(f17155,plain,
    spl0_842,
    inference(avatar_split_clause,[],[f22,f17153]) ).

fof(f17153,plain,
    ( spl0_842
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f22,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).

fof(f15698,plain,
    ( spl0_658
    | ~ spl0_190
    | spl0_647 ),
    inference(avatar_split_clause,[],[f9351,f9304,f2940,f9569]) ).

fof(f9351,plain,
    ( c_lessequals(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_190
    | spl0_647 ),
    inference(resolution,[],[f9306,f2941]) ).

fof(f9306,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | spl0_647 ),
    inference(avatar_component_clause,[],[f9304]) ).

fof(f15037,plain,
    spl0_841,
    inference(avatar_split_clause,[],[f2004,f15035]) ).

fof(f15035,plain,
    ( spl0_841
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f2004,plain,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f2003,f582]) ).

fof(f2003,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,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),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f2002,f582]) ).

fof(f2002,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,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),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1522,f582]) ).

fof(f1522,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,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),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

fof(f15033,plain,
    spl0_840,
    inference(avatar_split_clause,[],[f1997,f15031]) ).

fof(f15031,plain,
    ( spl0_840
  <=> ! [X18,X17] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f1997,plain,
    ! [X18,X17] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat) ),
    inference(forward_demodulation,[],[f1996,f582]) ).

fof(f1996,plain,
    ! [X18,X17] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1995,f582]) ).

fof(f1995,plain,
    ! [X18,X17] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1254,f582]) ).

fof(f1254,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

fof(f15029,plain,
    spl0_839,
    inference(avatar_split_clause,[],[f1935,f15027]) ).

fof(f15027,plain,
    ( spl0_839
  <=> ! [X18,X17] :
        ( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f1935,plain,
    ! [X18,X17] :
      ( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f1934,f1511]) ).

fof(f1511,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).

fof(f1934,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Ominus__class_Ominus(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1614,f1323]) ).

fof(f1323,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_nat__number__of__Pls_0) ).

fof(f1614,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),X17,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Ominus__class_Ominus(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__eq__diff__pred_0) ).

fof(f15025,plain,
    spl0_838,
    inference(avatar_split_clause,[],[f1900,f15023]) ).

fof(f15023,plain,
    ( spl0_838
  <=> ! [X19] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) = X19
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f1900,plain,
    ! [X19] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) = X19
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f249,f582]) ).

fof(f249,axiom,
    ! [X19] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__div__two__times__two_0) ).

fof(f15021,plain,
    spl0_837,
    inference(avatar_split_clause,[],[f1899,f15019]) ).

fof(f1899,plain,
    ! [X19] :
      ( c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f771,f582]) ).

fof(f771,axiom,
    ! [X19] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Divides_Odiv__class_Odiv(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X19),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).

fof(f15017,plain,
    spl0_836,
    inference(avatar_split_clause,[],[f1870,f15015]) ).

fof(f15015,plain,
    ( spl0_836
  <=> ! [X2,X0,X17] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f1870,plain,
    ! [X2,X0,X17] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17)),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1520,f1837]) ).

fof(f1520,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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)),X17)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).

fof(f15013,plain,
    spl0_835,
    inference(avatar_split_clause,[],[f1635,f15011]) ).

fof(f15011,plain,
    ( spl0_835
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f1635,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X23)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

fof(f15009,plain,
    spl0_834,
    inference(avatar_split_clause,[],[f1437,f15007]) ).

fof(f15007,plain,
    ( spl0_834
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | ~ c_lessequals(X23,X18,tc_nat)
        | ~ c_lessequals(X23,X17,tc_nat)
        | c_HOL_Ominus__class_Ominus(X18,X23,tc_nat) != c_HOL_Ominus__class_Ominus(X17,X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f1437,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | ~ c_lessequals(X23,X18,tc_nat)
      | ~ c_lessequals(X23,X17,tc_nat)
      | c_HOL_Ominus__class_Ominus(X18,X23,tc_nat) != c_HOL_Ominus__class_Ominus(X17,X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

fof(f15005,plain,
    spl0_833,
    inference(avatar_split_clause,[],[f1348,f15003]) ).

fof(f15003,plain,
    ( spl0_833
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f1348,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

fof(f15001,plain,
    spl0_832,
    inference(avatar_split_clause,[],[f1333,f14999]) ).

fof(f14999,plain,
    ( spl0_832
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f1333,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

fof(f14997,plain,
    spl0_831,
    inference(avatar_split_clause,[],[f1332,f14995]) ).

fof(f14995,plain,
    ( spl0_831
  <=> ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f1332,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X18)),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

fof(f14993,plain,
    spl0_830,
    inference(avatar_split_clause,[],[f1284,f14991]) ).

fof(f14991,plain,
    ( spl0_830
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f1284,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) = X23
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

fof(f14989,plain,
    spl0_829,
    inference(avatar_split_clause,[],[f1283,f14987]) ).

fof(f14987,plain,
    ( spl0_829
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) = X23
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f1283,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) = X23
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

fof(f14985,plain,
    spl0_828,
    inference(avatar_split_clause,[],[f1056,f14983]) ).

fof(f14983,plain,
    ( spl0_828
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f1056,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).

fof(f14981,plain,
    spl0_827,
    inference(avatar_split_clause,[],[f1054,f14979]) ).

fof(f14979,plain,
    ( spl0_827
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f1054,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).

fof(f14973,plain,
    ( ~ spl0_718
    | spl0_647
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f14854,f11320,f9304,f11709]) ).

fof(f14854,plain,
    ( ~ c_lessequals(v_i____,v_i____,tc_nat)
    | spl0_647
    | ~ spl0_717 ),
    inference(forward_demodulation,[],[f9306,f11322]) ).

fof(f14972,plain,
    spl0_826,
    inference(avatar_split_clause,[],[f1040,f14970]) ).

fof(f14970,plain,
    ( spl0_826
  <=> ! [X44,X19,X0,X25] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X19,X25,X0),X44,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X19,X44,X0),c_HOL_Oinverse__class_Odivide(X25,X44,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f1040,axiom,
    ! [X0,X19,X44,X25] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X19,X25,X0),X44,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X19,X44,X0),c_HOL_Oinverse__class_Odivide(X25,X44,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

fof(f14968,plain,
    spl0_825,
    inference(avatar_split_clause,[],[f1039,f14966]) ).

fof(f14966,plain,
    ( spl0_825
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f1039,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

fof(f14964,plain,
    spl0_824,
    inference(avatar_split_clause,[],[f1034,f14962]) ).

fof(f14962,plain,
    ( spl0_824
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X1,X0),X3,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f1034,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X1,X0),X3,X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).

fof(f14960,plain,
    spl0_823,
    inference(avatar_split_clause,[],[f1033,f14958]) ).

fof(f14958,plain,
    ( spl0_823
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X1,X0),X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f1033,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X1,X0),X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).

fof(f14956,plain,
    spl0_822,
    inference(avatar_split_clause,[],[f956,f14954]) ).

fof(f14954,plain,
    ( spl0_822
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f956,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X19,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).

fof(f14952,plain,
    spl0_821,
    inference(avatar_split_clause,[],[f949,f14950]) ).

fof(f14950,plain,
    ( spl0_821
  <=> ! [X0,X19] :
        ( ~ 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),X19,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X19,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f949,axiom,
    ! [X0,X19] :
      ( ~ 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),X19,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X19,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus1__divide_0) ).

fof(f14867,plain,
    ( spl0_820
    | ~ spl0_717
    | ~ spl0_819 ),
    inference(avatar_split_clause,[],[f14863,f14860,f11320,f14865]) ).

fof(f14860,plain,
    ( spl0_819
  <=> ! [X18] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f14863,plain,
    ( ! [X18] :
        ( c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,v_i____,tc_nat),tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_717
    | ~ spl0_819 ),
    inference(forward_demodulation,[],[f14861,f11322]) ).

fof(f14861,plain,
    ( ! [X18] :
        ( c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 )
    | ~ spl0_819 ),
    inference(avatar_component_clause,[],[f14860]) ).

fof(f14862,plain,
    spl0_819,
    inference(avatar_split_clause,[],[f944,f14860]) ).

fof(f944,axiom,
    ! [X18] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | c_Fact_Ofact__class_Ofact(X18,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__num__eq__if__nat_1) ).

fof(f14858,plain,
    spl0_818,
    inference(avatar_split_clause,[],[f825,f14856]) ).

fof(f14856,plain,
    ( spl0_818
  <=> ! [X19,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f825,axiom,
    ! [X2,X0,X19,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).

fof(f14796,plain,
    ( spl0_817
    | ~ spl0_315
    | ~ spl0_716 ),
    inference(avatar_split_clause,[],[f13751,f11316,f3967,f14793]) ).

fof(f14791,plain,
    spl0_816,
    inference(avatar_split_clause,[],[f816,f14789]) ).

fof(f14789,plain,
    ( spl0_816
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_Int_Onumber__class_Onumber__of(X19,X0) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X19,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f816,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | c_Int_Onumber__class_Onumber__of(X19,X0) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X19,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_1) ).

fof(f14787,plain,
    spl0_815,
    inference(avatar_split_clause,[],[f760,f14785]) ).

fof(f14785,plain,
    ( spl0_815
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f760,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X3,X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).

fof(f14783,plain,
    spl0_814,
    inference(avatar_split_clause,[],[f743,f14781]) ).

fof(f14781,plain,
    ( spl0_814
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f743,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).

fof(f14779,plain,
    spl0_813,
    inference(avatar_split_clause,[],[f650,f14777]) ).

fof(f14777,plain,
    ( spl0_813
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f650,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f14775,plain,
    spl0_812,
    inference(avatar_split_clause,[],[f649,f14773]) ).

fof(f14773,plain,
    ( spl0_812
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f649,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f14771,plain,
    spl0_811,
    inference(avatar_split_clause,[],[f648,f14769]) ).

fof(f14769,plain,
    ( spl0_811
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f648,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f14767,plain,
    spl0_810,
    inference(avatar_split_clause,[],[f647,f14765]) ).

fof(f14765,plain,
    ( spl0_810
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f647,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f14763,plain,
    spl0_809,
    inference(avatar_split_clause,[],[f646,f14761]) ).

fof(f14761,plain,
    ( spl0_809
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f646,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f14759,plain,
    spl0_808,
    inference(avatar_split_clause,[],[f645,f14757]) ).

fof(f14757,plain,
    ( spl0_808
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f645,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f14755,plain,
    spl0_807,
    inference(avatar_split_clause,[],[f597,f14753]) ).

fof(f14753,plain,
    ( spl0_807
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X27,X0) = X19
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) != X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f597,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X27,X0) = X19
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) != X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

fof(f14751,plain,
    spl0_806,
    inference(avatar_split_clause,[],[f547,f14749]) ).

fof(f14749,plain,
    ( spl0_806
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X19,X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f547,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ouminus__class_Ouminus(X19,X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_0) ).

fof(f14747,plain,
    spl0_805,
    inference(avatar_split_clause,[],[f448,f14745]) ).

fof(f14745,plain,
    ( spl0_805
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X19,X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f448,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X19,X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__even__abs_0) ).

fof(f14743,plain,
    spl0_804,
    inference(avatar_split_clause,[],[f419,f14741]) ).

fof(f14741,plain,
    ( spl0_804
  <=> ! [X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f419,axiom,
    ! [X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).

fof(f14739,plain,
    spl0_803,
    inference(avatar_split_clause,[],[f396,f14737]) ).

fof(f14737,plain,
    ( spl0_803
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f396,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

fof(f14735,plain,
    spl0_802,
    inference(avatar_split_clause,[],[f367,f14733]) ).

fof(f14733,plain,
    ( spl0_802
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X25 = X27
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f367,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X25 = X27
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

fof(f14731,plain,
    spl0_801,
    inference(avatar_split_clause,[],[f275,f14729]) ).

fof(f14729,plain,
    ( spl0_801
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f275,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).

fof(f14727,plain,
    spl0_800,
    inference(avatar_split_clause,[],[f247,f14725]) ).

fof(f14725,plain,
    ( spl0_800
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X23,X24,tc_nat)
        | ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f247,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X23,X24,tc_nat)
      | ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

fof(f14723,plain,
    spl0_799,
    inference(avatar_split_clause,[],[f141,f14721]) ).

fof(f14721,plain,
    ( spl0_799
  <=> ! [X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | ~ 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)),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f141,axiom,
    ! [X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | ~ 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)),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).

fof(f14719,plain,
    spl0_798,
    inference(avatar_split_clause,[],[f118,f14717]) ).

fof(f14717,plain,
    ( spl0_798
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | X2 = X3
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Oinverse(X2,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f118,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | X2 = X3
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Oinverse(X2,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

fof(f14715,plain,
    spl0_797,
    inference(avatar_split_clause,[],[f56,f14713]) ).

fof(f14713,plain,
    ( spl0_797
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f56,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

fof(f14666,plain,
    spl0_796,
    inference(avatar_split_clause,[],[f55,f14664]) ).

fof(f14664,plain,
    ( spl0_796
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f55,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

fof(f14662,plain,
    spl0_795,
    inference(avatar_split_clause,[],[f54,f14660]) ).

fof(f14660,plain,
    ( spl0_795
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f54,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

fof(f14658,plain,
    spl0_794,
    inference(avatar_split_clause,[],[f53,f14656]) ).

fof(f14656,plain,
    ( spl0_794
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f53,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

fof(f14654,plain,
    spl0_793,
    inference(avatar_split_clause,[],[f52,f14652]) ).

fof(f14652,plain,
    ( spl0_793
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f52,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

fof(f14650,plain,
    spl0_792,
    inference(avatar_split_clause,[],[f51,f14648]) ).

fof(f14648,plain,
    ( spl0_792
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f51,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

fof(f14646,plain,
    spl0_791,
    inference(avatar_split_clause,[],[f8,f14644]) ).

fof(f14644,plain,
    ( spl0_791
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X1,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f8,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X1,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f13824,plain,
    ( spl0_647
    | ~ spl0_317
    | ~ spl0_659 ),
    inference(avatar_split_clause,[],[f10952,f10394,f3975,f9304]) ).

fof(f10952,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_317
    | ~ spl0_659 ),
    inference(trivial_inequality_removal,[],[f10926]) ).

fof(f10926,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_317
    | ~ spl0_659 ),
    inference(superposition,[],[f3976,f10396]) ).

fof(f13715,plain,
    spl0_790,
    inference(avatar_split_clause,[],[f2001,f13713]) ).

fof(f13713,plain,
    ( spl0_790
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f2001,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f2000,f582]) ).

fof(f2000,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1524,f582]) ).

fof(f1524,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

fof(f13711,plain,
    spl0_789,
    inference(avatar_split_clause,[],[f1999,f13709]) ).

fof(f13709,plain,
    ( spl0_789
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f1999,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),tc_nat) ),
    inference(forward_demodulation,[],[f1998,f582]) ).

fof(f1998,plain,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),tc_nat) ),
    inference(forward_demodulation,[],[f1523,f582]) ).

fof(f1523,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

fof(f13707,plain,
    spl0_788,
    inference(avatar_split_clause,[],[f1960,f13705]) ).

fof(f13705,plain,
    ( spl0_788
  <=> ! [X2,X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f1960,plain,
    ! [X2,X0] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2 ),
    inference(forward_demodulation,[],[f1564,f1837]) ).

fof(f1564,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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(f13703,plain,
    spl0_787,
    inference(avatar_split_clause,[],[f1861,f13701]) ).

fof(f13701,plain,
    ( spl0_787
  <=> ! [X18] : c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(c_Suc,X18)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f1861,plain,
    ! [X18] : c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(c_Suc,X18)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(forward_demodulation,[],[f1545,f1837]) ).

fof(f1545,axiom,
    ! [X18] : c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(c_Suc,X18)),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_mod2__Suc__Suc_0) ).

fof(f13699,plain,
    spl0_786,
    inference(avatar_split_clause,[],[f1828,f13697]) ).

fof(f13697,plain,
    ( spl0_786
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),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_786])]) ).

fof(f1828,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),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)) ),
    inference(duplicate_literal_removal,[],[f280]) ).

fof(f280,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),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_add__nonneg__eq__0__iff_2) ).

fof(f13695,plain,
    spl0_785,
    inference(avatar_split_clause,[],[f1633,f13693]) ).

fof(f13693,plain,
    ( spl0_785
  <=> ! [X19,X0,X50,X49,X25] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X49,X50,X0)
        | c_HOL_Ominus__class_Ominus(X19,X25,X0) != c_HOL_Ominus__class_Ominus(X49,X50,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f1633,axiom,
    ! [X50,X0,X49,X19,X25] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X49,X50,X0)
      | c_HOL_Ominus__class_Ominus(X19,X25,X0) != c_HOL_Ominus__class_Ominus(X49,X50,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

fof(f13687,plain,
    spl0_784,
    inference(avatar_split_clause,[],[f1613,f13685]) ).

fof(f13685,plain,
    ( spl0_784
  <=> ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat),hAPP(c_Suc,X23),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X23,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f1613,axiom,
    ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat),hAPP(c_Suc,X23),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X23,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

fof(f13683,plain,
    spl0_783,
    inference(avatar_split_clause,[],[f1543,f13681]) ).

fof(f13681,plain,
    ( spl0_783
  <=> ! [X0,X27] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f1543,axiom,
    ! [X0,X27] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).

fof(f13679,plain,
    spl0_782,
    inference(avatar_split_clause,[],[f1542,f13677]) ).

fof(f13677,plain,
    ( spl0_782
  <=> ! [X0,X27] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f1542,axiom,
    ! [X0,X27] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X27),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).

fof(f13675,plain,
    spl0_781,
    inference(avatar_split_clause,[],[f1427,f13673]) ).

fof(f13673,plain,
    ( spl0_781
  <=> ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f1427,axiom,
    ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

fof(f13671,plain,
    spl0_780,
    inference(avatar_split_clause,[],[f1426,f13669]) ).

fof(f13669,plain,
    ( spl0_780
  <=> ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f1426,axiom,
    ! [X18,X17,X23] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

fof(f13667,plain,
    spl0_779,
    inference(avatar_split_clause,[],[f1393,f13665]) ).

fof(f13665,plain,
    ( spl0_779
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f1393,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,X17)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

fof(f13663,plain,
    spl0_778,
    inference(avatar_split_clause,[],[f1371,f13661]) ).

fof(f13661,plain,
    ( spl0_778
  <=> ! [X17,X19] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | 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_Power_Opower__class_Opower(tc_nat),X19),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f1371,axiom,
    ! [X19,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | 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_Power_Opower__class_Opower(tc_nat),X19),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_0) ).

fof(f13659,plain,
    spl0_777,
    inference(avatar_split_clause,[],[f1346,f13657]) ).

fof(f13657,plain,
    ( spl0_777
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f1346,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

fof(f13655,plain,
    spl0_776,
    inference(avatar_split_clause,[],[f1345,f13653]) ).

fof(f13653,plain,
    ( spl0_776
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f1345,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

fof(f13651,plain,
    spl0_775,
    inference(avatar_split_clause,[],[f1265,f13649]) ).

fof(f13649,plain,
    ( spl0_775
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f1265,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

fof(f13645,plain,
    ( spl0_717
    | ~ spl0_177
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_697 ),
    inference(avatar_split_clause,[],[f13598,f10688,f9304,f5394,f2867,f11320]) ).

fof(f13598,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | ~ spl0_177
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_697 ),
    inference(forward_demodulation,[],[f13597,f2868]) ).

fof(f13597,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_456
    | ~ spl0_647
    | ~ spl0_697 ),
    inference(forward_demodulation,[],[f9753,f10690]) ).

fof(f10690,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_697 ),
    inference(avatar_component_clause,[],[f10688]) ).

fof(f13644,plain,
    spl0_774,
    inference(avatar_split_clause,[],[f1264,f13642]) ).

fof(f13642,plain,
    ( spl0_774
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f1264,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

fof(f13640,plain,
    spl0_773,
    inference(avatar_split_clause,[],[f1215,f13638]) ).

fof(f13638,plain,
    ( spl0_773
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),X17) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f1215,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),X17) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).

fof(f13636,plain,
    spl0_772,
    inference(avatar_split_clause,[],[f1053,f13634]) ).

fof(f13634,plain,
    ( spl0_772
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f1053,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).

fof(f13632,plain,
    spl0_771,
    inference(avatar_split_clause,[],[f1038,f13630]) ).

fof(f13630,plain,
    ( spl0_771
  <=> ! [X0,X50,X49,X25,X19] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X50,X49,X0)
        | c_lessequals(X25,X19,X0)
        | c_HOL_Ominus__class_Ominus(X19,X25,X0) != c_HOL_Ominus__class_Ominus(X49,X50,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f1038,axiom,
    ! [X50,X0,X49,X19,X25] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X50,X49,X0)
      | c_lessequals(X25,X19,X0)
      | c_HOL_Ominus__class_Ominus(X19,X25,X0) != c_HOL_Ominus__class_Ominus(X49,X50,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

fof(f13628,plain,
    spl0_770,
    inference(avatar_split_clause,[],[f995,f13626]) ).

fof(f13626,plain,
    ( spl0_770
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f995,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

fof(f13621,plain,
    spl0_769,
    inference(avatar_split_clause,[],[f983,f13619]) ).

fof(f13619,plain,
    ( spl0_769
  <=> ! [X18,X23] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X23,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18)),X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f983,axiom,
    ! [X18,X23] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X23,tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18)),X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

fof(f13617,plain,
    spl0_768,
    inference(avatar_split_clause,[],[f982,f13615]) ).

fof(f13615,plain,
    ( spl0_768
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X18,X17,tc_nat))),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f982,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X18,X17,tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).

fof(f13613,plain,
    spl0_767,
    inference(avatar_split_clause,[],[f893,f13611]) ).

fof(f13611,plain,
    ( spl0_767
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f893,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

fof(f13609,plain,
    spl0_766,
    inference(avatar_split_clause,[],[f890,f13607]) ).

fof(f13607,plain,
    ( spl0_766
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f890,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

fof(f13605,plain,
    spl0_765,
    inference(avatar_split_clause,[],[f889,f13603]) ).

fof(f13603,plain,
    ( spl0_765
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f889,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

fof(f13585,plain,
    ( spl0_764
    | spl0_717
    | ~ spl0_341
    | ~ spl0_658 ),
    inference(avatar_split_clause,[],[f10596,f9569,f4074,f11320,f13582]) ).

fof(f4074,plain,
    ( spl0_341
  <=> ! [X18,X17] :
        ( X17 = X18
        | ~ c_lessequals(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f10596,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | c_HOL_Oord__class_Oless(v_i____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_341
    | ~ spl0_658 ),
    inference(resolution,[],[f9571,f4075]) ).

fof(f4075,plain,
    ( ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | X17 = X18
        | c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f4074]) ).

fof(f13580,plain,
    spl0_763,
    inference(avatar_split_clause,[],[f880,f13578]) ).

fof(f13578,plain,
    ( spl0_763
  <=> ! [X2,X0,X3] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f880,axiom,
    ! [X2,X3,X0] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

fof(f13576,plain,
    spl0_762,
    inference(avatar_split_clause,[],[f877,f13574]) ).

fof(f13574,plain,
    ( spl0_762
  <=> ! [X45,X0,X19] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),c_HOL_Ouminus__class_Ouminus(X19,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f877,axiom,
    ! [X0,X19,X45] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),c_HOL_Ouminus__class_Ouminus(X19,X0)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X45),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).

fof(f13572,plain,
    spl0_761,
    inference(avatar_split_clause,[],[f876,f13570]) ).

fof(f13570,plain,
    ( spl0_761
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X3,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f876,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X3,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

fof(f13568,plain,
    spl0_760,
    inference(avatar_split_clause,[],[f875,f13566]) ).

fof(f13566,plain,
    ( spl0_760
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f875,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),c_HOL_Ouminus__class_Ouminus(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

fof(f13564,plain,
    spl0_759,
    inference(avatar_split_clause,[],[f870,f13562]) ).

fof(f13562,plain,
    ( spl0_759
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f870,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oabs__class_Oabs(X2,X0)),c_HOL_Oabs__class_Oabs(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).

fof(f13560,plain,
    spl0_758,
    inference(avatar_split_clause,[],[f857,f13558]) ).

fof(f13558,plain,
    ( spl0_758
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f857,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

fof(f13556,plain,
    spl0_757,
    inference(avatar_split_clause,[],[f762,f13554]) ).

fof(f13554,plain,
    ( spl0_757
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f762,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).

fof(f13552,plain,
    spl0_756,
    inference(avatar_split_clause,[],[f700,f13550]) ).

fof(f13550,plain,
    ( spl0_756
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0)),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f700,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0)),X1) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

fof(f13548,plain,
    spl0_755,
    inference(avatar_split_clause,[],[f608,f13546]) ).

fof(f608,axiom,
    ! [X18,X17,X23] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17)),X18),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).

fof(f13544,plain,
    spl0_754,
    inference(avatar_split_clause,[],[f573,f13542]) ).

fof(f13542,plain,
    ( spl0_754
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Odiv(X23,X17,tc_nat),c_Divides_Odiv__class_Odiv(X23,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f573,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_lessequals(c_Divides_Odiv__class_Odiv(X23,X17,tc_nat),c_Divides_Odiv__class_Odiv(X23,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono2_0) ).

fof(f13495,plain,
    spl0_753,
    inference(avatar_split_clause,[],[f317,f13493]) ).

fof(f13493,plain,
    ( spl0_753
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f317,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

fof(f13491,plain,
    spl0_752,
    inference(avatar_split_clause,[],[f268,f13489]) ).

fof(f13489,plain,
    ( spl0_752
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f268,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

fof(f13487,plain,
    spl0_751,
    inference(avatar_split_clause,[],[f115,f13485]) ).

fof(f13485,plain,
    ( spl0_751
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f115,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).

fof(f12397,plain,
    spl0_750,
    inference(avatar_split_clause,[],[f1959,f12395]) ).

fof(f12395,plain,
    ( spl0_750
  <=> ! [X2,X0] :
        ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1959,plain,
    ! [X2,X0] :
      ( c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2 ),
    inference(forward_demodulation,[],[f1554,f1837]) ).

fof(f1554,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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(f12393,plain,
    spl0_749,
    inference(avatar_split_clause,[],[f1929,f12391]) ).

fof(f12391,plain,
    ( spl0_749
  <=> ! [X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f1929,plain,
    ! [X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f1928,f267]) ).

fof(f267,axiom,
    ! [X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(c_Suc,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

fof(f1928,plain,
    ! [X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f1450,f1837]) ).

fof(f1450,axiom,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),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),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__div__2__gt__zero_0) ).

fof(f12389,plain,
    spl0_748,
    inference(avatar_split_clause,[],[f1894,f12387]) ).

fof(f12387,plain,
    ( spl0_748
  <=> ! [X0,X19] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f1894,plain,
    ! [X0,X19] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
    inference(forward_demodulation,[],[f1588,f1837]) ).

fof(f1588,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X19) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),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(f12385,plain,
    spl0_747,
    inference(avatar_split_clause,[],[f1888,f12383]) ).

fof(f12383,plain,
    ( spl0_747
  <=> ! [X2,X0] :
        ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_OrderedGroup_Omonoid__mult(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f1888,plain,
    ! [X2,X0] :
      ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_OrderedGroup_Omonoid__mult(X0) ),
    inference(forward_demodulation,[],[f1630,f1837]) ).

fof(f1630,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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(f12381,plain,
    spl0_746,
    inference(avatar_split_clause,[],[f1643,f12379]) ).

fof(f12379,plain,
    ( spl0_746
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f1643,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

fof(f12377,plain,
    ( spl0_658
    | ~ spl0_190
    | spl0_647 ),
    inference(avatar_split_clause,[],[f9351,f9304,f2940,f9569]) ).

fof(f12376,plain,
    spl0_745,
    inference(avatar_split_clause,[],[f1642,f12374]) ).

fof(f12374,plain,
    ( spl0_745
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f1642,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

fof(f12372,plain,
    spl0_744,
    inference(avatar_split_clause,[],[f1603,f12370]) ).

fof(f12370,plain,
    ( spl0_744
  <=> ! [X41,X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X41,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X41,X17,tc_nat),c_HOL_Ominus__class_Ominus(X41,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f1603,axiom,
    ! [X41,X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,X41,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X41,X17,tc_nat),c_HOL_Ominus__class_Ominus(X41,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

fof(f12368,plain,
    spl0_743,
    inference(avatar_split_clause,[],[f1536,f12366]) ).

fof(f12366,plain,
    ( spl0_743
  <=> ! [X17] : hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,X17))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f1536,axiom,
    ! [X17] : hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,X17))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).

fof(f12364,plain,
    spl0_742,
    inference(avatar_split_clause,[],[f1395,f12362]) ).

fof(f12362,plain,
    ( spl0_742
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f1395,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X23),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).

fof(f12360,plain,
    spl0_741,
    inference(avatar_split_clause,[],[f1394,f12358]) ).

fof(f12358,plain,
    ( spl0_741
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f1394,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

fof(f12356,plain,
    spl0_740,
    inference(avatar_split_clause,[],[f1353,f12354]) ).

fof(f12354,plain,
    ( spl0_740
  <=> ! [X2,X1,X3] :
        ( ~ c_lessequals(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f1353,axiom,
    ! [X2,X3,X1] :
      ( ~ c_lessequals(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

fof(f12352,plain,
    spl0_739,
    inference(avatar_split_clause,[],[f1247,f12350]) ).

fof(f12350,plain,
    ( spl0_739
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
        | c_Int_Onumber__class_Onumber__of(X47,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f1247,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
      | c_Int_Onumber__class_Onumber__of(X47,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nat__number__of_0) ).

fof(f12348,plain,
    spl0_738,
    inference(avatar_split_clause,[],[f1218,f12346]) ).

fof(f12346,plain,
    ( spl0_738
  <=> ! [X22,X24,X23] :
        ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f1218,axiom,
    ! [X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

fof(f12344,plain,
    spl0_737,
    inference(avatar_split_clause,[],[f1217,f12342]) ).

fof(f12342,plain,
    ( spl0_737
  <=> ! [X18,X17,X23] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f1217,axiom,
    ! [X18,X17,X23] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

fof(f12340,plain,
    spl0_736,
    inference(avatar_split_clause,[],[f1216,f12338]) ).

fof(f12338,plain,
    ( spl0_736
  <=> ! [X18,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f1216,axiom,
    ! [X18,X17,X23] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

fof(f12332,plain,
    spl0_735,
    inference(avatar_split_clause,[],[f1137,f12330]) ).

fof(f12330,plain,
    ( spl0_735
  <=> ! [X19,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X5,X0),X19,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f1137,axiom,
    ! [X2,X0,X19,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X5,X0),X19,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X19,X2,X0),X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).

fof(f12328,plain,
    spl0_734,
    inference(avatar_split_clause,[],[f398,f12326]) ).

fof(f12326,plain,
    ( spl0_734
  <=> ! [X2,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(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f398,axiom,
    ! [X2,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(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

fof(f12324,plain,
    spl0_733,
    inference(avatar_split_clause,[],[f370,f12322]) ).

fof(f12322,plain,
    ( spl0_733
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X1 = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f370,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X1 = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f12320,plain,
    spl0_732,
    inference(avatar_split_clause,[],[f369,f12318]) ).

fof(f12318,plain,
    ( spl0_732
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X1 = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f369,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X1 = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f12316,plain,
    spl0_731,
    inference(avatar_split_clause,[],[f368,f12314]) ).

fof(f12314,plain,
    ( spl0_731
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X1 = X3
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f368,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X1 = X3
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f12312,plain,
    spl0_730,
    inference(avatar_split_clause,[],[f361,f12310]) ).

fof(f12310,plain,
    ( spl0_730
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f361,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__leI_0) ).

fof(f12308,plain,
    spl0_729,
    inference(avatar_split_clause,[],[f344,f12306]) ).

fof(f12306,plain,
    ( spl0_729
  <=> ! [X2,X31,X33,X1,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X2),X1) = hAPP(hAPP(X31,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f344,axiom,
    ! [X31,X2,X29,X0,X1,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X2),X1) = hAPP(hAPP(X31,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).

fof(f12304,plain,
    spl0_728,
    inference(avatar_split_clause,[],[f327,f12302]) ).

fof(f12302,plain,
    ( spl0_728
  <=> ! [X2,X31,X33,X3,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X2),X3) = hAPP(hAPP(X32,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f327,axiom,
    ! [X31,X2,X3,X29,X0,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X2),X3) = hAPP(hAPP(X32,X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).

fof(f12300,plain,
    spl0_727,
    inference(avatar_split_clause,[],[f295,f12298]) ).

fof(f12298,plain,
    ( spl0_727
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Oring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X0),X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f295,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Oring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X0),X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).

fof(f12296,plain,
    spl0_726,
    inference(avatar_split_clause,[],[f140,f12294]) ).

fof(f12294,plain,
    ( spl0_726
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f140,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).

fof(f12292,plain,
    spl0_725,
    inference(avatar_split_clause,[],[f59,f12290]) ).

fof(f12290,plain,
    ( spl0_725
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f59,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

fof(f12288,plain,
    spl0_724,
    inference(avatar_split_clause,[],[f58,f12286]) ).

fof(f12286,plain,
    ( spl0_724
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f58,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X23),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

fof(f12284,plain,
    spl0_723,
    inference(avatar_split_clause,[],[f57,f12282]) ).

fof(f12282,plain,
    ( spl0_723
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f57,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

fof(f12280,plain,
    spl0_722,
    inference(avatar_split_clause,[],[f44,f12278]) ).

fof(f12278,plain,
    ( spl0_722
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f44,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).

fof(f12276,plain,
    spl0_721,
    inference(avatar_split_clause,[],[f43,f12274]) ).

fof(f12274,plain,
    ( spl0_721
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f43,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).

fof(f12272,plain,
    spl0_720,
    inference(avatar_split_clause,[],[f26,f12270]) ).

fof(f12270,plain,
    ( spl0_720
  <=> ! [X0,X17] :
        ( ~ class_Ring__and__Field_Osemiring__0(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f26,axiom,
    ! [X0,X17] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

fof(f12268,plain,
    spl0_719,
    inference(avatar_split_clause,[],[f20,f12266]) ).

fof(f12266,plain,
    ( spl0_719
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f20,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).

fof(f12215,plain,
    ( ~ spl0_131
    | spl0_718 ),
    inference(avatar_contradiction_clause,[],[f12207]) ).

fof(f12207,plain,
    ( $false
    | ~ spl0_131
    | spl0_718 ),
    inference(resolution,[],[f11711,f2667]) ).

fof(f2667,plain,
    ( ! [X19] : c_lessequals(X19,X19,tc_nat)
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f2666]) ).

fof(f2666,plain,
    ( spl0_131
  <=> ! [X19] : c_lessequals(X19,X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f11711,plain,
    ( ~ c_lessequals(v_i____,v_i____,tc_nat)
    | spl0_718 ),
    inference(avatar_component_clause,[],[f11709]) ).

fof(f11712,plain,
    ( ~ spl0_718
    | ~ spl0_215
    | ~ spl0_574
    | spl0_647
    | ~ spl0_658
    | ~ spl0_659 ),
    inference(avatar_split_clause,[],[f11339,f10394,f9569,f9304,f8150,f3075,f11709]) ).

fof(f11339,plain,
    ( ~ c_lessequals(v_i____,v_i____,tc_nat)
    | ~ spl0_215
    | ~ spl0_574
    | spl0_647
    | ~ spl0_658
    | ~ spl0_659 ),
    inference(forward_demodulation,[],[f9306,f11327]) ).

fof(f11323,plain,
    ( spl0_716
    | spl0_717
    | ~ spl0_341
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f9751,f9304,f4074,f11320,f11316]) ).

fof(f9751,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = v_i____
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_341
    | ~ spl0_647 ),
    inference(resolution,[],[f9305,f4075]) ).

fof(f10781,plain,
    spl0_715,
    inference(avatar_split_clause,[],[f1991,f10779]) ).

fof(f10779,plain,
    ( spl0_715
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
        | c_HOL_Oone__class_Oone(tc_nat) = X17
        | c_HOL_Oone__class_Oone(tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f1991,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
      | c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Oone__class_Oone(tc_nat) = X18 ),
    inference(forward_demodulation,[],[f1990,f582]) ).

fof(f1990,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Oone__class_Oone(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    inference(forward_demodulation,[],[f1989,f582]) ).

fof(f1989,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    inference(forward_demodulation,[],[f124,f582]) ).

fof(f124,axiom,
    ! [X18,X17] :
      ( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

fof(f10777,plain,
    spl0_714,
    inference(avatar_split_clause,[],[f1984,f10775]) ).

fof(f10775,plain,
    ( spl0_714
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
        | c_HOL_Oone__class_Oone(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f1984,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
      | c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1983,f582]) ).

fof(f1983,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    inference(forward_demodulation,[],[f391,f582]) ).

fof(f391,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

fof(f10773,plain,
    spl0_713,
    inference(avatar_split_clause,[],[f1982,f10771]) ).

fof(f10771,plain,
    ( spl0_713
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
        | c_HOL_Oone__class_Oone(tc_nat) = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f1982,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
      | c_HOL_Oone__class_Oone(tc_nat) = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ),
    inference(forward_demodulation,[],[f1981,f582]) ).

fof(f1981,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    inference(forward_demodulation,[],[f465,f582]) ).

fof(f465,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

fof(f10769,plain,
    spl0_712,
    inference(avatar_split_clause,[],[f1980,f10767]) ).

fof(f10767,plain,
    ( spl0_712
  <=> ! [X18,X19] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X18)
        | c_HOL_Oone__class_Oone(tc_nat) = X19
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1980,plain,
    ! [X18,X19] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X18)
      | c_HOL_Oone__class_Oone(tc_nat) = X19
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ),
    inference(forward_demodulation,[],[f1979,f582]) ).

fof(f1979,plain,
    ! [X18,X19] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X19
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X18) ),
    inference(forward_demodulation,[],[f1369,f582]) ).

fof(f1369,axiom,
    ! [X18,X19] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(c_Suc,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),X19),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).

fof(f10765,plain,
    spl0_711,
    inference(avatar_split_clause,[],[f1973,f10763]) ).

fof(f10763,plain,
    ( spl0_711
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f1973,plain,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18 ),
    inference(forward_demodulation,[],[f586,f582]) ).

fof(f586,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

fof(f10761,plain,
    spl0_710,
    inference(avatar_split_clause,[],[f1905,f10759]) ).

fof(f1905,plain,
    ! [X17] :
      ( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat) ),
    inference(forward_demodulation,[],[f1518,f1837]) ).

fof(f1518,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | 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)),c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1(X17))) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_0) ).

fof(f10757,plain,
    spl0_709,
    inference(avatar_split_clause,[],[f1855,f10755]) ).

fof(f1855,plain,
    ! [X18,X17] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),tc_nat),
    inference(forward_demodulation,[],[f1418,f1669]) ).

fof(f1418,axiom,
    ! [X18,X17] : c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__div__equality_H_0) ).

fof(f10753,plain,
    spl0_708,
    inference(avatar_split_clause,[],[f1436,f10751]) ).

fof(f10751,plain,
    ( spl0_708
  <=> ! [X24,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X23),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f10733,plain,
    spl0_707,
    inference(avatar_split_clause,[],[f1429,f10731]) ).

fof(f10731,plain,
    ( spl0_707
  <=> ! [X18,X17] :
        ( X17 = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X17,X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f1429,axiom,
    ! [X18,X17] :
      ( X17 = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X17,X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

fof(f10729,plain,
    spl0_706,
    inference(avatar_split_clause,[],[f1412,f10727]) ).

fof(f1412,axiom,
    ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_H_0) ).

fof(f10725,plain,
    spl0_705,
    inference(avatar_split_clause,[],[f1411,f10723]) ).

fof(f1411,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)) = c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X18,X17,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__div__cancel_0) ).

fof(f10721,plain,
    spl0_704,
    inference(avatar_split_clause,[],[f1398,f10719]) ).

fof(f10719,plain,
    ( spl0_704
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f1398,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

fof(f10717,plain,
    spl0_703,
    inference(avatar_split_clause,[],[f1364,f10715]) ).

fof(f10715,plain,
    ( spl0_703
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f1364,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

fof(f10713,plain,
    spl0_702,
    inference(avatar_split_clause,[],[f1350,f10711]) ).

fof(f1350,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X17,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),X17,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

fof(f10709,plain,
    spl0_701,
    inference(avatar_split_clause,[],[f1277,f10707]) ).

fof(f10707,plain,
    ( spl0_701
  <=> ! [X2,X1,X3] : c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X1),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f10705,plain,
    spl0_700,
    inference(avatar_split_clause,[],[f1148,f10703]) ).

fof(f10703,plain,
    ( spl0_700
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(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_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f1148,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(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_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

fof(f10701,plain,
    spl0_699,
    inference(avatar_split_clause,[],[f1147,f10699]) ).

fof(f10699,plain,
    ( spl0_699
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1147,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

fof(f10697,plain,
    spl0_698,
    inference(avatar_split_clause,[],[f1087,f10695]) ).

fof(f10695,plain,
    ( spl0_698
  <=> ! [X18,X17] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X18)),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f1087,axiom,
    ! [X18,X17] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X18)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

fof(f10691,plain,
    ( spl0_697
    | ~ spl0_316
    | ~ spl0_658 ),
    inference(avatar_split_clause,[],[f10595,f9569,f3971,f10688]) ).

fof(f10686,plain,
    spl0_696,
    inference(avatar_split_clause,[],[f1086,f10684]) ).

fof(f1086,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(c_Suc,X17)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

fof(f10682,plain,
    spl0_695,
    inference(avatar_split_clause,[],[f1067,f10680]) ).

fof(f10680,plain,
    ( spl0_695
  <=> ! [X0,X19] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f1067,axiom,
    ! [X0,X19] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).

fof(f10678,plain,
    spl0_694,
    inference(avatar_split_clause,[],[f1031,f10676]) ).

fof(f10676,plain,
    ( spl0_694
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f1031,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).

fof(f10674,plain,
    spl0_693,
    inference(avatar_split_clause,[],[f985,f10672]) ).

fof(f10672,plain,
    ( spl0_693
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f985,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nat__number__of_0) ).

fof(f10670,plain,
    spl0_692,
    inference(avatar_split_clause,[],[f965,f10668]) ).

fof(f10668,plain,
    ( spl0_692
  <=> ! [X0,X1] :
        ( ~ 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)),X1),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f965,axiom,
    ! [X0,X1] :
      ( ~ 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)),X1),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

fof(f10666,plain,
    spl0_691,
    inference(avatar_split_clause,[],[f961,f10664]) ).

fof(f10664,plain,
    ( spl0_691
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f961,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_Divides_Odiv__class_Odiv(X18,X17,tc_nat)),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_1) ).

fof(f10662,plain,
    spl0_690,
    inference(avatar_split_clause,[],[f774,f10660]) ).

fof(f10660,plain,
    ( spl0_690
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f774,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

fof(f10658,plain,
    spl0_689,
    inference(avatar_split_clause,[],[f773,f10656]) ).

fof(f10656,plain,
    ( spl0_689
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f773,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

fof(f10654,plain,
    spl0_688,
    inference(avatar_split_clause,[],[f767,f10652]) ).

fof(f10652,plain,
    ( spl0_688
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(X18,tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f767,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(X18,tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__less__mono__nat_0) ).

fof(f10650,plain,
    spl0_687,
    inference(avatar_split_clause,[],[f751,f10648]) ).

fof(f10648,plain,
    ( spl0_687
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X18,X17,tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f751,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X18,X17,tc_nat),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).

fof(f10646,plain,
    spl0_686,
    inference(avatar_split_clause,[],[f734,f10644]) ).

fof(f10644,plain,
    ( spl0_686
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f734,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

fof(f10642,plain,
    spl0_685,
    inference(avatar_split_clause,[],[f733,f10640]) ).

fof(f10640,plain,
    ( spl0_685
  <=> ! [X25,X0,X27] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X27,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f733,axiom,
    ! [X0,X27,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X27,X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X25),X27)) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

fof(f10638,plain,
    spl0_684,
    inference(avatar_split_clause,[],[f696,f10636]) ).

fof(f10636,plain,
    ( spl0_684
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f696,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).

fof(f10634,plain,
    spl0_683,
    inference(avatar_split_clause,[],[f600,f10632]) ).

fof(f10632,plain,
    ( spl0_683
  <=> ! [X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f600,axiom,
    ! [X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).

fof(f10630,plain,
    spl0_682,
    inference(avatar_split_clause,[],[f548,f10628]) ).

fof(f10628,plain,
    ( spl0_682
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_lessequals(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f548,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_lessequals(c_HOL_Oone__class_Oone(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

fof(f10626,plain,
    spl0_681,
    inference(avatar_split_clause,[],[f538,f10624]) ).

fof(f10624,plain,
    ( spl0_681
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f538,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

fof(f10622,plain,
    spl0_680,
    inference(avatar_split_clause,[],[f537,f10620]) ).

fof(f10620,plain,
    ( spl0_680
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f537,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).

fof(f10618,plain,
    spl0_679,
    inference(avatar_split_clause,[],[f521,f10616]) ).

fof(f10616,plain,
    ( spl0_679
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f521,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

fof(f10614,plain,
    spl0_678,
    inference(avatar_split_clause,[],[f520,f10612]) ).

fof(f10612,plain,
    ( spl0_678
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f520,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

fof(f10610,plain,
    spl0_677,
    inference(avatar_split_clause,[],[f458,f10608]) ).

fof(f10608,plain,
    ( spl0_677
  <=> ! [X18,X17] :
        ( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) != X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f458,axiom,
    ! [X18,X17] :
      ( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)) != X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

fof(f10593,plain,
    spl0_676,
    inference(avatar_split_clause,[],[f425,f10591]) ).

fof(f10591,plain,
    ( spl0_676
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ class_OrderedGroup_Omonoid__mult(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f425,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ class_OrderedGroup_Omonoid__mult(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).

fof(f10589,plain,
    spl0_675,
    inference(avatar_split_clause,[],[f421,f10587]) ).

fof(f10587,plain,
    ( spl0_675
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f421,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

fof(f10585,plain,
    spl0_674,
    inference(avatar_split_clause,[],[f371,f10583]) ).

fof(f10583,plain,
    ( spl0_674
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f371,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).

fof(f10581,plain,
    spl0_673,
    inference(avatar_split_clause,[],[f209,f10579]) ).

fof(f10579,plain,
    ( spl0_673
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f209,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

fof(f10577,plain,
    spl0_672,
    inference(avatar_split_clause,[],[f208,f10575]) ).

fof(f10575,plain,
    ( spl0_672
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f208,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

fof(f10573,plain,
    spl0_671,
    inference(avatar_split_clause,[],[f207,f10571]) ).

fof(f10571,plain,
    ( spl0_671
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f207,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),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(f10569,plain,
    spl0_670,
    inference(avatar_split_clause,[],[f206,f10567]) ).

fof(f10567,plain,
    ( spl0_670
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f206,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),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(f10565,plain,
    spl0_669,
    inference(avatar_split_clause,[],[f171,f10563]) ).

fof(f10563,plain,
    ( spl0_669
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Oinverse(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f171,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Oinverse(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).

fof(f10561,plain,
    spl0_668,
    inference(avatar_split_clause,[],[f170,f10559]) ).

fof(f10559,plain,
    ( spl0_668
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f170,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).

fof(f10557,plain,
    spl0_667,
    inference(avatar_split_clause,[],[f169,f10555]) ).

fof(f10555,plain,
    ( spl0_667
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f169,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oinverse__class_Oinverse(X2,X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).

fof(f10549,plain,
    spl0_666,
    inference(avatar_split_clause,[],[f148,f10547]) ).

fof(f10547,plain,
    ( spl0_666
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f148,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

fof(f10545,plain,
    spl0_665,
    inference(avatar_split_clause,[],[f146,f10543]) ).

fof(f10543,plain,
    ( spl0_665
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f146,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(f10541,plain,
    spl0_664,
    inference(avatar_split_clause,[],[f145,f10539]) ).

fof(f10539,plain,
    ( spl0_664
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f145,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(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),X2),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(f10537,plain,
    spl0_663,
    inference(avatar_split_clause,[],[f88,f10535]) ).

fof(f10535,plain,
    ( spl0_663
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X3,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f88,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X3,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).

fof(f10533,plain,
    spl0_662,
    inference(avatar_split_clause,[],[f87,f10531]) ).

fof(f10531,plain,
    ( spl0_662
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X3,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f87,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X3,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).

fof(f10529,plain,
    spl0_661,
    inference(avatar_split_clause,[],[f72,f10527]) ).

fof(f10527,plain,
    ( spl0_661
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X1,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f72,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X1,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

fof(f10525,plain,
    spl0_660,
    inference(avatar_split_clause,[],[f11,f10523]) ).

fof(f10523,plain,
    ( spl0_660
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f11,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ouminus__class_Ouminus(X2,X0)),X3)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

fof(f10397,plain,
    ( spl0_659
    | ~ spl0_316
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f9750,f9304,f3971,f10394]) ).

fof(f9572,plain,
    ( spl0_658
    | ~ spl0_190
    | spl0_647 ),
    inference(avatar_split_clause,[],[f9351,f9304,f2940,f9569]) ).

fof(f9347,plain,
    spl0_657,
    inference(avatar_split_clause,[],[f1926,f9345]) ).

fof(f9345,plain,
    ( spl0_657
  <=> ! [X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(X17,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f1926,plain,
    ! [X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(X17,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f1100,f1837]) ).

fof(f1100,axiom,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__2__gt__zero_0) ).

fof(f9343,plain,
    spl0_656,
    inference(avatar_split_clause,[],[f1869,f9341]) ).

fof(f9341,plain,
    ( spl0_656
  <=> ! [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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f1869,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)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1565,f1837]) ).

fof(f1565,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(f9339,plain,
    spl0_655,
    inference(avatar_split_clause,[],[f1858,f9337]) ).

fof(f1858,plain,
    ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X27),
    inference(forward_demodulation,[],[f1558,f1837]) ).

fof(f1558,axiom,
    ! [X27] : 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)),X27) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).

fof(f9335,plain,
    spl0_654,
    inference(avatar_split_clause,[],[f1856,f9333]) ).

fof(f9333,plain,
    ( spl0_654
  <=> ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f1856,plain,
    ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),
    inference(forward_demodulation,[],[f1559,f1837]) ).

fof(f1559,axiom,
    ! [X27] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X27) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),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_nat__mult__2__right_0) ).

fof(f9331,plain,
    spl0_653,
    inference(avatar_split_clause,[],[f1527,f9329]) ).

fof(f9329,plain,
    ( spl0_653
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X47,c_Int_OPls,tc_Int_Oint)
        | c_Int_Onumber__class_Onumber__of(X34,tc_nat) = c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f1527,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X47,c_Int_OPls,tc_Int_Oint)
      | c_Int_Onumber__class_Onumber__of(X34,tc_nat) = c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__nat__number__of_0) ).

fof(f9327,plain,
    spl0_652,
    inference(avatar_split_clause,[],[f1513,f9325]) ).

fof(f9325,plain,
    ( spl0_652
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OPls,X47,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f1513,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OPls,X47,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_2) ).

fof(f9323,plain,
    spl0_651,
    inference(avatar_split_clause,[],[f1512,f9321]) ).

fof(f9321,plain,
    ( spl0_651
  <=> ! [X34,X47] :
        ( ~ c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OPls,X47,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f1512,axiom,
    ! [X47,X34] :
      ( ~ c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OPls,X47,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_0) ).

fof(f9319,plain,
    spl0_650,
    inference(avatar_split_clause,[],[f1446,f9317]) ).

fof(f1446,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_2) ).

fof(f9315,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f1363,f9313]) ).

fof(f9313,plain,
    ( spl0_649
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f1363,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).

fof(f9311,plain,
    ( ~ spl0_647
    | spl0_648
    | ~ spl0_455
    | ~ spl0_605 ),
    inference(avatar_split_clause,[],[f9086,f8290,f5390,f9308,f9304]) ).

fof(f9308,plain,
    ( spl0_648
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f5390,plain,
    ( spl0_455
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | c_lessequals(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f8290,plain,
    ( spl0_605
  <=> ! [X18,X17] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f9086,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),v_i____,tc_nat)
    | ~ spl0_455
    | ~ spl0_605 ),
    inference(resolution,[],[f8291,f5391]) ).

fof(f5391,plain,
    ( ! [X0] :
        ( c_lessequals(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_455 ),
    inference(avatar_component_clause,[],[f5390]) ).

fof(f8291,plain,
    ( ! [X18,X17] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) )
    | ~ spl0_605 ),
    inference(avatar_component_clause,[],[f8290]) ).

fof(f9302,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f1362,f9300]) ).

fof(f9300,plain,
    ( spl0_646
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f1362,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).

fof(f9298,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f1361,f9296]) ).

fof(f9296,plain,
    ( spl0_645
  <=> ! [X2,X28,X3] :
        ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ hBOOL(hAPP(X28,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f1361,axiom,
    ! [X2,X3,X28] :
      ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
      | hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X28,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

fof(f9294,plain,
    spl0_644,
    inference(avatar_split_clause,[],[f1360,f9292]) ).

fof(f9292,plain,
    ( spl0_644
  <=> ! [X24,X22,X23] :
        ( ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f1360,axiom,
    ! [X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

fof(f9290,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f1359,f9288]) ).

fof(f9288,plain,
    ( spl0_643
  <=> ! [X24,X22,X23] :
        ( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f1359,axiom,
    ! [X24,X22,X23] :
      ( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),X24,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

fof(f9286,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f1354,f9284]) ).

fof(f9284,plain,
    ( spl0_642
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f1354,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

fof(f9282,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f1334,f9280]) ).

fof(f1334,axiom,
    ! [X19] : c_Fact_Ofact__class_Ofact(hAPP(c_Suc,X19),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X19)),c_Fact_Ofact__class_Ofact(X19,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fact_Ofact__Suc_0) ).

fof(f9278,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f1262,f9276]) ).

fof(f9276,plain,
    ( spl0_640
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),X17,tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f1262,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),X17,tc_nat) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).

fof(f9274,plain,
    spl0_639,
    inference(avatar_split_clause,[],[f1261,f9272]) ).

fof(f9272,plain,
    ( spl0_639
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),X17,tc_nat) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f1261,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),X18),X17,tc_nat) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).

fof(f9270,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f1167,f9268]) ).

fof(f9268,plain,
    ( spl0_638
  <=> ! [X0,X17] :
        ( ~ 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,X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f1167,axiom,
    ! [X0,X17] :
      ( ~ 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,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

fof(f9266,plain,
    spl0_637,
    inference(avatar_split_clause,[],[f1164,f9264]) ).

fof(f9264,plain,
    ( spl0_637
  <=> ! [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_637])]) ).

fof(f1164,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(f9258,plain,
    spl0_636,
    inference(avatar_split_clause,[],[f1153,f9256]) ).

fof(f9256,plain,
    ( spl0_636
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(X19,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1153,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(X19,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I4_J_1) ).

fof(f9254,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f1152,f9252]) ).

fof(f9252,plain,
    ( spl0_635
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(X19,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f1152,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(X19,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I4_J_0) ).

fof(f9250,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f1151,f9248]) ).

fof(f9248,plain,
    ( spl0_634
  <=> ! [X25,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X25,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f1151,axiom,
    ! [X0,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X25,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I2_J_1) ).

fof(f9246,plain,
    spl0_633,
    inference(avatar_split_clause,[],[f1150,f9244]) ).

fof(f9244,plain,
    ( spl0_633
  <=> ! [X25,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X25,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f1150,axiom,
    ! [X0,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X25,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I2_J_0) ).

fof(f9242,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f1134,f9240]) ).

fof(f9240,plain,
    ( spl0_632
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f1134,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__number__of_0) ).

fof(f9238,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f1133,f9236]) ).

fof(f9236,plain,
    ( spl0_631
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f1133,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__number__of_1) ).

fof(f9234,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f1079,f9232]) ).

fof(f9232,plain,
    ( spl0_630
  <=> ! [X18,X17] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f1079,axiom,
    ! [X18,X17] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X18),X17,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X18,X17,tc_nat)),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

fof(f9230,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f729,f9228]) ).

fof(f9228,plain,
    ( spl0_629
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X19,X0) = c_HOL_Oinverse__class_Odivide(X19,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f729,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X19,X0) = c_HOL_Oinverse__class_Odivide(X19,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__minus1_0) ).

fof(f9226,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f708,f9224]) ).

fof(f9224,plain,
    ( spl0_628
  <=> ! [X0,X17] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),c_HOL_Ozero__class_Ozero(X0)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f708,axiom,
    ! [X0,X17] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),c_HOL_Ozero__class_Ozero(X0)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one_0) ).

fof(f9222,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f697,f9220]) ).

fof(f9220,plain,
    ( spl0_627
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f697,axiom,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).

fof(f9218,plain,
    ( ~ spl0_30
    | ~ spl0_626
    | ~ spl0_267
    | ~ spl0_610 ),
    inference(avatar_split_clause,[],[f9163,f8810,f3377,f9215,f2162]) ).

fof(f2162,plain,
    ( spl0_30
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f9215,plain,
    ( spl0_626
  <=> c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f3377,plain,
    ( spl0_267
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X25,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f8810,plain,
    ( spl0_610
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f9163,plain,
    ( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_267
    | ~ spl0_610 ),
    inference(resolution,[],[f8812,f3378]) ).

fof(f3378,plain,
    ( ! [X0,X19,X25] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | ~ c_lessequals(X25,X19,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_267 ),
    inference(avatar_component_clause,[],[f3377]) ).

fof(f8812,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_610 ),
    inference(avatar_component_clause,[],[f8810]) ).

fof(f9213,plain,
    spl0_625,
    inference(avatar_split_clause,[],[f593,f9211]) ).

fof(f9211,plain,
    ( spl0_625
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f593,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

fof(f9209,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f592,f9207]) ).

fof(f9207,plain,
    ( spl0_624
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = X3
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f592,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = X3
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).

fof(f9205,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f589,f9203]) ).

fof(f9203,plain,
    ( spl0_623
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X22,tc_nat)
        | c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f589,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X22,tc_nat)
      | c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

fof(f9201,plain,
    spl0_622,
    inference(avatar_split_clause,[],[f588,f9199]) ).

fof(f9199,plain,
    ( spl0_622
  <=> ! [X22,X24,X23] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X22,tc_nat)
        | ~ c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f588,axiom,
    ! [X24,X22,X23] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X24,X23,tc_nat),X22,tc_nat)
      | ~ c_lessequals(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X23),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

fof(f9197,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f457,f9195]) ).

fof(f9195,plain,
    ( spl0_621
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X23,X17,tc_nat)
        | c_lessequals(X18,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f457,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X23,X17,tc_nat)
      | c_lessequals(X18,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

fof(f9193,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f366,f9191]) ).

fof(f9191,plain,
    ( spl0_620
  <=> ! [X25,X27,X19] :
        ( X25 = X27
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f366,axiom,
    ! [X19,X27,X25] :
      ( X25 = X27
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

fof(f9189,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f364,f9187]) ).

fof(f9187,plain,
    ( spl0_619
  <=> ! [X18,X17,X23] :
        ( X17 = X18
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f364,axiom,
    ! [X18,X17,X23] :
      ( X17 = X18
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

fof(f9185,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f231,f9183]) ).

fof(f9183,plain,
    ( spl0_618
  <=> ! [X2,X0,X19] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2) != X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f231,axiom,
    ! [X2,X0,X19] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2) != X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

fof(f9181,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f223,f9179]) ).

fof(f9179,plain,
    ( spl0_617
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f223,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
      | ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).

fof(f9177,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f210,f9175]) ).

fof(f9175,plain,
    ( spl0_616
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f210,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X17,X18,tc_nat)
      | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

fof(f9154,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f138,f9152]) ).

fof(f9152,plain,
    ( spl0_615
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X2 = X3
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f138,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X2 = X3
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

fof(f9150,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f114,f9148]) ).

fof(f9148,plain,
    ( spl0_614
  <=> ! [X0,X19] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f114,axiom,
    ! [X0,X19] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,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)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).

fof(f9146,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f103,f9144]) ).

fof(f9144,plain,
    ( spl0_613
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Oinverse__class_Oinverse(X2,X0) = X3
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f103,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Oinverse__class_Oinverse(X2,X0) = X3
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).

fof(f9142,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f19,f9140]) ).

fof(f9140,plain,
    ( spl0_612
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f19,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

fof(f9138,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f18,f9136]) ).

fof(f9136,plain,
    ( spl0_611
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) = c_Divides_Odiv__class_Omod(X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f18,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) = c_Divides_Odiv__class_Omod(X2,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

fof(f9067,plain,
    ( ~ spl0_138
    | spl0_609 ),
    inference(avatar_contradiction_clause,[],[f9062]) ).

fof(f9062,plain,
    ( $false
    | ~ spl0_138
    | spl0_609 ),
    inference(resolution,[],[f8808,f2699]) ).

fof(f8808,plain,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat)
    | spl0_609 ),
    inference(avatar_component_clause,[],[f8806]) ).

fof(f8806,plain,
    ( spl0_609
  <=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f8813,plain,
    ( ~ spl0_609
    | spl0_610
    | ~ spl0_551
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f8526,f8190,f7312,f8810,f8806]) ).

fof(f7312,plain,
    ( spl0_551
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f8190,plain,
    ( spl0_584
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f8526,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat)
    | ~ spl0_551
    | ~ spl0_584 ),
    inference(resolution,[],[f8191,f7313]) ).

fof(f7313,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_551 ),
    inference(avatar_component_clause,[],[f7312]) ).

fof(f8191,plain,
    ( ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) )
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f8190]) ).

fof(f8394,plain,
    ( spl0_608
    | ~ spl0_131
    | ~ spl0_583 ),
    inference(avatar_split_clause,[],[f8313,f8186,f2666,f8391]) ).

fof(f8391,plain,
    ( spl0_608
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(v_i____,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f8186,plain,
    ( spl0_583
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f8313,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(v_i____,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_131
    | ~ spl0_583 ),
    inference(resolution,[],[f8187,f2667]) ).

fof(f8187,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) )
    | ~ spl0_583 ),
    inference(avatar_component_clause,[],[f8186]) ).

fof(f8300,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f1976,f8298]) ).

fof(f1976,plain,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1975,f1837]) ).

fof(f1975,plain,
    ! [X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | ~ c_HOL_Oord__class_Oless(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1567,f582]) ).

fof(f1567,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X17
      | ~ c_HOL_Oord__class_Oless(X17,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(f8296,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f1948,f8294]) ).

fof(f8294,plain,
    ( spl0_606
  <=> ! [X18,X17] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f1948,plain,
    ! [X18,X17] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat) ),
    inference(forward_demodulation,[],[f1947,f582]) ).

fof(f1947,plain,
    ! [X18,X17] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1256,f582]) ).

fof(f1256,axiom,
    ! [X18,X17] :
      ( c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

fof(f8292,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f1946,f8290]) ).

fof(f1946,plain,
    ! [X18,X17] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat)
      | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat) ),
    inference(forward_demodulation,[],[f1945,f582]) ).

fof(f1945,plain,
    ! [X18,X17] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X17,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1257,f582]) ).

fof(f1257,axiom,
    ! [X18,X17] :
      ( c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X17,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

fof(f8288,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f1941,f8286]) ).

fof(f8286,plain,
    ( spl0_604
  <=> ! [X22,X17] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X22,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f1941,plain,
    ! [X17,X22] :
      ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X22,tc_nat) ),
    inference(forward_demodulation,[],[f1940,f582]) ).

fof(f1940,plain,
    ! [X17,X22] :
      ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X22,tc_nat)
      | c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) ),
    inference(forward_demodulation,[],[f1445,f582]) ).

fof(f1445,axiom,
    ! [X17,X22] :
      ( ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X22,tc_nat)
      | c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X22),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__one__le__power_0) ).

fof(f8276,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f1887,f8274]) ).

fof(f8274,plain,
    ( spl0_603
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Osemiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f1887,plain,
    ! [X0] :
      ( c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Osemiring__1(X0) ),
    inference(forward_demodulation,[],[f1555,f1837]) ).

fof(f1555,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(f8272,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f1886,f8270]) ).

fof(f8270,plain,
    ( spl0_602
  <=> ! [X0] :
        ( c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Osemiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f1886,plain,
    ! [X0] :
      ( c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oone__class_Oone(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Osemiring__1(X0) ),
    inference(forward_demodulation,[],[f1552,f1837]) ).

fof(f1552,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(f8268,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f1868,f8266]) ).

fof(f8266,plain,
    ( spl0_601
  <=> ! [X2,X0] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f1868,plain,
    ! [X2,X0] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1378,f1837]) ).

fof(f1378,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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__le__power2_0) ).

fof(f8264,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f1867,f8262]) ).

fof(f8262,plain,
    ( spl0_600
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f1867,plain,
    ! [X0] :
      ( c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1556,f1837]) ).

fof(f1556,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(f8260,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f1866,f8258]) ).

fof(f8258,plain,
    ( spl0_599
  <=> ! [X2,X0] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f1866,plain,
    ! [X2,X0] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(forward_demodulation,[],[f1566,f1837]) ).

fof(f1566,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),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(f8256,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f1853,f8254]) ).

fof(f1853,plain,
    ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X17),
    inference(forward_demodulation,[],[f1547,f1837]) ).

fof(f1547,axiom,
    ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).

fof(f8252,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f1852,f8250]) ).

fof(f8250,plain,
    ( spl0_597
  <=> ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f1852,plain,
    ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),
    inference(forward_demodulation,[],[f1546,f1837]) ).

fof(f1546,axiom,
    ! [X17] : hAPP(c_Suc,hAPP(c_Suc,X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),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_add__2__eq__Suc_H_0) ).

fof(f8248,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f1688,f8246]) ).

fof(f8246,plain,
    ( spl0_596
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | hAPP(c_Suc,X18) = X17
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f1688,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | hAPP(c_Suc,X18) = X17
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f8244,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f1684,f8242]) ).

fof(f1684,axiom,
    ! [X24,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X24,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X23,tc_nat),X24,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

fof(f8240,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f1670,f8238]) ).

fof(f1670,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f8228,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f1504,f8226]) ).

fof(f8226,plain,
    ( spl0_593
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f1504,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__numeral__1_0) ).

fof(f8224,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f1491,f8222]) ).

fof(f8222,plain,
    ( spl0_592
  <=> ! [X25,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(c_Int_OPls,X25,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f1491,axiom,
    ! [X0,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(c_Int_OPls,X25,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I1_J_0) ).

fof(f8220,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f1490,f8218]) ).

fof(f8218,plain,
    ( spl0_591
  <=> ! [X25,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(c_Int_OPls,X25,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f1490,axiom,
    ! [X0,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(c_Int_OPls,X25,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I1_J_1) ).

fof(f8216,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f1489,f8214]) ).

fof(f8214,plain,
    ( spl0_590
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oord__class_Oless(X19,c_Int_OPls,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f1489,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oord__class_Oless(X19,c_Int_OPls,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I3_J_0) ).

fof(f8212,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f1488,f8210]) ).

fof(f8210,plain,
    ( spl0_589
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_HOL_Oord__class_Oless(X19,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f1488,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_HOL_Oord__class_Oless(X19,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X19,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I3_J_1) ).

fof(f8208,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f1374,f8206]) ).

fof(f8206,plain,
    ( spl0_588
  <=> ! [X17,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_Power_Opower__class_Opower(tc_nat),X19),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1374,axiom,
    ! [X19,X17] :
      ( ~ 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_Power_Opower__class_Opower(tc_nat),X19),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_2) ).

fof(f8204,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f1365,f8202]) ).

fof(f8202,plain,
    ( spl0_587
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f1365,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

fof(f8200,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f1351,f8198]) ).

fof(f8198,plain,
    ( spl0_586
  <=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,hAPP(c_Suc,X17),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f1351,axiom,
    ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,hAPP(c_Suc,X17),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

fof(f8196,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f1344,f8194]) ).

fof(f8194,plain,
    ( spl0_585
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f1344,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

fof(f8192,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f1343,f8190]) ).

fof(f1343,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

fof(f8188,plain,
    ( spl0_583
    | ~ spl0_315
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f7572,f7312,f3967,f8186]) ).

fof(f7572,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_315
    | ~ spl0_551 ),
    inference(forward_demodulation,[],[f7546,f1277]) ).

fof(f7546,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) )
    | ~ spl0_315
    | ~ spl0_551 ),
    inference(resolution,[],[f7313,f3968]) ).

fof(f8184,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f1212,f8182]) ).

fof(f8182,plain,
    ( spl0_582
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f1212,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

fof(f8180,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f1163,f8178]) ).

fof(f8178,plain,
    ( spl0_581
  <=> ! [X20,X0] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X20,X0),X0)
        | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1163,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X20,X0),X0)
      | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_0) ).

fof(f8176,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f1162,f8174]) ).

fof(f8174,plain,
    ( spl0_580
  <=> ! [X20,X0] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X20,X0),X0)
        | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1162,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(X20,X0),X0)
      | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X20),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit0_1) ).

fof(f8172,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f1089,f8170]) ).

fof(f8170,plain,
    ( spl0_579
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | hAPP(c_Suc,X17) = X18
        | ~ c_lessequals(X18,hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f1089,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | hAPP(c_Suc,X17) = X18
      | ~ c_lessequals(X18,hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

fof(f8168,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f1066,f8166]) ).

fof(f8166,plain,
    ( spl0_578
  <=> ! [X0,X19] :
        ( ~ 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(X19,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f1066,axiom,
    ! [X0,X19] :
      ( ~ 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(X19,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).

fof(f8164,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f1058,f8162]) ).

fof(f8162,plain,
    ( spl0_577
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f1058,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).

fof(f8160,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f1036,f8158]) ).

fof(f8158,plain,
    ( spl0_576
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f1036,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).

fof(f8156,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f765,f8154]) ).

fof(f8154,plain,
    ( spl0_575
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Oinverse(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f765,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(X2,X3,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oinverse__class_Oinverse(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).

fof(f8152,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f746,f8150]) ).

fof(f746,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X17,X18,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat)) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

fof(f8148,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f728,f8146]) ).

fof(f8146,plain,
    ( spl0_573
  <=> ! [X31,X33,X19,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,X19),c_HOL_Oone__class_Oone(tc_nat)) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f728,axiom,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),c_HOL_Oone__class_Oone(tc_nat)) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I33_J_0) ).

fof(f8144,plain,
    ( spl0_572
    | ~ spl0_239
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f7550,f7312,f3172,f8142]) ).

fof(f3172,plain,
    ( spl0_239
  <=> ! [X22,X24] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X22),X22,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f7550,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat)
    | ~ spl0_239
    | ~ spl0_551 ),
    inference(resolution,[],[f7313,f3173]) ).

fof(f3173,plain,
    ( ! [X24,X22] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X22),X22,tc_nat)
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f3172]) ).

fof(f8140,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f605,f8138]) ).

fof(f8138,plain,
    ( spl0_571
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f605,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

fof(f8136,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f564,f8134]) ).

fof(f8134,plain,
    ( spl0_570
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f564,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f8132,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f561,f8130]) ).

fof(f8130,plain,
    ( spl0_569
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f561,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(f8128,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f447,f8126]) ).

fof(f447,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__num__iff_1) ).

fof(f8124,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f446,f8122]) ).

fof(f8122,plain,
    ( spl0_567
  <=> ! [X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f446,axiom,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__num__iff_0) ).

fof(f8120,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f423,f8118]) ).

fof(f8118,plain,
    ( spl0_566
  <=> ! [X0,X17,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f423,axiom,
    ! [X0,X19,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).

fof(f8116,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f422,f8114]) ).

fof(f8114,plain,
    ( spl0_565
  <=> ! [X25,X0,X19] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X19,X0),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X19,X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f422,axiom,
    ! [X0,X19,X25] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X19,X0),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X19,X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).

fof(f8112,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f315,f8110]) ).

fof(f8110,plain,
    ( spl0_564
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X2,X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f315,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X2,X3,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ouminus__class_Ouminus(X3,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

fof(f8108,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f314,f8106]) ).

fof(f8106,plain,
    ( spl0_563
  <=> ! [X25,X0,X19] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ominus__class_Ominus(X19,X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ouminus__class_Ouminus(X25,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f314,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ominus__class_Ominus(X19,X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ouminus__class_Ouminus(X25,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

fof(f8104,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f313,f8102]) ).

fof(f8102,plain,
    ( spl0_562
  <=> ! [X25,X0,X19] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X19,X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ouminus__class_Ouminus(X25,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f313,axiom,
    ! [X0,X19,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X19,X25,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ouminus__class_Ouminus(X25,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).

fof(f8100,plain,
    ( spl0_561
    | ~ spl0_238
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f7549,f7312,f3168,f8098]) ).

fof(f3168,plain,
    ( spl0_238
  <=> ! [X22,X24] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X22,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f7549,plain,
    ( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),X0),v_i____,tc_nat)
    | ~ spl0_238
    | ~ spl0_551 ),
    inference(resolution,[],[f7313,f3169]) ).

fof(f3169,plain,
    ( ! [X24,X22] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X22,tc_nat)
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f3168]) ).

fof(f8096,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f258,f8094]) ).

fof(f8094,plain,
    ( spl0_560
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f258,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X0),X0),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one__right_0) ).

fof(f8092,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f217,f8090]) ).

fof(f8090,plain,
    ( spl0_559
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f217,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

fof(f8088,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f159,f8086]) ).

fof(f8086,plain,
    ( spl0_558
  <=> ! [X31,X33,X19,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X29,X19),c_HOL_Ozero__class_Ozero(tc_nat)) = X30 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f159,axiom,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X29,X19),c_HOL_Ozero__class_Ozero(tc_nat)) = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).

fof(f8084,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f149,f8082]) ).

fof(f8082,plain,
    ( spl0_557
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f149,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

fof(f8080,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f139,f8078]) ).

fof(f8078,plain,
    ( spl0_556
  <=> ! [X0,X19] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X19,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f139,axiom,
    ! [X0,X19] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X19,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

fof(f8076,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f130,f8074]) ).

fof(f8074,plain,
    ( spl0_555
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f130,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).

fof(f8072,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f3,f8070]) ).

fof(f8070,plain,
    ( spl0_554
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X3,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f3,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X3,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).

fof(f7755,plain,
    ( ~ spl0_552
    | spl0_553
    | ~ spl0_139
    | ~ spl0_531 ),
    inference(avatar_split_clause,[],[f7674,f6618,f2702,f7753,f7749]) ).

fof(f7749,plain,
    ( spl0_552
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f7753,plain,
    ( spl0_553
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f6618,plain,
    ( spl0_531
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f7674,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
    | ~ spl0_139
    | ~ spl0_531 ),
    inference(resolution,[],[f6619,f2703]) ).

fof(f6619,plain,
    ( ! [X2,X3,X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
    | ~ spl0_531 ),
    inference(avatar_component_clause,[],[f6618]) ).

fof(f7314,plain,
    ( ~ spl0_32
    | spl0_551
    | ~ spl0_143
    | ~ spl0_508 ),
    inference(avatar_split_clause,[],[f7095,f6518,f2721,f7312,f2172]) ).

fof(f2172,plain,
    ( spl0_32
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f6518,plain,
    ( spl0_508
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X27,X25,X0)
        | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
        | c_HOL_Oord__class_Oless(X27,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f7095,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) )
    | ~ spl0_143
    | ~ spl0_508 ),
    inference(resolution,[],[f6519,f2723]) ).

fof(f6519,plain,
    ( ! [X0,X19,X27,X25] :
        ( ~ c_HOL_Oord__class_Oless(X25,X19,X0)
        | ~ c_lessequals(X27,X25,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X27,X19,X0) )
    | ~ spl0_508 ),
    inference(avatar_component_clause,[],[f6518]) ).

fof(f6966,plain,
    ( spl0_550
    | ~ spl0_351
    | ~ spl0_491 ),
    inference(avatar_split_clause,[],[f6923,f6445,f4274,f6964]) ).

fof(f6964,plain,
    ( spl0_550
  <=> ! [X0] :
        ( c_lessequals(c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f4274,plain,
    ( spl0_351
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f6445,plain,
    ( spl0_491
  <=> ! [X18,X17,X23] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Odiv(X18,X23,tc_nat),c_Divides_Odiv__class_Odiv(X17,X23,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f6923,plain,
    ( ! [X0] :
        ( c_lessequals(c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X0,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_351
    | ~ spl0_491 ),
    inference(forward_demodulation,[],[f6919,f1277]) ).

fof(f6919,plain,
    ( ! [X0] :
        ( c_lessequals(c_Divides_Odiv__class_Odiv(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(X0,v_i____,tc_nat) )
    | ~ spl0_351
    | ~ spl0_491 ),
    inference(superposition,[],[f6446,f4276]) ).

fof(f4276,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_351 ),
    inference(avatar_component_clause,[],[f4274]) ).

fof(f6446,plain,
    ( ! [X18,X17,X23] :
        ( c_lessequals(c_Divides_Odiv__class_Odiv(X18,X23,tc_nat),c_Divides_Odiv__class_Odiv(X17,X23,tc_nat),tc_nat)
        | ~ c_lessequals(X18,X17,tc_nat) )
    | ~ spl0_491 ),
    inference(avatar_component_clause,[],[f6445]) ).

fof(f6928,plain,
    ( spl0_549
    | ~ spl0_251
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f4236,f3971,f3233,f6925]) ).

fof(f6925,plain,
    ( spl0_549
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f3233,plain,
    ( spl0_251
  <=> c_lessequals(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f4236,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_251
    | ~ spl0_316 ),
    inference(resolution,[],[f3972,f3235]) ).

fof(f3235,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f3233]) ).

fof(f6704,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f1851,f6701]) ).

fof(f6701,plain,
    ( spl0_548
  <=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f1851,plain,
    c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)),tc_nat),
    inference(forward_demodulation,[],[f1622,f1837]) ).

fof(f1622,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(f6699,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f1850,f6697]) ).

fof(f1850,plain,
    ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X18),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = X18,
    inference(forward_demodulation,[],[f1319,f1837]) ).

fof(f1319,axiom,
    ! [X18] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X18),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__self__div__2_0) ).

fof(f6695,plain,
    ( spl0_546
    | ~ spl0_163
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4219,f3967,f2807,f6692]) ).

fof(f6692,plain,
    ( spl0_546
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f4219,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_163
    | ~ spl0_315 ),
    inference(resolution,[],[f3968,f2809]) ).

fof(f6690,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f1677,f6688]) ).

fof(f6688,plain,
    ( spl0_545
  <=> ! [X25,X0,X19] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X19 = X25
        | c_Int_Onumber__class_Onumber__of(X19,X0) != c_Int_Onumber__class_Onumber__of(X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f1677,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X19 = X25
      | c_Int_Onumber__class_Onumber__of(X19,X0) != c_Int_Onumber__class_Onumber__of(X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

fof(f6686,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f1674,f6684]) ).

fof(f6684,plain,
    ( spl0_544
  <=> ! [X0,X50,X49,X19] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X49 = X50
        | c_HOL_Ominus__class_Ominus(X49,X50,X0) != c_HOL_Ominus__class_Ominus(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f1674,axiom,
    ! [X50,X0,X49,X19] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X49 = X50
      | c_HOL_Ominus__class_Ominus(X49,X50,X0) != c_HOL_Ominus__class_Ominus(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

fof(f6682,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f1673,f6680]) ).

fof(f6680,plain,
    ( spl0_543
  <=> ! [X59,X58,X0,X56,X57,X28] : hAPP(c_COMBB(X28,X56,X57,X0,X58),X59) = hAPP(X28,hAPP(X56,X59)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f1673,axiom,
    ! [X28,X58,X0,X59,X56,X57] : hAPP(c_COMBB(X28,X56,X57,X0,X58),X59) = hAPP(X28,hAPP(X56,X59)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

fof(f6678,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f1672,f6676]) ).

fof(f6676,plain,
    ( spl0_542
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | ~ c_HOL_Oord__class_Oless(X25,X27,X0)
        | c_HOL_Oord__class_Oless(X19,X27,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f1672,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
      | ~ c_HOL_Oord__class_Oless(X25,X27,X0)
      | c_HOL_Oord__class_Oless(X19,X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f6674,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f1671,f6672]) ).

fof(f6672,plain,
    ( spl0_541
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X27,X25,X0)
        | c_HOL_Oord__class_Oless(X27,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f1671,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X27,X25,X0)
      | c_HOL_Oord__class_Oless(X27,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f6670,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f1646,f6668]) ).

fof(f6668,plain,
    ( spl0_540
  <=> ! [X22,X24,X23] :
        ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X22),X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f1646,axiom,
    ! [X24,X22,X23] :
      ( ~ c_HOL_Oord__class_Oless(X22,X24,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X22),X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f6666,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f1526,f6664]) ).

fof(f6664,plain,
    ( spl0_539
  <=> ! [X22,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,hAPP(c_Suc,X22),tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f1526,axiom,
    ! [X17,X22] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,hAPP(c_Suc,X22),tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

fof(f6662,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f1435,f6660]) ).

fof(f6660,plain,
    ( spl0_538
  <=> ! [X41,X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X41,X17,tc_nat),c_HOL_Ominus__class_Ominus(X41,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1435,axiom,
    ! [X41,X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X41,X17,tc_nat),c_HOL_Ominus__class_Ominus(X41,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

fof(f6658,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f1434,f6656]) ).

fof(f6656,plain,
    ( spl0_537
  <=> ! [X41,X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X18,X41,tc_nat),c_HOL_Ominus__class_Ominus(X17,X41,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1434,axiom,
    ! [X41,X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X18,X41,tc_nat),c_HOL_Ominus__class_Ominus(X17,X41,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

fof(f6654,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f1303,f6652]) ).

fof(f6652,plain,
    ( spl0_536
  <=> ! [X17] :
        ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1303,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).

fof(f6636,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f1302,f6634]) ).

fof(f6634,plain,
    ( spl0_535
  <=> ! [X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1302,axiom,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).

fof(f6632,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f1288,f6630]) ).

fof(f6630,plain,
    ( spl0_534
  <=> ! [X18] : c_lessequals(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X18)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1288,axiom,
    ! [X18] : c_lessequals(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X18)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).

fof(f6628,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f1276,f6626]) ).

fof(f6626,plain,
    ( spl0_533
  <=> ! [X25,X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f1276,axiom,
    ! [X19,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_0) ).

fof(f6624,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f1139,f6622]) ).

fof(f6622,plain,
    ( spl0_532
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f1139,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

fof(f6620,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f1138,f6618]) ).

fof(f1138,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

fof(f6616,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f1049,f6614]) ).

fof(f6614,plain,
    ( spl0_530
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | X19 = X25
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f1049,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | X19 = X25
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

fof(f6612,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f1023,f6610]) ).

fof(f6610,plain,
    ( spl0_529
  <=> ! [X0,X27] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X27,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f1023,axiom,
    ! [X0,X27] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X27,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).

fof(f6608,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f1022,f6606]) ).

fof(f6606,plain,
    ( spl0_528
  <=> ! [X0,X27] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X27,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X27) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f1022,axiom,
    ! [X0,X27] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X27,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1_0) ).

fof(f6604,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f988,f6602]) ).

fof(f6602,plain,
    ( spl0_527
  <=> ! [X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f988,axiom,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

fof(f6600,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f958,f6598]) ).

fof(f6598,plain,
    ( spl0_526
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(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),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f958,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(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),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

fof(f6596,plain,
    ( spl0_525
    | ~ spl0_316
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f5896,f5755,f3971,f6593]) ).

fof(f6593,plain,
    ( spl0_525
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f5755,plain,
    ( spl0_472
  <=> c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f5896,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),tc_nat)
    | ~ spl0_316
    | ~ spl0_472 ),
    inference(resolution,[],[f5757,f3972]) ).

fof(f5757,plain,
    ( c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),tc_nat)
    | ~ spl0_472 ),
    inference(avatar_component_clause,[],[f5755]) ).

fof(f6591,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f957,f6589]) ).

fof(f6589,plain,
    ( spl0_524
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(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),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f957,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(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),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

fof(f6587,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f943,f6585]) ).

fof(f6585,plain,
    ( spl0_523
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f943,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X3),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

fof(f6583,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f942,f6581]) ).

fof(f6581,plain,
    ( spl0_522
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f942,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X2),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

fof(f6579,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f938,f6577]) ).

fof(f6577,plain,
    ( spl0_521
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X25,X19,X0)
        | ~ c_lessequals(X27,X25,X0)
        | c_lessequals(X27,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f938,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X25,X19,X0)
      | ~ c_lessequals(X27,X25,X0)
      | c_lessequals(X27,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f6575,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f936,f6573]) ).

fof(f6573,plain,
    ( spl0_520
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X19,X25,X0)
        | ~ c_lessequals(X25,X27,X0)
        | c_lessequals(X19,X27,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f936,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X19,X25,X0)
      | ~ c_lessequals(X25,X27,X0)
      | c_lessequals(X19,X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f6571,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f775,f6569]) ).

fof(f6569,plain,
    ( spl0_519
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = X2
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f775,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
      | ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).

fof(f6567,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f732,f6565]) ).

fof(f6565,plain,
    ( spl0_518
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f732,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

fof(f6563,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f731,f6561]) ).

fof(f6561,plain,
    ( spl0_517
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f731,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

fof(f6559,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f677,f6557]) ).

fof(f6557,plain,
    ( spl0_516
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
        | c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f677,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
      | c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

fof(f6555,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f674,f6553]) ).

fof(f6553,plain,
    ( spl0_515
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f674,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

fof(f6544,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f665,f6542]) ).

fof(f6542,plain,
    ( spl0_514
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f665,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

fof(f6540,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f664,f6538]) ).

fof(f6538,plain,
    ( spl0_513
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f664,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

fof(f6536,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f654,f6534]) ).

fof(f6534,plain,
    ( spl0_512
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X19,X25,X0)
        | c_lessequals(X25,X19,X0)
        | c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f654,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X19,X25,X0)
      | c_lessequals(X25,X19,X0)
      | c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

fof(f6532,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f644,f6530]) ).

fof(f6530,plain,
    ( spl0_511
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X19,X25,X0)
        | ~ c_HOL_Oord__class_Oless(X25,X27,X0)
        | c_HOL_Oord__class_Oless(X19,X27,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f644,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X19,X25,X0)
      | ~ c_HOL_Oord__class_Oless(X25,X27,X0)
      | c_HOL_Oord__class_Oless(X19,X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

fof(f6528,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f643,f6526]) ).

fof(f6526,plain,
    ( spl0_510
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X25,X27,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X19,X27,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f643,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X25,X27,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X19,X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

fof(f6524,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f642,f6522]) ).

fof(f6522,plain,
    ( spl0_509
  <=> ! [X19,X0,X27,X25] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X25,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X27,X25,X0)
        | c_HOL_Oord__class_Oless(X27,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f642,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X25,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X27,X25,X0)
      | c_HOL_Oord__class_Oless(X27,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

fof(f6520,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f641,f6518]) ).

fof(f641,axiom,
    ! [X0,X19,X27,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X27,X25,X0)
      | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
      | c_HOL_Oord__class_Oless(X27,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

fof(f6516,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f639,f6514]) ).

fof(f6514,plain,
    ( spl0_507
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
        | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f639,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
      | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

fof(f6512,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f637,f6510]) ).

fof(f6510,plain,
    ( spl0_506
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f637,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

fof(f6508,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f603,f6506]) ).

fof(f6506,plain,
    ( spl0_505
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f603,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).

fof(f6504,plain,
    ( ~ spl0_30
    | ~ spl0_504
    | ~ spl0_163
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3802,f3481,f2807,f6501,f2162]) ).

fof(f6501,plain,
    ( spl0_504
  <=> c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f3481,plain,
    ( spl0_292
  <=> ! [X2,X0,X3] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(X3,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f3802,plain,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_163
    | ~ spl0_292 ),
    inference(resolution,[],[f3482,f2809]) ).

fof(f3482,plain,
    ( ! [X2,X3,X0] :
        ( ~ c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f3481]) ).

fof(f6499,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f602,f6497]) ).

fof(f6497,plain,
    ( spl0_503
  <=> ! [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_503])]) ).

fof(f602,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(f6495,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f526,f6493]) ).

fof(f6493,plain,
    ( spl0_502
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f526,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X3,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

fof(f6491,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f511,f6489]) ).

fof(f6489,plain,
    ( spl0_501
  <=> ! [X2,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f511,axiom,
    ! [X2,X0,X17] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_HOL_Oabs__class_Oabs(X2,X0)),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).

fof(f6487,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f497,f6485]) ).

fof(f6485,plain,
    ( spl0_500
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f497,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).

fof(f6483,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f496,f6481]) ).

fof(f6481,plain,
    ( spl0_499
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f496,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).

fof(f6479,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f454,f6477]) ).

fof(f6477,plain,
    ( spl0_498
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oone__class_Oone(X0) = X19
        | c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f454,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oone__class_Oone(X0) = X19
      | c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).

fof(f6475,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f350,f6473]) ).

fof(f6473,plain,
    ( spl0_497
  <=> ! [X31,X33,X19,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X30),X19) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f350,axiom,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X30),X19) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).

fof(f6471,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f349,f6469]) ).

fof(f6469,plain,
    ( spl0_496
  <=> ! [X31,X33,X19,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X33),X19) = X33 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f349,axiom,
    ! [X31,X29,X0,X19,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X33),X19) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).

fof(f6467,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f332,f6465]) ).

fof(f6465,plain,
    ( spl0_495
  <=> ! [X2,X31,X33,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X2),X30) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f332,axiom,
    ! [X31,X2,X29,X0,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X2),X30) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).

fof(f6463,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f330,f6461]) ).

fof(f6461,plain,
    ( spl0_494
  <=> ! [X2,X31,X33,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X32,X2),X33) = X33 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f330,axiom,
    ! [X31,X2,X29,X0,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X32,X2),X33) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).

fof(f6455,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f326,f6453]) ).

fof(f6453,plain,
    ( spl0_493
  <=> ! [X2,X31,X33,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X2),X33) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f326,axiom,
    ! [X31,X2,X29,X0,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X2),X33) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).

fof(f6451,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f325,f6449]) ).

fof(f6449,plain,
    ( spl0_492
  <=> ! [X2,X31,X33,X0,X29,X32,X30] :
        ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
        | hAPP(hAPP(X31,X33),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f325,axiom,
    ! [X31,X2,X29,X0,X32,X30,X33] :
      ( ~ c_Groebner__Basis_Ogb__semiring(X31,X32,X29,X33,X30,X0)
      | hAPP(hAPP(X31,X33),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).

fof(f6447,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f318,f6445]) ).

fof(f318,axiom,
    ! [X18,X17,X23] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(c_Divides_Odiv__class_Odiv(X18,X23,tc_nat),c_Divides_Odiv__class_Odiv(X17,X23,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono_0) ).

fof(f6443,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f271,f6441]) ).

fof(f6441,plain,
    ( spl0_490
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f271,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

fof(f6439,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f270,f6437]) ).

fof(f6437,plain,
    ( spl0_489
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f270,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).

fof(f6435,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f251,f6433]) ).

fof(f6433,plain,
    ( spl0_488
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(X2,X3,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f251,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(X2,X3,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

fof(f6431,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f250,f6429]) ).

fof(f6429,plain,
    ( spl0_487
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f250,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

fof(f6427,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f222,f6425]) ).

fof(f6425,plain,
    ( spl0_486
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oabs__if(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f222,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oabs__if(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).

fof(f6423,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f221,f6421]) ).

fof(f6421,plain,
    ( spl0_485
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f221,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Oabs__class_Oabs(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).

fof(f6419,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f195,f6417]) ).

fof(f6417,plain,
    ( spl0_484
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f195,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).

fof(f6415,plain,
    ( ~ spl0_30
    | ~ spl0_483
    | ~ spl0_163
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3579,f3377,f2807,f6412,f2162]) ).

fof(f6412,plain,
    ( spl0_483
  <=> c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f3579,plain,
    ( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_163
    | ~ spl0_267 ),
    inference(resolution,[],[f3378,f2809]) ).

fof(f6410,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f193,f6408]) ).

fof(f6408,plain,
    ( spl0_482
  <=> ! [X18,X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f193,axiom,
    ! [X18,X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_0) ).

fof(f6406,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f189,f6404]) ).

fof(f6404,plain,
    ( spl0_481
  <=> ! [X18,X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f189,axiom,
    ! [X18,X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_0) ).

fof(f6402,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f188,f6400]) ).

fof(f6400,plain,
    ( spl0_480
  <=> ! [X18,X17] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f188,axiom,
    ! [X18,X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X18,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_1) ).

fof(f6398,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f182,f6396]) ).

fof(f6396,plain,
    ( spl0_479
  <=> ! [X25,X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f182,axiom,
    ! [X19,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).

fof(f6394,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f168,f6392]) ).

fof(f6392,plain,
    ( spl0_478
  <=> ! [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_478])]) ).

fof(f168,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(f6390,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f117,f6388]) ).

fof(f6388,plain,
    ( spl0_477
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | X2 = X3
        | c_HOL_Oinverse__class_Oinverse(X2,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f117,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | X2 = X3
      | c_HOL_Oinverse__class_Oinverse(X2,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

fof(f6386,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f36,f6384]) ).

fof(f6384,plain,
    ( spl0_476
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f36,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).

fof(f6382,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f35,f6380]) ).

fof(f6380,plain,
    ( spl0_475
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f35,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).

fof(f6378,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f13,f6376]) ).

fof(f6376,plain,
    ( spl0_474
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f13,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).

fof(f6085,plain,
    ( ~ spl0_122
    | spl0_473
    | ~ spl0_174
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f3517,f3348,f2855,f6082,f2622]) ).

fof(f2622,plain,
    ( spl0_122
  <=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f6082,plain,
    ( spl0_473
  <=> c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f2855,plain,
    ( spl0_174
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f3348,plain,
    ( spl0_260
  <=> 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_260])]) ).

fof(f3517,plain,
    ( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
    | ~ spl0_174
    | ~ spl0_260 ),
    inference(superposition,[],[f2856,f3350]) ).

fof(f3350,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f3348]) ).

fof(f2856,plain,
    ( ! [X0] :
        ( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0)
        | ~ class_Int_Onumber__ring(X0) )
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f2855]) ).

fof(f5758,plain,
    ( spl0_472
    | ~ spl0_190
    | spl0_471 ),
    inference(avatar_split_clause,[],[f5606,f5514,f2940,f5755]) ).

fof(f5514,plain,
    ( spl0_471
  <=> c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f5606,plain,
    ( c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),tc_nat)
    | ~ spl0_190
    | spl0_471 ),
    inference(resolution,[],[f5516,f2941]) ).

fof(f5516,plain,
    ( ~ c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat)
    | spl0_471 ),
    inference(avatar_component_clause,[],[f5514]) ).

fof(f5517,plain,
    ( ~ spl0_471
    | ~ spl0_150
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f5437,f5390,f2751,f5514]) ).

fof(f2751,plain,
    ( spl0_150
  <=> ! [X17] : ~ c_lessequals(hAPP(c_Suc,X17),X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f5437,plain,
    ( ~ c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))),v_i____,tc_nat)
    | ~ spl0_150
    | ~ spl0_455 ),
    inference(resolution,[],[f5391,f2752]) ).

fof(f2752,plain,
    ( ! [X17] : ~ c_lessequals(hAPP(c_Suc,X17),X17,tc_nat)
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f2751]) ).

fof(f5462,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f1904,f5460]) ).

fof(f1904,plain,
    ! [X19] :
      ( c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f305,f582]) ).

fof(f305,axiom,
    ! [X19] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).

fof(f5458,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f1903,f5456]) ).

fof(f1903,plain,
    ! [X19] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f25,f582]) ).

fof(f25,axiom,
    ! [X19] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).

fof(f5454,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f1898,f5452]) ).

fof(f5452,plain,
    ( spl0_468
  <=> ! [X19] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f1898,plain,
    ! [X19] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f304,f582]) ).

fof(f304,axiom,
    ! [X19] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).

fof(f5450,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f1897,f5448]) ).

fof(f1897,plain,
    ! [X19] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat) ),
    inference(forward_demodulation,[],[f24,f582]) ).

fof(f24,axiom,
    ! [X19] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X19,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).

fof(f5446,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f1842,f5444]) ).

fof(f1842,plain,
    ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19)),tc_nat),
    inference(forward_demodulation,[],[f1569,f1837]) ).

fof(f1569,axiom,
    ! [X19] : ~ 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)),X19)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).

fof(f5432,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f1669,f5430]) ).

fof(f5428,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f1659,f5426]) ).

fof(f5426,plain,
    ( spl0_464
  <=> ! [X2,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f1659,axiom,
    ! [X2,X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).

fof(f5424,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f1658,f5422]) ).

fof(f5422,plain,
    ( spl0_463
  <=> ! [X2,X0] :
        ( ~ 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)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f1658,axiom,
    ! [X2,X0] :
      ( ~ 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)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).

fof(f5420,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f1649,f5418]) ).

fof(f5418,plain,
    ( spl0_462
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | X19 = X25
        | c_HOL_Oord__class_Oless(X25,X19,X0)
        | c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f1649,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | X19 = X25
      | c_HOL_Oord__class_Oless(X25,X19,X0)
      | c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

fof(f5416,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f1647,f5414]) ).

fof(f5414,plain,
    ( spl0_461
  <=> ! [X25,X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | X19 = X25
        | c_HOL_Oord__class_Oless(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X25,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f1647,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | X19 = X25
      | c_HOL_Oord__class_Oless(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X25,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

fof(f5412,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f1597,f5410]) ).

fof(f5410,plain,
    ( spl0_460
  <=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f1597,axiom,
    ! [X18,X17] : c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

fof(f5408,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f1595,f5406]) ).

fof(f5406,plain,
    ( spl0_459
  <=> ! [X18,X17] :
        ( X17 = X18
        | c_HOL_Oord__class_Oless(X17,X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f1595,axiom,
    ! [X18,X17] :
      ( X17 = X18
      | c_HOL_Oord__class_Oless(X17,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

fof(f5404,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f1503,f5402]) ).

fof(f5402,plain,
    ( spl0_458
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oinverse__class_Odivide(X19,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f1503,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oinverse__class_Odivide(X19,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).

fof(f5400,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f1447,f5398]) ).

fof(f5398,plain,
    ( spl0_457
  <=> ! [X25,X19] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f1447,axiom,
    ! [X19,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_1) ).

fof(f5396,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f1428,f5394]) ).

fof(f1428,axiom,
    ! [X17,X22] :
      ( ~ c_lessequals(X22,X17,tc_nat)
      | c_HOL_Ominus__class_Ominus(X17,c_HOL_Ominus__class_Ominus(X17,X22,tc_nat),tc_nat) = X22 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

fof(f5392,plain,
    ( spl0_455
    | ~ spl0_231
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4966,f4648,f3139,f5390]) ).

fof(f3139,plain,
    ( spl0_231
  <=> c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f4648,plain,
    ( spl0_385
  <=> ! [X22,X24,X23] :
        ( ~ c_lessequals(X22,X24,tc_nat)
        | ~ c_lessequals(X24,X23,tc_nat)
        | c_lessequals(X22,X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f4966,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_i____,tc_nat)
        | c_lessequals(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) )
    | ~ spl0_231
    | ~ spl0_385 ),
    inference(resolution,[],[f4649,f3141]) ).

fof(f3141,plain,
    ( c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f3139]) ).

fof(f4649,plain,
    ( ! [X24,X22,X23] :
        ( ~ c_lessequals(X24,X23,tc_nat)
        | ~ c_lessequals(X22,X24,tc_nat)
        | c_lessequals(X22,X23,tc_nat) )
    | ~ spl0_385 ),
    inference(avatar_component_clause,[],[f4648]) ).

fof(f5388,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f1405,f5386]) ).

fof(f5386,plain,
    ( spl0_454
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X17
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != c_HOL_Oone__class_Oone(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1405,axiom,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X17
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

fof(f5384,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f1404,f5382]) ).

fof(f5382,plain,
    ( spl0_453
  <=> ! [X18,X17] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X18
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != c_HOL_Oone__class_Oone(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1404,axiom,
    ! [X18,X17] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X18
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X17) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

fof(f5380,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f1235,f5378]) ).

fof(f5378,plain,
    ( spl0_452
  <=> ! [X22,X24,X23] :
        ( c_HOL_Oord__class_Oless(X22,X23,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1235,axiom,
    ! [X24,X22,X23] :
      ( c_HOL_Oord__class_Oless(X22,X23,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

fof(f5376,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f1234,f5374]) ).

fof(f5374,plain,
    ( spl0_451
  <=> ! [X25,X27,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X27,tc_nat)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f1234,axiom,
    ! [X19,X27,X25] :
      ( ~ c_HOL_Oord__class_Oless(X19,X27,tc_nat)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

fof(f5372,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f1233,f5370]) ).

fof(f5370,plain,
    ( spl0_450
  <=> ! [X25,X27,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f1233,axiom,
    ! [X19,X27,X25] :
      ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

fof(f5368,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f1187,f5366]) ).

fof(f5366,plain,
    ( spl0_449
  <=> ! [X18,X17] :
        ( X17 = X18
        | ~ c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1187,axiom,
    ! [X18,X17] :
      ( X17 = X18
      | ~ c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

fof(f5364,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f1055,f5362]) ).

fof(f5362,plain,
    ( spl0_448
  <=> ! [X0,X19] :
        ( ~ 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),X19),c_HOL_Ozero__class_Ozero(tc_nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f1055,axiom,
    ! [X0,X19] :
      ( ~ 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),X19),c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).

fof(f5360,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f1052,f5358]) ).

fof(f5358,plain,
    ( spl0_447
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X3,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f1052,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X3,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

fof(f5356,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f1051,f5354]) ).

fof(f5354,plain,
    ( spl0_446
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f1051,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X3),X3,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

fof(f5352,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f1046,f5350]) ).

fof(f5350,plain,
    ( spl0_445
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f1046,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X2,X3,X0)),X3) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

fof(f5347,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f963,f5345]) ).

fof(f5345,plain,
    ( spl0_444
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f963,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

fof(f5343,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f962,f5341]) ).

fof(f5341,plain,
    ( spl0_443
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f962,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).

fof(f5338,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f759,f5336]) ).

fof(f5336,plain,
    ( spl0_442
  <=> ! [X28,X17] :
        ( hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f759,axiom,
    ! [X28,X17] :
      ( hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).

fof(f5333,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f758,f5331]) ).

fof(f5331,plain,
    ( spl0_441
  <=> ! [X28,X17] :
        ( ~ hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
        | hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f758,axiom,
    ! [X28,X17] :
      ( ~ hBOOL(hAPP(X28,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X28,c_Divides_Odiv__class_Odiv(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_5) ).

fof(f5329,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f742,f5327]) ).

fof(f5327,plain,
    ( spl0_440
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f742,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).

fof(f5325,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f663,f5323]) ).

fof(f5323,plain,
    ( spl0_439
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Oorder(X0)
        | X19 = X25
        | ~ c_lessequals(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f663,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | X19 = X25
      | ~ c_lessequals(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

fof(f5321,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f659,f5319]) ).

fof(f5319,plain,
    ( spl0_438
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | X19 = X25
        | ~ c_lessequals(X19,X25,X0)
        | c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f659,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | X19 = X25
      | ~ c_lessequals(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

fof(f5317,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f613,f5315]) ).

fof(f5315,plain,
    ( spl0_437
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ozero__class_Ozero(X0)) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f613,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),c_HOL_Ozero__class_Ozero(X0)) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f5313,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f562,f5311]) ).

fof(f562,axiom,
    ! [X18,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

fof(f5309,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f552,f5307]) ).

fof(f5307,plain,
    ( spl0_435
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f552,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).

fof(f5305,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f546,f5303]) ).

fof(f5303,plain,
    ( spl0_434
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f546,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

fof(f5301,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f545,f5299]) ).

fof(f5299,plain,
    ( spl0_433
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f545,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

fof(f5297,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f544,f5295]) ).

fof(f5295,plain,
    ( spl0_432
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f544,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

fof(f5293,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f543,f5291]) ).

fof(f5291,plain,
    ( spl0_431
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f543,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

fof(f5289,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f542,f5287]) ).

fof(f5287,plain,
    ( spl0_430
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f542,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).

fof(f5285,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f541,f5283]) ).

fof(f5283,plain,
    ( spl0_429
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f541,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).

fof(f5281,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f540,f5279]) ).

fof(f5279,plain,
    ( spl0_428
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f540,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).

fof(f5277,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f539,f5275]) ).

fof(f5275,plain,
    ( spl0_427
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f539,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).

fof(f5273,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f527,f5271]) ).

fof(f5271,plain,
    ( spl0_426
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f527,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X2,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).

fof(f5269,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f431,f5267]) ).

fof(f5267,plain,
    ( spl0_425
  <=> ! [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_425])]) ).

fof(f431,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_left__minus_0) ).

fof(f5265,plain,
    ( ~ spl0_424
    | spl0_410
    | ~ spl0_352
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f5018,f4668,f4413,f5006,f5262]) ).

fof(f5262,plain,
    ( spl0_424
  <=> class_OrderedGroup_Ogroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f5006,plain,
    ( spl0_410
  <=> v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f4668,plain,
    ( spl0_390
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X2 = X3
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f5018,plain,
    ( v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))
    | ~ class_OrderedGroup_Ogroup__add(tc_nat)
    | ~ spl0_352
    | ~ spl0_390 ),
    inference(trivial_inequality_removal,[],[f5017]) ).

fof(f5017,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))
    | ~ class_OrderedGroup_Ogroup__add(tc_nat)
    | ~ spl0_352
    | ~ spl0_390 ),
    inference(superposition,[],[f4669,f4415]) ).

fof(f4669,plain,
    ( ! [X2,X3,X0] :
        ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0)
        | X2 = X3
        | ~ class_OrderedGroup_Ogroup__add(X0) )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f4668]) ).

fof(f5260,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f430,f5258]) ).

fof(f5258,plain,
    ( spl0_423
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ouminus__class_Ouminus(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f430,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ouminus__class_Ouminus(X2,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).

fof(f5256,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f429,f5254]) ).

fof(f5254,plain,
    ( spl0_422
  <=> ! [X2,X0] :
        ( ~ 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(X2,X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f429,axiom,
    ! [X2,X0] :
      ( ~ 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(X2,X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

fof(f5252,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f406,f5250]) ).

fof(f5250,plain,
    ( spl0_421
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X19
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f406,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X19
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

fof(f5248,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f403,f5246]) ).

fof(f5246,plain,
    ( spl0_420
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X23,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f403,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X23,X17,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

fof(f5244,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f402,f5242]) ).

fof(f5242,plain,
    ( spl0_419
  <=> ! [X18,X17,X23] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f402,axiom,
    ! [X18,X17,X23] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X23),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

fof(f5240,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f401,f5238]) ).

fof(f5238,plain,
    ( spl0_418
  <=> ! [X25,X27,X19] :
        ( ~ c_lessequals(X19,X27,tc_nat)
        | c_lessequals(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f401,axiom,
    ! [X19,X27,X25] :
      ( ~ c_lessequals(X19,X27,tc_nat)
      | c_lessequals(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

fof(f5236,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f400,f5234]) ).

fof(f5234,plain,
    ( spl0_417
  <=> ! [X25,X27,X19] :
        ( ~ c_lessequals(X19,X25,tc_nat)
        | c_lessequals(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f400,axiom,
    ! [X19,X27,X25] :
      ( ~ c_lessequals(X19,X25,tc_nat)
      | c_lessequals(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X27),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

fof(f5232,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f384,f5230]) ).

fof(f5230,plain,
    ( spl0_416
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f384,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

fof(f5228,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f282,f5226]) ).

fof(f5226,plain,
    ( spl0_415
  <=> ! [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_415])]) ).

fof(f282,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(f5224,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f216,f5222]) ).

fof(f5222,plain,
    ( spl0_414
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f216,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

fof(f5220,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f215,f5218]) ).

fof(f5218,plain,
    ( spl0_413
  <=> ! [X18,X17] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f215,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X18
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

fof(f5216,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f80,f5214]) ).

fof(f5214,plain,
    ( spl0_412
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f80,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).

fof(f5212,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f67,f5210]) ).

fof(f5210,plain,
    ( spl0_411
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Oorder(X0)
        | X19 = X25
        | ~ c_lessequals(X19,X25,X0)
        | ~ c_lessequals(X25,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f67,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | X19 = X25
      | ~ c_lessequals(X19,X25,X0)
      | ~ c_lessequals(X25,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

fof(f5009,plain,
    ( ~ spl0_409
    | spl0_410
    | ~ spl0_352
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4998,f4660,f4413,f5006,f5002]) ).

fof(f5002,plain,
    ( spl0_409
  <=> class_OrderedGroup_Oab__group__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f4660,plain,
    ( spl0_388
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X2 = X3
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f4998,plain,
    ( v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))
    | ~ class_OrderedGroup_Oab__group__add(tc_nat)
    | ~ spl0_352
    | ~ spl0_388 ),
    inference(trivial_inequality_removal,[],[f4997]) ).

fof(f4997,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____))
    | ~ class_OrderedGroup_Oab__group__add(tc_nat)
    | ~ spl0_352
    | ~ spl0_388 ),
    inference(superposition,[],[f4661,f4415]) ).

fof(f4661,plain,
    ( ! [X2,X3,X0] :
        ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0)
        | X2 = X3
        | ~ class_OrderedGroup_Oab__group__add(X0) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f4660]) ).

fof(f4769,plain,
    ( spl0_408
    | ~ spl0_243
    | ~ spl0_350 ),
    inference(avatar_split_clause,[],[f4507,f4111,f3188,f4766]) ).

fof(f4766,plain,
    ( spl0_408
  <=> 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_408])]) ).

fof(f4507,plain,
    ( c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_243
    | ~ spl0_350 ),
    inference(superposition,[],[f4112,f3189]) ).

fof(f4740,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f1910,f4738]) ).

fof(f4738,plain,
    ( spl0_407
  <=> ! [X34] :
        ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(X34,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f1910,plain,
    ! [X34] :
      ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(X34,tc_nat))
      | ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint) ),
    inference(forward_demodulation,[],[f246,f266]) ).

fof(f266,axiom,
    ! [X17] : hAPP(c_Suc,X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

fof(f246,axiom,
    ! [X34] :
      ( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Int_Onumber__class_Onumber__of(X34,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__add__number__of_0) ).

fof(f4736,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f1846,f4733]) ).

fof(f4733,plain,
    ( spl0_406
  <=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f1846,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_HOL_Oone__class_Oone(tc_nat))),
    inference(forward_demodulation,[],[f1537,f582]) ).

fof(f1537,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(f4731,plain,
    ~ spl0_405,
    inference(avatar_split_clause,[],[f1840,f4728]) ).

fof(f1840,plain,
    ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),
    inference(forward_demodulation,[],[f1690,f1837]) ).

fof(f1690,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_False_0) ).

fof(f4726,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f1692,f4724]) ).

fof(f4724,plain,
    ( spl0_404
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f1692,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f4722,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f1691,f4720]) ).

fof(f4720,plain,
    ( spl0_403
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1691,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

fof(f4718,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f1440,f4716]) ).

fof(f4716,plain,
    ( spl0_402
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1440,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).

fof(f4714,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f1439,f4712]) ).

fof(f1439,axiom,
    ! [X19,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).

fof(f4710,plain,
    ( spl0_400
    | ~ spl0_134
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f3902,f3509,f2679,f4708]) ).

fof(f4708,plain,
    ( spl0_400
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f3509,plain,
    ( spl0_299
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f3902,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
    | ~ spl0_134
    | ~ spl0_299 ),
    inference(resolution,[],[f3510,f2680]) ).

fof(f3510,plain,
    ( ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f3509]) ).

fof(f4706,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f1356,f4704]) ).

fof(f4704,plain,
    ( spl0_399
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f1356,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

fof(f4702,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f1355,f4700]) ).

fof(f4700,plain,
    ( spl0_398
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f1355,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X17,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

fof(f4698,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f1326,f4696]) ).

fof(f4696,plain,
    ( spl0_397
  <=> ! [X34,X47] :
        ( c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1326,axiom,
    ! [X47,X34] :
      ( c_HOL_Oord__class_Oless(X34,X47,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X47,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_1) ).

fof(f4694,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f1210,f4692]) ).

fof(f4692,plain,
    ( spl0_396
  <=> ! [X0,X17] :
        ( ~ 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)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1210,axiom,
    ! [X0,X17] :
      ( ~ 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)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

fof(f4690,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f1158,f4688]) ).

fof(f4688,plain,
    ( spl0_395
  <=> ! [X2,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f1158,axiom,
    ! [X2,X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).

fof(f4686,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f1157,f4684]) ).

fof(f4684,plain,
    ( spl0_394
  <=> ! [X2,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1157,axiom,
    ! [X2,X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).

fof(f4682,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f1128,f4680]) ).

fof(f4680,plain,
    ( spl0_393
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1128,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

fof(f4678,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f1078,f4676]) ).

fof(f4676,plain,
    ( spl0_392
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X17,X18,tc_nat)
        | c_lessequals(hAPP(c_Suc,X17),hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1078,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X17,X18,tc_nat)
      | c_lessequals(hAPP(c_Suc,X17),hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

fof(f4674,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f1077,f4672]) ).

fof(f4672,plain,
    ( spl0_391
  <=> ! [X18,X17] :
        ( c_lessequals(X17,X18,tc_nat)
        | ~ c_lessequals(hAPP(c_Suc,X17),hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f1077,axiom,
    ! [X18,X17] :
      ( c_lessequals(X17,X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,X17),hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

fof(f4670,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f1048,f4668]) ).

fof(f1048,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X2 = X3
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

fof(f4666,plain,
    ( spl0_389
    | ~ spl0_155
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f3630,f3385,f2772,f4664]) ).

fof(f4664,plain,
    ( spl0_389
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f2772,plain,
    ( spl0_155
  <=> ! [X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f3630,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_155
    | ~ spl0_269 ),
    inference(duplicate_literal_removal,[],[f3608]) ).

fof(f3608,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_155
    | ~ spl0_269 ),
    inference(resolution,[],[f3386,f2773]) ).

fof(f2773,plain,
    ( ! [X0,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X19,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f2772]) ).

fof(f4662,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f1047,f4660]) ).

fof(f1047,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X2 = X3
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

fof(f4658,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f951,f4656]) ).

fof(f4656,plain,
    ( spl0_387
  <=> ! [X0,X3] :
        ( ~ 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(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f951,axiom,
    ! [X3,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(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

fof(f4654,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f941,f4652]) ).

fof(f4652,plain,
    ( spl0_386
  <=> ! [X19,X26] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X26),X19),X26,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f941,axiom,
    ! [X19,X26] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X26),X19),X26,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).

fof(f4650,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f933,f4648]) ).

fof(f933,axiom,
    ! [X24,X22,X23] :
      ( ~ c_lessequals(X22,X24,tc_nat)
      | ~ c_lessequals(X24,X23,tc_nat)
      | c_lessequals(X22,X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

fof(f4645,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f929,f4643]) ).

fof(f4643,plain,
    ( spl0_384
  <=> ! [X17,X28] :
        ( hBOOL(hAPP(X28,X17))
        | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f929,axiom,
    ! [X28,X17] :
      ( hBOOL(hAPP(X28,X17))
      | ~ hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).

fof(f4640,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f928,f4638]) ).

fof(f4638,plain,
    ( spl0_383
  <=> ! [X17,X28] :
        ( ~ hBOOL(hAPP(X28,X17))
        | hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f928,axiom,
    ! [X28,X17] :
      ( ~ hBOOL(hAPP(X28,X17))
      | hBOOL(hAPP(X28,c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).

fof(f4636,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f922,f4634]) ).

fof(f4634,plain,
    ( spl0_382
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f922,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).

fof(f4632,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f867,f4630]) ).

fof(f4630,plain,
    ( spl0_381
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f867,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f4628,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f866,f4626]) ).

fof(f4626,plain,
    ( spl0_380
  <=> ! [X25,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)),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f866,axiom,
    ! [X0,X25] :
      ( ~ 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)),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

fof(f4624,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f864,f4622]) ).

fof(f4622,plain,
    ( spl0_379
  <=> ! [X2,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f864,axiom,
    ! [X2,X0] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

fof(f4618,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f862,f4616]) ).

fof(f4616,plain,
    ( spl0_378
  <=> ! [X0,X19] :
        ( ~ 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)),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f862,axiom,
    ! [X0,X19] :
      ( ~ 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)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

fof(f4614,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f861,f4612]) ).

fof(f4612,plain,
    ( spl0_377
  <=> ! [X2,X0] :
        ( ~ 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)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f861,axiom,
    ! [X2,X0] :
      ( ~ 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)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f4610,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f860,f4608]) ).

fof(f4608,plain,
    ( spl0_376
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f860,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f4606,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f859,f4604]) ).

fof(f4604,plain,
    ( spl0_375
  <=> ! [X0,X3] :
        ( ~ 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)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f859,axiom,
    ! [X3,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)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

fof(f4602,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f858,f4600]) ).

fof(f4600,plain,
    ( spl0_374
  <=> ! [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),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f858,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),X2),c_HOL_Ozero__class_Ozero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

fof(f4598,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f776,f4596]) ).

fof(f4596,plain,
    ( spl0_373
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oabs__if(X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = X2
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f776,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oabs__if(X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).

fof(f4594,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f755,f4592]) ).

fof(f4592,plain,
    ( spl0_372
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f755,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

fof(f4590,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f655,f4588]) ).

fof(f4588,plain,
    ( spl0_371
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oord__class_Oless(X2,X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f655,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).

fof(f4586,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f574,f4584]) ).

fof(f4584,plain,
    ( spl0_370
  <=> ! [X2,X0,X3] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f574,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).

fof(f4582,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f498,f4580]) ).

fof(f4580,plain,
    ( spl0_369
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f498,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

fof(f4578,plain,
    ( ~ spl0_83
    | ~ spl0_368
    | ~ spl0_127
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3581,f3377,f2647,f4575,f2427]) ).

fof(f2427,plain,
    ( spl0_83
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f4575,plain,
    ( spl0_368
  <=> c_lessequals(c_Int_OPls,c_Int_OMin,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f2647,plain,
    ( spl0_127
  <=> c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f3581,plain,
    ( ~ c_lessequals(c_Int_OPls,c_Int_OMin,tc_Int_Oint)
    | ~ class_Orderings_Opreorder(tc_Int_Oint)
    | ~ spl0_127
    | ~ spl0_267 ),
    inference(resolution,[],[f3378,f2649]) ).

fof(f2649,plain,
    ( c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint)
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f2647]) ).

fof(f4573,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f461,f4571]) ).

fof(f4571,plain,
    ( spl0_367
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f461,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).

fof(f4569,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f416,f4567]) ).

fof(f4567,plain,
    ( spl0_366
  <=> ! [X18,X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f416,axiom,
    ! [X18,X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

fof(f4565,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f257,f4563]) ).

fof(f4563,plain,
    ( spl0_365
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(c_Fact_Ofact__class_Ofact(X18,tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f257,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(c_Fact_Ofact__class_Ofact(X18,tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__mono__nat_0) ).

fof(f4561,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f254,f4559]) ).

fof(f4559,plain,
    ( spl0_364
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(X2,X3,X0)
        | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f254,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(X2,X3,X0)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).

fof(f4557,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f236,f4555]) ).

fof(f4555,plain,
    ( spl0_363
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f236,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
      | c_lessequals(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

fof(f4553,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f233,f4551]) ).

fof(f233,axiom,
    ! [X18,X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17) != X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

fof(f4549,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f134,f4547]) ).

fof(f4547,plain,
    ( spl0_361
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f134,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

fof(f4545,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f106,f4543]) ).

fof(f4543,plain,
    ( spl0_360
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f106,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).

fof(f4541,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f82,f4539]) ).

fof(f4539,plain,
    ( spl0_359
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f82,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

fof(f4537,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f69,f4535]) ).

fof(f4535,plain,
    ( spl0_358
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X2 = X3
        | c_HOL_Ouminus__class_Ouminus(X2,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f69,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X2 = X3
      | c_HOL_Ouminus__class_Ouminus(X2,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

fof(f4527,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f68,f4525]) ).

fof(f4525,plain,
    ( spl0_357
  <=> ! [X25,X0,X19] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | X19 = X25
        | c_HOL_Ouminus__class_Ouminus(X19,X0) != c_HOL_Ouminus__class_Ouminus(X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f68,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | X19 = X25
      | c_HOL_Ouminus__class_Ouminus(X19,X0) != c_HOL_Ouminus__class_Ouminus(X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

fof(f4523,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f61,f4521]) ).

fof(f4521,plain,
    ( spl0_356
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f61,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).

fof(f4519,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f42,f4517]) ).

fof(f4517,plain,
    ( spl0_355
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f42,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f4515,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f33,f4513]) ).

fof(f4513,plain,
    ( spl0_354
  <=> ! [X2,X0] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f33,axiom,
    ! [X2,X0] :
      ( ~ class_Power_Opower(X0)
      | c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

fof(f4511,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f32,f4509]) ).

fof(f4509,plain,
    ( spl0_353
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f32,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

fof(f4416,plain,
    ( spl0_352
    | ~ spl0_231
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f4235,f3971,f3139,f4413]) ).

fof(f4235,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_231
    | ~ spl0_316 ),
    inference(resolution,[],[f3972,f3141]) ).

fof(f4277,plain,
    ( spl0_351
    | ~ spl0_143
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4221,f3967,f2721,f4274]) ).

fof(f4221,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_143
    | ~ spl0_315 ),
    inference(resolution,[],[f3968,f2723]) ).

fof(f4113,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f1839,f4111]) ).

fof(f1839,plain,
    ! [X19] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),X19),tc_nat),
    inference(forward_demodulation,[],[f1560,f1837]) ).

fof(f1560,axiom,
    ! [X19] : 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)),X19),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).

fof(f4109,plain,
    ( spl0_349
    | ~ spl0_83
    | ~ spl0_127
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f3547,f3369,f2647,f2427,f4106]) ).

fof(f4106,plain,
    ( spl0_349
  <=> c_lessequals(c_Int_OMin,c_Int_OPls,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f3369,plain,
    ( spl0_265
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | c_lessequals(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f3547,plain,
    ( ~ class_Orderings_Opreorder(tc_Int_Oint)
    | c_lessequals(c_Int_OMin,c_Int_OPls,tc_Int_Oint)
    | ~ spl0_127
    | ~ spl0_265 ),
    inference(resolution,[],[f3370,f2649]) ).

fof(f3370,plain,
    ( ! [X0,X19,X25] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X19,X25,X0) )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f3369]) ).

fof(f4104,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f1653,f4102]) ).

fof(f4102,plain,
    ( spl0_348
  <=> ! [X25,X19] :
        ( X19 = X25
        | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | c_HOL_Oord__class_Oless(X25,X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1653,axiom,
    ! [X19,X25] :
      ( X19 = X25
      | c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | c_HOL_Oord__class_Oless(X25,X19,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

fof(f4100,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f1578,f4098]) ).

fof(f4098,plain,
    ( spl0_347
  <=> ! [X24,X17,X23] :
        ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X17,tc_nat),X23,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f1578,axiom,
    ! [X17,X24,X23] :
      ( ~ c_HOL_Oord__class_Oless(X24,X23,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X24,X17,tc_nat),X23,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

fof(f4096,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f1448,f4094]) ).

fof(f4094,plain,
    ( spl0_346
  <=> ! [X25,X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f1448,axiom,
    ! [X19,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_0) ).

fof(f4092,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f1444,f4090]) ).

fof(f1444,axiom,
    ! [X18,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),X17,tc_nat) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

fof(f4088,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f1443,f4086]) ).

fof(f4086,plain,
    ( spl0_344
  <=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),X17,tc_nat) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f1443,axiom,
    ! [X18,X17] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),X17,tc_nat) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

fof(f4084,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f1286,f4082]) ).

fof(f4082,plain,
    ( spl0_343
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f1286,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).

fof(f4080,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f1285,f4078]) ).

fof(f4078,plain,
    ( spl0_342
  <=> ! [X25,X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f1285,axiom,
    ! [X19,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X19),X25),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).

fof(f4076,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f1231,f4074]) ).

fof(f1231,axiom,
    ! [X18,X17] :
      ( X17 = X18
      | ~ c_lessequals(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

fof(f4072,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f1209,f4070]) ).

fof(f4070,plain,
    ( spl0_340
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Oone__class_Oone(tc_nat)) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f1209,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X19),c_HOL_Oone__class_Oone(tc_nat)) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

fof(f4068,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f1208,f4066]) ).

fof(f4066,plain,
    ( spl0_339
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f1208,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).

fof(f4063,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f1177,f4061]) ).

fof(f4061,plain,
    ( spl0_338
  <=> ! [X22,X18] : c_HOL_Oord__class_Oless(X22,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X22)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f1177,axiom,
    ! [X18,X22] : c_HOL_Oord__class_Oless(X22,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X22)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

fof(f4059,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f1176,f4057]) ).

fof(f4057,plain,
    ( spl0_337
  <=> ! [X18,X19] : c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X19)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f1176,axiom,
    ! [X18,X19] : c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X19)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

fof(f4055,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f1061,f4053]) ).

fof(f4053,plain,
    ( spl0_336
  <=> ! [X0] :
        ( ~ class_Power_Opower(X0)
        | c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f1061,axiom,
    ! [X0] :
      ( ~ class_Power_Opower(X0)
      | c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__power__power_0) ).

fof(f4051,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f1045,f4049]) ).

fof(f4049,plain,
    ( spl0_335
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f1045,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

fof(f4047,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f1002,f4045]) ).

fof(f4045,plain,
    ( spl0_334
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f1002,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f4043,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f1001,f4041]) ).

fof(f4041,plain,
    ( spl0_333
  <=> ! [X0,X19] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X19) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f1001,axiom,
    ! [X0,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X19) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

fof(f4039,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f1000,f4037]) ).

fof(f4037,plain,
    ( spl0_332
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1000,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f4035,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f999,f4033]) ).

fof(f4033,plain,
    ( spl0_331
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f999,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f4031,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f998,f4029]) ).

fof(f4029,plain,
    ( spl0_330
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f998,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f4027,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f980,f4025]) ).

fof(f4025,plain,
    ( spl0_329
  <=> ! [X34] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f980,axiom,
    ! [X34] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__0__number__of_1) ).

fof(f4022,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f979,f4020]) ).

fof(f4020,plain,
    ( spl0_328
  <=> ! [X34] :
        ( c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f979,axiom,
    ! [X34] :
      ( c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__0__number__of_0) ).

fof(f4018,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f920,f4016]) ).

fof(f4016,plain,
    ( spl0_327
  <=> ! [X15,X0,X14,X2] : hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f920,axiom,
    ! [X2,X0,X14,X15] : hAPP(hAPP(c_Power_Opower_Opower(X14,X15,X0),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power_Opower_Opower__0_0) ).

fof(f4014,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f735,f4012]) ).

fof(f4012,plain,
    ( spl0_326
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f735,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).

fof(f4010,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f620,f4008]) ).

fof(f4008,plain,
    ( spl0_325
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f620,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(f4006,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f619,f4004]) ).

fof(f4004,plain,
    ( spl0_324
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f619,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f4002,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f615,f4000]) ).

fof(f4000,plain,
    ( spl0_323
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f615,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f3998,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f612,f3996]) ).

fof(f3996,plain,
    ( spl0_322
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f612,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f3994,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f611,f3992]) ).

fof(f3992,plain,
    ( spl0_321
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f611,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f3990,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f610,f3988]) ).

fof(f3988,plain,
    ( spl0_320
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f610,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f3986,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f549,f3984]) ).

fof(f3984,plain,
    ( spl0_319
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f549,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).

fof(f3982,plain,
    ( ~ spl0_30
    | ~ spl0_318
    | ~ spl0_143
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3814,f3481,f2721,f3979,f2162]) ).

fof(f3979,plain,
    ( spl0_318
  <=> c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f3814,plain,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_143
    | ~ spl0_292 ),
    inference(resolution,[],[f3482,f2723]) ).

fof(f3977,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f536,f3975]) ).

fof(f536,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

fof(f3973,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f535,f3971]) ).

fof(f535,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

fof(f3969,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f471,f3967]) ).

fof(f471,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X18,X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).

fof(f3965,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f363,f3963]) ).

fof(f3963,plain,
    ( spl0_314
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f363,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).

fof(f3961,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f306,f3959]) ).

fof(f3959,plain,
    ( spl0_313
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f306,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

fof(f3957,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f277,f3955]) ).

fof(f3955,plain,
    ( spl0_312
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f277,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

fof(f3953,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f267,f3951]) ).

fof(f3951,plain,
    ( spl0_311
  <=> ! [X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(c_Suc,X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3949,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f266,f3947]) ).

fof(f3947,plain,
    ( spl0_310
  <=> ! [X17] : hAPP(c_Suc,X17) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3945,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f255,f3943]) ).

fof(f3943,plain,
    ( spl0_309
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Oinverse(X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f255,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Oinverse(X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

fof(f3941,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f245,f3939]) ).

fof(f3939,plain,
    ( spl0_308
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f245,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).

fof(f3937,plain,
    ( spl0_307
    | ~ spl0_143
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3772,f3456,f2721,f3934]) ).

fof(f3934,plain,
    ( spl0_307
  <=> v_i____ = c_Divides_Odiv__class_Omod(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f3772,plain,
    ( v_i____ = c_Divides_Odiv__class_Omod(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_143
    | ~ spl0_286 ),
    inference(resolution,[],[f3457,f2723]) ).

fof(f3932,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f161,f3930]) ).

fof(f3930,plain,
    ( spl0_306
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f161,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f3928,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f65,f3926]) ).

fof(f3926,plain,
    ( spl0_305
  <=> ! [X25,X19] :
        ( X19 = X25
        | c_HOL_Oord__class_Oless(X25,X19,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f65,axiom,
    ! [X19,X25] :
      ( X19 = X25
      | c_HOL_Oord__class_Oless(X25,X19,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(X19,X25,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zless__linear_0) ).

fof(f3924,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f64,f3922]) ).

fof(f3922,plain,
    ( spl0_304
  <=> ! [X18,X17] :
        ( X17 = X18
        | ~ c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(X17,X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f64,axiom,
    ! [X18,X17] :
      ( X17 = X18
      | ~ c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(X17,X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

fof(f3742,plain,
    ( ~ spl0_30
    | ~ spl0_303
    | ~ spl0_143
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3588,f3377,f2721,f3739,f2162]) ).

fof(f3739,plain,
    ( spl0_303
  <=> c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3588,plain,
    ( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),v_i____,tc_nat)
    | ~ class_Orderings_Opreorder(tc_nat)
    | ~ spl0_143
    | ~ spl0_267 ),
    inference(resolution,[],[f3378,f2723]) ).

fof(f3537,plain,
    ( ~ spl0_88
    | spl0_302
    | ~ spl0_174
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f3475,f3308,f2855,f3534,f2452]) ).

fof(f2452,plain,
    ( spl0_88
  <=> class_Int_Onumber__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f3534,plain,
    ( spl0_302
  <=> c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f3308,plain,
    ( spl0_254
  <=> 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_254])]) ).

fof(f3475,plain,
    ( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
    | ~ class_Int_Onumber__ring(tc_Int_Oint)
    | ~ spl0_174
    | ~ spl0_254 ),
    inference(superposition,[],[f2856,f3310]) ).

fof(f3310,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f3308]) ).

fof(f3521,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f1843,f3519]) ).

fof(f3519,plain,
    ( spl0_301
  <=> ! [X18] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f1843,plain,
    ! [X18] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X18),
    inference(forward_demodulation,[],[f1368,f582]) ).

fof(f1368,axiom,
    ! [X18] : 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))),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).

fof(f3516,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f1837,f3513]) ).

fof(f3511,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f1637,f3509]) ).

fof(f1637,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

fof(f3507,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f1636,f3505]) ).

fof(f3505,plain,
    ( spl0_298
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f1636,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

fof(f3503,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f1618,f3501]) ).

fof(f1618,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f3499,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f1617,f3497]) ).

fof(f3497,plain,
    ( spl0_296
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f1617,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f3495,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f1599,f3493]) ).

fof(f3493,plain,
    ( spl0_295
  <=> ! [X25,X19] :
        ( X19 = X25
        | hAPP(c_Suc,X19) != hAPP(c_Suc,X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f1599,axiom,
    ! [X19,X25] :
      ( X19 = X25
      | hAPP(c_Suc,X19) != hAPP(c_Suc,X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

fof(f3491,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f1593,f3489]) ).

fof(f3489,plain,
    ( spl0_294
  <=> ! [X2,X0,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f1593,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f3487,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f1592,f3485]) ).

fof(f3485,plain,
    ( spl0_293
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f1592,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X25,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f3483,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f1591,f3481]) ).

fof(f1591,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X3,X0)
      | ~ c_HOL_Oord__class_Oless(X3,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

fof(f3479,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f1352,f3477]) ).

fof(f3477,plain,
    ( spl0_291
  <=> ! [X25,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f1352,axiom,
    ! [X19,X25] :
      ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X19,X25,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).

fof(f3474,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f1279,f3472]) ).

fof(f1279,axiom,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

fof(f3470,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f1278,f3468]) ).

fof(f1278,axiom,
    ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

fof(f3466,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f1243,f3464]) ).

fof(f3464,plain,
    ( spl0_288
  <=> ! [X41,X23] :
        ( c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OBit0(X41),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f1243,axiom,
    ! [X41,X23] :
      ( c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OBit0(X41),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I14_J_0) ).

fof(f3462,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f1242,f3460]) ).

fof(f3460,plain,
    ( spl0_287
  <=> ! [X41,X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OBit0(X41),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1242,axiom,
    ! [X41,X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OBit0(X41),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I14_J_1) ).

fof(f3458,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f1232,f3456]) ).

fof(f1232,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_Divides_Odiv__class_Omod(X18,X17,tc_nat) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

fof(f3454,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f1199,f3452]) ).

fof(f3452,plain,
    ( spl0_285
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1199,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

fof(f3450,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f1198,f3448]) ).

fof(f3448,plain,
    ( spl0_284
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1198,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

fof(f3446,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f1184,f3444]) ).

fof(f3444,plain,
    ( spl0_283
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1184,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

fof(f3442,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f1183,f3440]) ).

fof(f3440,plain,
    ( spl0_282
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f1183,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_HOL_Oord__class_Oless(X18,hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

fof(f3438,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f1182,f3436]) ).

fof(f3436,plain,
    ( spl0_281
  <=> ! [X18,X17] :
        ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
        | c_lessequals(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f1182,axiom,
    ! [X18,X17] :
      ( ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat)
      | c_lessequals(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

fof(f3433,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f1179,f3431]) ).

fof(f3431,plain,
    ( spl0_280
  <=> ! [X18,X17] :
        ( c_HOL_Oord__class_Oless(X17,X18,tc_nat)
        | ~ c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1179,axiom,
    ! [X18,X17] :
      ( c_HOL_Oord__class_Oless(X17,X18,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,X17),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

fof(f3429,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f1170,f3427]) ).

fof(f3427,plain,
    ( spl0_279
  <=> ! [X52,X51] :
        ( c_HOL_Oord__class_Oless(X51,X52,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X51),c_Int_OBit0(X52),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1170,axiom,
    ! [X51,X52] :
      ( c_HOL_Oord__class_Oless(X51,X52,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X51),c_Int_OBit0(X52),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__int__code_I15_J_0) ).

fof(f3425,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f1169,f3423]) ).

fof(f3423,plain,
    ( spl0_278
  <=> ! [X41,X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit0(X41),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f1169,axiom,
    ! [X41,X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit0(X41),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I16_J_1) ).

fof(f3421,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f1156,f3419]) ).

fof(f3419,plain,
    ( spl0_277
  <=> ! [X20,X0] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Int_Onumber__ring(X0)
        | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X20),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1156,axiom,
    ! [X0,X20] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Int_Onumber__ring(X0)
      | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X20),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Bit1_0) ).

fof(f3417,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f1082,f3415]) ).

fof(f3415,plain,
    ( spl0_276
  <=> ! [X18,X17] :
        ( ~ c_lessequals(X18,X17,tc_nat)
        | c_lessequals(X18,hAPP(c_Suc,X17),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f1082,axiom,
    ! [X18,X17] :
      ( ~ c_lessequals(X18,X17,tc_nat)
      | c_lessequals(X18,hAPP(c_Suc,X17),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

fof(f3413,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f1081,f3411]) ).

fof(f3411,plain,
    ( spl0_275
  <=> ! [X18,X17] :
        ( c_lessequals(X18,X17,tc_nat)
        | ~ c_lessequals(hAPP(c_Suc,X18),X17,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f1081,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | ~ c_lessequals(hAPP(c_Suc,X18),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

fof(f3409,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f1075,f3407]) ).

fof(f3407,plain,
    ( spl0_274
  <=> ! [X41,X23] :
        ( c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit1(X41),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f1075,axiom,
    ! [X41,X23] :
      ( c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit1(X41),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I17_J_0) ).

fof(f3405,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f1074,f3403]) ).

fof(f3403,plain,
    ( spl0_273
  <=> ! [X41,X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit1(X41),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f1074,axiom,
    ! [X41,X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,X41,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OBit1(X41),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I17_J_1) ).

fof(f3401,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f968,f3399]) ).

fof(f3399,plain,
    ( spl0_272
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X19,X25,X0)
        | c_lessequals(X25,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f968,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X19,X25,X0)
      | c_lessequals(X25,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f3397,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f923,f3395]) ).

fof(f3395,plain,
    ( spl0_271
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f923,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).

fof(f3391,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f713,f3389]) ).

fof(f3389,plain,
    ( spl0_270
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f713,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

fof(f3387,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f672,f3385]) ).

fof(f672,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X19,X25,X0)
      | c_HOL_Oord__class_Oless(X25,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

fof(f3383,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f670,f3381]) ).

fof(f3381,plain,
    ( spl0_268
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X25,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f670,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X25,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

fof(f3379,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f666,f3377]) ).

fof(f666,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X25,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f3375,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f652,f3373]) ).

fof(f3373,plain,
    ( spl0_266
  <=> ! [X25,X0,X19] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
        | c_lessequals(X19,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f652,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
      | c_lessequals(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

fof(f3371,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f651,f3369]) ).

fof(f651,axiom,
    ! [X0,X19,X25] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X25,X0)
      | c_lessequals(X19,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

fof(f3367,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f581,f3365]) ).

fof(f3365,plain,
    ( spl0_264
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f581,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).

fof(f3363,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f439,f3361]) ).

fof(f3361,plain,
    ( spl0_263
  <=> ! [X25,X0] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f439,axiom,
    ! [X0,X25] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

fof(f3359,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f436,f3357]) ).

fof(f3357,plain,
    ( spl0_262
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f436,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

fof(f3355,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f426,f3353]) ).

fof(f3353,plain,
    ( spl0_261
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f426,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).

fof(f3351,plain,
    ( spl0_260
    | ~ spl0_122
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2999,f2944,f2622,f3348]) ).

fof(f2944,plain,
    ( spl0_191
  <=> ! [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_191])]) ).

fof(f2999,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
    | ~ spl0_122
    | ~ spl0_191 ),
    inference(resolution,[],[f2945,f2624]) ).

fof(f2624,plain,
    ( class_Int_Onumber__ring(tc_Complex_Ocomplex)
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f2622]) ).

fof(f2945,plain,
    ( ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f2944]) ).

fof(f3346,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f381,f3344]) ).

fof(f381,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).

fof(f3342,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f272,f3340]) ).

fof(f3340,plain,
    ( spl0_258
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f272,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

fof(f3338,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f212,f3336]) ).

fof(f3336,plain,
    ( spl0_257
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f212,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).

fof(f3334,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f211,f3332]) ).

fof(f3332,plain,
    ( spl0_256
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f211,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).

fof(f3330,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f34,f3328]) ).

fof(f3328,plain,
    ( spl0_255
  <=> ! [X21] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f34,axiom,
    ! [X21] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X21),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__if_0) ).

fof(f3311,plain,
    ( spl0_254
    | ~ spl0_88
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2998,f2944,f2452,f3308]) ).

fof(f2998,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
    | ~ spl0_88
    | ~ spl0_191 ),
    inference(resolution,[],[f2945,f2454]) ).

fof(f2454,plain,
    ( class_Int_Onumber__ring(tc_Int_Oint)
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f2452]) ).

fof(f3288,plain,
    ( spl0_253
    | ~ spl0_150
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f2993,f2940,f2751,f3286]) ).

fof(f3286,plain,
    ( spl0_253
  <=> ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f2993,plain,
    ( ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat)
    | ~ spl0_150
    | ~ spl0_190 ),
    inference(resolution,[],[f2941,f2752]) ).

fof(f3271,plain,
    ( ~ spl0_252
    | ~ spl0_150
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2898,f2842,f2751,f3268]) ).

fof(f3268,plain,
    ( spl0_252
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2898,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_150
    | ~ spl0_171 ),
    inference(superposition,[],[f2752,f2844]) ).

fof(f3236,plain,
    ( spl0_251
    | ~ spl0_163
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f3009,f2956,f2807,f3233]) ).

fof(f3009,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_163
    | ~ spl0_194 ),
    inference(resolution,[],[f2957,f2809]) ).

fof(f3222,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f1920,f3220]) ).

fof(f1920,plain,
    ! [X17] :
      ( ~ c_HOL_Oord__class_Oless(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X17 ),
    inference(forward_demodulation,[],[f1175,f582]) ).

fof(f1175,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | ~ c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

fof(f3218,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f1860,f3215]) ).

fof(f3215,plain,
    ( spl0_249
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f1860,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1859,f1278]) ).

fof(f1859,plain,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X18),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f23,f1278]) ).

fof(f23,axiom,
    ! [X18,X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).

fof(f3213,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f1609,f3211]) ).

fof(f1609,axiom,
    ! [X18,X17] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),hAPP(c_Suc,X18),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

fof(f3209,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f1563,f3206]) ).

fof(f3206,plain,
    ( spl0_247
  <=> c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f1563,axiom,
    c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root4_0) ).

fof(f3203,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f1557,f3200]) ).

fof(f3200,plain,
    ( spl0_246
  <=> 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_246])]) ).

fof(f1557,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(f3198,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f1501,f3196]) ).

fof(f3196,plain,
    ( spl0_245
  <=> ! [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_245])]) ).

fof(f1501,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_numeral__1__eq__1_0) ).

fof(f3194,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f1407,f3192]) ).

fof(f3192,plain,
    ( spl0_244
  <=> ! [X18] : c_lessequals(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X18),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f1407,axiom,
    ! [X18] : c_lessequals(X18,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X18),X18),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).

fof(f3190,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f1401,f3188]) ).

fof(f1401,axiom,
    ! [X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X17),c_HOL_Oone__class_Oone(tc_nat)) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).

fof(f3186,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f1400,f3184]) ).

fof(f3184,plain,
    ( spl0_242
  <=> ! [X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X17) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f1400,axiom,
    ! [X17] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X17) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).

fof(f3182,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f1349,f3180]) ).

fof(f1349,axiom,
    ! [X17] : c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).

fof(f3178,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f1222,f3176]) ).

fof(f1222,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f3174,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f1220,f3172]) ).

fof(f1220,axiom,
    ! [X24,X22] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X22),X22,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

fof(f3170,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f1219,f3168]) ).

fof(f1219,axiom,
    ! [X24,X22] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X24),X22,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

fof(f3166,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f1191,f3164]) ).

fof(f3164,plain,
    ( spl0_237
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X23,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f1191,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X23,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I4_J_1) ).

fof(f3162,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f1190,f3160]) ).

fof(f3160,plain,
    ( spl0_236
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(c_Int_OPls,X23,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f1190,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(c_Int_OPls,X23,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I4_J_0) ).

fof(f3158,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f1189,f3156]) ).

fof(f3156,plain,
    ( spl0_235
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f1189,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OPls,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I10_J_1) ).

fof(f3154,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f1188,f3152]) ).

fof(f3152,plain,
    ( spl0_234
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f1188,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X23),c_Int_OPls,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I10_J_0) ).

fof(f3150,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f1166,f3148]) ).

fof(f3148,plain,
    ( spl0_233
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f1166,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OPls,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I12_J_1) ).

fof(f3146,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f1165,f3144]) ).

fof(f3144,plain,
    ( spl0_232
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OPls,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f1165,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(X23,c_Int_OPls,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OPls,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I12_J_0) ).

fof(f3142,plain,
    ( spl0_231
    | ~ spl0_143
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f3010,f2956,f2721,f3139]) ).

fof(f3010,plain,
    ( c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_143
    | ~ spl0_194 ),
    inference(resolution,[],[f2957,f2723]) ).

fof(f3137,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f1044,f3135]) ).

fof(f3135,plain,
    ( spl0_230
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f1044,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

fof(f3133,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f1043,f3131]) ).

fof(f3131,plain,
    ( spl0_229
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f1043,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

fof(f3129,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f1041,f3127]) ).

fof(f3127,plain,
    ( spl0_228
  <=> ! [X0,X19] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f1041,axiom,
    ! [X0,X19] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

fof(f3125,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f964,f3123]) ).

fof(f3123,plain,
    ( spl0_227
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f964,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).

fof(f3121,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f764,f3119]) ).

fof(f3119,plain,
    ( spl0_226
  <=> ! [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_226])]) ).

fof(f764,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(f3117,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f748,f3115]) ).

fof(f3115,plain,
    ( spl0_225
  <=> ! [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_225])]) ).

fof(f748,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(f3113,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f741,f3111]) ).

fof(f3111,plain,
    ( spl0_224
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f741,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).

fof(f3109,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f737,f3107]) ).

fof(f3107,plain,
    ( spl0_223
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Odivision__ring(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f737,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Odivision__ring(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).

fof(f3105,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f723,f3103]) ).

fof(f3103,plain,
    ( spl0_222
  <=> ! [X18,X17] : c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f723,axiom,
    ! [X18,X17] : c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

fof(f3101,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f722,f3099]) ).

fof(f3099,plain,
    ( spl0_221
  <=> ! [X18,X17] : c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f722,axiom,
    ! [X18,X17] : c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

fof(f3097,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f712,f3095]) ).

fof(f712,axiom,
    ! [X0,X27] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | ~ c_Int_Oiszero(X27,X0)
      | c_HOL_Ozero__class_Ozero(X0) = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__def_0) ).

fof(f3093,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f634,f3091]) ).

fof(f3091,plain,
    ( spl0_219
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f634,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).

fof(f3089,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f632,f3087]) ).

fof(f3087,plain,
    ( spl0_218
  <=> ! [X0,X19] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X19,X0),X0) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f632,axiom,
    ! [X0,X19] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X19,X0),X0) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

fof(f3085,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f630,f3083]) ).

fof(f3083,plain,
    ( spl0_217
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f630,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

fof(f3081,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f618,f3079]) ).

fof(f618,axiom,
    ! [X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X17) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

fof(f3077,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f616,f3075]) ).

fof(f616,axiom,
    ! [X19] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

fof(f3073,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f560,f3071]) ).

fof(f3071,plain,
    ( spl0_214
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f560,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

fof(f3069,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f559,f3067]) ).

fof(f3067,plain,
    ( spl0_213
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f559,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

fof(f3065,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f556,f3063]) ).

fof(f3063,plain,
    ( spl0_212
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f556,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I9_J_1) ).

fof(f3061,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f555,f3059]) ).

fof(f3059,plain,
    ( spl0_211
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f555,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I9_J_0) ).

fof(f3057,plain,
    ( ~ spl0_21
    | ~ spl0_146
    | spl0_196 ),
    inference(avatar_split_clause,[],[f3019,f2964,f2735,f2117]) ).

fof(f2735,plain,
    ( spl0_146
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f3019,plain,
    ( ~ class_Ring__and__Field_Osemiring__1(tc_nat)
    | ~ spl0_146
    | spl0_196 ),
    inference(resolution,[],[f2966,f2736]) ).

fof(f2736,plain,
    ( ! [X0] :
        ( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Ring__and__Field_Osemiring__1(X0) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f2735]) ).

fof(f2966,plain,
    ( ~ c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | spl0_196 ),
    inference(avatar_component_clause,[],[f2964]) ).

fof(f3056,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f554,f3054]) ).

fof(f3054,plain,
    ( spl0_210
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f554,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I8_J_1) ).

fof(f3052,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f553,f3050]) ).

fof(f3050,plain,
    ( spl0_209
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X23),tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f553,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(c_Int_OMin,X23,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X23),tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I8_J_0) ).

fof(f3048,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f468,f3046]) ).

fof(f3046,plain,
    ( spl0_208
  <=> ! [X23] :
        ( c_HOL_Oord__class_Oless(X23,c_Int_OMin,tc_Int_Oint)
        | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OMin,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f468,axiom,
    ! [X23] :
      ( c_HOL_Oord__class_Oless(X23,c_Int_OMin,tc_Int_Oint)
      | ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OMin,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I13_J_0) ).

fof(f3044,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f467,f3042]) ).

fof(f3042,plain,
    ( spl0_207
  <=> ! [X23] :
        ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OMin,tc_Int_Oint)
        | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OMin,tc_Int_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f467,axiom,
    ! [X23] :
      ( ~ c_HOL_Oord__class_Oless(X23,c_Int_OMin,tc_Int_Oint)
      | c_HOL_Oord__class_Oless(c_Int_OBit1(X23),c_Int_OMin,tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I13_J_1) ).

fof(f3040,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f359,f3038]) ).

fof(f3038,plain,
    ( spl0_206
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f359,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).

fof(f3036,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f284,f3034]) ).

fof(f3034,plain,
    ( spl0_205
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f284,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).

fof(f3032,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f167,f3030]) ).

fof(f3030,plain,
    ( spl0_204
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f167,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).

fof(f3028,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f120,f3026]) ).

fof(f3026,plain,
    ( spl0_203
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f120,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).

fof(f3024,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f70,f3022]) ).

fof(f70,axiom,
    ! [X17] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X17
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

fof(f2987,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f1833,f2985]) ).

fof(f1833,plain,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f707,f582]) ).

fof(f707,axiom,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X18,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

fof(f2983,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f1662,f2981]) ).

fof(f2981,plain,
    ( spl0_200
  <=> ! [X41,X23] :
        ( X23 = X41
        | c_Int_OBit1(X23) != c_Int_OBit1(X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1662,axiom,
    ! [X41,X23] :
      ( X23 = X41
      | c_Int_OBit1(X23) != c_Int_OBit1(X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).

fof(f2979,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f1610,f2977]) ).

fof(f2977,plain,
    ( spl0_199
  <=> ! [X41,X23] :
        ( X23 = X41
        | c_Int_OBit0(X23) != c_Int_OBit0(X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1610,axiom,
    ! [X41,X23] :
      ( X23 = X41
      | c_Int_OBit0(X23) != c_Int_OBit0(X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).

fof(f2975,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f1499,f2973]) ).

fof(f2973,plain,
    ( spl0_198
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1499,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__Numeral1_0) ).

fof(f2971,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f1438,f2969]) ).

fof(f1438,axiom,
    ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

fof(f2967,plain,
    ( ~ spl0_195
    | ~ spl0_196
    | ~ spl0_145
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2895,f2834,f2730,f2964,f2960]) ).

fof(f2960,plain,
    ( spl0_195
  <=> class_Int_Onumber__ring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f2730,plain,
    ( spl0_145
  <=> 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_145])]) ).

fof(f2834,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f2895,plain,
    ( ~ c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ class_Int_Onumber__ring(tc_nat)
    | ~ spl0_145
    | ~ spl0_169 ),
    inference(superposition,[],[f2835,f2732]) ).

fof(f2732,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f2730]) ).

fof(f2835,plain,
    ( ! [X0] :
        ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0)
        | ~ class_Int_Onumber__ring(X0) )
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f2834]) ).

fof(f2958,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f1223,f2956]) ).

fof(f1223,axiom,
    ! [X19,X25] :
      ( ~ c_HOL_Oord__class_Oless(X19,X25,tc_nat)
      | c_lessequals(X19,X25,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

fof(f2954,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f1202,f2952]) ).

fof(f2952,plain,
    ( spl0_193
  <=> ! [X19] :
        ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f1202,axiom,
    ! [X19] :
      ( c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).

fof(f2950,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f1201,f2948]) ).

fof(f2948,plain,
    ( spl0_192
  <=> ! [X19] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X19),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1201,axiom,
    ! [X19] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X19,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X19),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).

fof(f2946,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f1161,f2944]) ).

fof(f1161,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_comp__arith_I112_J_0) ).

fof(f2942,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f969,f2940]) ).

fof(f969,axiom,
    ! [X18,X17] :
      ( c_lessequals(X18,X17,tc_nat)
      | c_lessequals(X17,X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

fof(f2938,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f744,f2936]) ).

fof(f2936,plain,
    ( spl0_189
  <=> ! [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_189])]) ).

fof(f744,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(f2934,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f724,f2932]) ).

fof(f2932,plain,
    ( spl0_188
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f724,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

fof(f2930,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f702,f2928]) ).

fof(f2928,plain,
    ( spl0_187
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f702,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

fof(f2926,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f694,f2924]) ).

fof(f2924,plain,
    ( spl0_186
  <=> ! [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_186])]) ).

fof(f694,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(f2922,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f583,f2920]) ).

fof(f2920,plain,
    ( spl0_185
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f583,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).

fof(f2918,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f449,f2916]) ).

fof(f449,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).

fof(f2907,plain,
    ( ~ spl0_183
    | ~ spl0_144
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f2891,f2812,f2726,f2904]) ).

fof(f2904,plain,
    ( spl0_183
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f2726,plain,
    ( spl0_144
  <=> ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Fact_Ofact__class_Ofact(X17,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f2891,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_144
    | ~ spl0_164 ),
    inference(superposition,[],[f2727,f2814]) ).

fof(f2727,plain,
    ( ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Fact_Ofact__class_Ofact(X17,tc_nat)
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f2726]) ).

fof(f2890,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f1831,f2888]) ).

fof(f1831,plain,
    ! [X18] : c_Divides_Odiv__class_Odiv(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X18,
    inference(forward_demodulation,[],[f160,f582]) ).

fof(f160,axiom,
    ! [X18] : c_Divides_Odiv__class_Odiv(X18,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).

fof(f2886,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f1827,f2884]) ).

fof(f2884,plain,
    ( spl0_181
  <=> ! [X0,X62,X63] :
        ( X62 = X63
        | ~ c_fequal(X62,X63,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1827,axiom,
    ! [X0,X62,X63] :
      ( X62 = X63
      | ~ c_fequal(X62,X63,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f2882,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f1661,f2880]) ).

fof(f2880,plain,
    ( spl0_180
  <=> ! [X41] :
        ( c_Int_OPls = X41
        | c_Int_OPls != c_Int_OBit0(X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1661,axiom,
    ! [X41] :
      ( c_Int_OPls = X41
      | c_Int_OPls != c_Int_OBit0(X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).

fof(f2878,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f1511,f2875]) ).

fof(f2875,plain,
    ( spl0_179
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f2873,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f1441,f2871]) ).

fof(f1441,axiom,
    ! [X18,X17] : c_lessequals(c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),X18,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

fof(f2869,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f1431,f2867]) ).

fof(f1431,axiom,
    ! [X18] : c_HOL_Ominus__class_Ominus(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

fof(f2865,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f1430,f2863]) ).

fof(f1430,axiom,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,X18,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

fof(f2861,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f1172,f2859]) ).

fof(f1172,axiom,
    ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

fof(f2857,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f1159,f2855]) ).

fof(f1159,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__number__of__Pls_0) ).

fof(f2853,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f1071,f2851]) ).

fof(f2851,plain,
    ( spl0_173
  <=> ! [X41] :
        ( c_Int_OMin = X41
        | c_Int_OMin != c_Int_OBit1(X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1071,axiom,
    ! [X41] :
      ( c_Int_OMin = X41
      | c_Int_OMin != c_Int_OBit1(X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).

fof(f2849,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f698,f2847]) ).

fof(f2847,plain,
    ( spl0_172
  <=> ! [X17] : c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f698,axiom,
    ! [X17] : c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__ge__one__nat_0) ).

fof(f2845,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f582,f2842]) ).

fof(f2840,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f456,f2838]) ).

fof(f2838,plain,
    ( spl0_170
  <=> ! [X18,X17] : c_lessequals(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X18,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f456,axiom,
    ! [X18,X17] : c_lessequals(c_Divides_Odiv__class_Omod(X18,X17,tc_nat),X18,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

fof(f2836,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f453,f2834]) ).

fof(f453,axiom,
    ! [X0] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__number__of__Min_0) ).

fof(f2832,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f445,f2829]) ).

fof(f445,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__num__eq__if__nat_0) ).

fof(f2827,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f393,f2825]) ).

fof(f2825,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f393,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_zero__neq__one_0) ).

fof(f2823,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f274,f2821]) ).

fof(f274,axiom,
    ! [X18,X17] : c_lessequals(c_Divides_Odiv__class_Odiv(X18,X17,tc_nat),X18,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__dividend_0) ).

fof(f2819,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f102,f2817]) ).

fof(f102,axiom,
    ! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Fact_Ofact__class_Ofact(X17,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__gt__zero__nat_0) ).

fof(f2815,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f62,f2812]) ).

fof(f62,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__1__nat_0) ).

fof(f2810,plain,
    ( spl0_163
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2805,f2801,f2807]) ).

fof(f2801,plain,
    ( spl0_162
  <=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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),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_162])]) ).

fof(f2805,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat)
    | ~ spl0_162 ),
    inference(forward_demodulation,[],[f2803,f1837]) ).

fof(f2803,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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),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_162 ),
    inference(avatar_component_clause,[],[f2801]) ).

fof(f2804,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f1695,f2801]) ).

fof(f1695,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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),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_conjecture_1) ).

fof(f2799,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f1835,f2796]) ).

fof(f2796,plain,
    ( spl0_161
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f1835,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f1373,f34]) ).

fof(f1373,axiom,
    ! [X19] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X19),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_1) ).

fof(f2794,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f1699,f2792]) ).

fof(f2792,plain,
    ( spl0_160
  <=> ! [X61,X60] :
        ( ~ class_Orderings_Oorder(X61)
        | class_Orderings_Oorder(tc_fun(X60,X61)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1699,axiom,
    ! [X60,X61] :
      ( ~ class_Orderings_Oorder(X61)
      | class_Orderings_Oorder(tc_fun(X60,X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f2790,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f1698,f2788]) ).

fof(f2788,plain,
    ( spl0_159
  <=> ! [X61,X60] :
        ( ~ class_Orderings_Opreorder(X61)
        | class_Orderings_Opreorder(tc_fun(X60,X61)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1698,axiom,
    ! [X60,X61] :
      ( ~ class_Orderings_Opreorder(X61)
      | class_Orderings_Opreorder(tc_fun(X60,X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f2786,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f1697,f2784]) ).

fof(f2784,plain,
    ( spl0_158
  <=> ! [X61,X60] :
        ( ~ class_Lattices_Oboolean__algebra(X61)
        | class_Lattices_Oboolean__algebra(tc_fun(X60,X61)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1697,axiom,
    ! [X60,X61] :
      ( ~ class_Lattices_Oboolean__algebra(X61)
      | class_Lattices_Oboolean__algebra(tc_fun(X60,X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

fof(f2782,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f1644,f2780]) ).

fof(f1644,axiom,
    ! [X17] : c_HOL_Oord__class_Oless(X17,hAPP(c_Suc,X17),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

fof(f2778,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f1583,f2776]) ).

fof(f2776,plain,
    ( spl0_156
  <=> ! [X0,X19] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1583,axiom,
    ! [X0,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f2774,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f1582,f2772]) ).

fof(f1582,axiom,
    ! [X0,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f2770,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f1579,f2768]) ).

fof(f2768,plain,
    ( spl0_154
  <=> ! [X0,X19] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1579,axiom,
    ! [X0,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f2766,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f1323,f2763]) ).

fof(f2763,plain,
    ( spl0_153
  <=> 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_153])]) ).

fof(f2761,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f1196,f2759]) ).

fof(f2759,plain,
    ( spl0_152
  <=> ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X18) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1196,axiom,
    ! [X18] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

fof(f2757,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f1094,f2755]) ).

fof(f1094,axiom,
    ! [X2] : c_FFT__Mirabelle_OFFT(c_HOL_Ozero__class_Ozero(tc_nat),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FFT_Osimps_I1_J_0) ).

fof(f2753,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f1080,f2751]) ).

fof(f1080,axiom,
    ! [X17] : ~ c_lessequals(hAPP(c_Suc,X17),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

fof(f2749,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f950,f2747]) ).

fof(f2747,plain,
    ( spl0_149
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f950,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).

fof(f2745,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f931,f2743]) ).

fof(f2743,plain,
    ( spl0_148
  <=> ! [X0,X19] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f931,axiom,
    ! [X0,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f2741,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f930,f2739]) ).

fof(f2739,plain,
    ( spl0_147
  <=> ! [X0,X19] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X19,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f930,axiom,
    ! [X0,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | c_lessequals(X19,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f2737,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f768,f2735]) ).

fof(f768,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__0_0) ).

fof(f2733,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f505,f2730]) ).

fof(f505,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(f2728,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f385,f2726]) ).

fof(f385,axiom,
    ! [X17] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Fact_Ofact__class_Ofact(X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).

fof(f2724,plain,
    ( spl0_143
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f2719,f2715,f2721]) ).

fof(f2715,plain,
    ( spl0_142
  <=> c_HOL_Oord__class_Oless(v_i____,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_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f2719,plain,
    ( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)),tc_nat)
    | ~ spl0_142 ),
    inference(forward_demodulation,[],[f2717,f1837]) ).

fof(f2717,plain,
    ( c_HOL_Oord__class_Oless(v_i____,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_nat)
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f2715]) ).

fof(f2718,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f1694,f2715]) ).

fof(f1694,axiom,
    c_HOL_Oord__class_Oless(v_i____,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_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f2712,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f1689,f2710]) ).

fof(f2710,plain,
    ( spl0_141
  <=> ! [X41,X23] : c_Int_OBit0(X23) != c_Int_OBit1(X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1689,axiom,
    ! [X41,X23] : c_Int_OBit0(X23) != c_Int_OBit1(X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).

fof(f2708,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f1640,f2706]) ).

fof(f2706,plain,
    ( spl0_140
  <=> ! [X17] : hAPP(c_Suc,X17) != X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1640,axiom,
    ! [X17] : hAPP(c_Suc,X17) != X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f2704,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f1228,f2702]) ).

fof(f1228,axiom,
    ! [X18] : ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

fof(f2700,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f443,f2698]) ).

fof(f443,axiom,
    ! [X17] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

fof(f2694,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f1826,f2692]) ).

fof(f2692,plain,
    ( spl0_137
  <=> ! [X0,X19] : c_fequal(X19,X19,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1826,axiom,
    ! [X0,X19] : c_fequal(X19,X19,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f2690,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f1607,f2688]) ).

fof(f2688,plain,
    ( spl0_136
  <=> ! [X23] : c_Int_OPls != c_Int_OBit1(X23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1607,axiom,
    ! [X23] : c_Int_OPls != c_Int_OBit1(X23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).

fof(f2686,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f1585,f2683]) ).

fof(f2683,plain,
    ( spl0_135
  <=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1585,axiom,
    c_Int_OPls = c_Int_OBit0(c_Int_OPls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).

fof(f2681,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f1581,f2679]) ).

fof(f1581,axiom,
    ! [X19] : ~ c_HOL_Oord__class_Oless(X19,X19,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f2677,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f1238,f2675]) ).

fof(f2675,plain,
    ( spl0_133
  <=> ! [X41] : c_Int_OMin != c_Int_OBit0(X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1238,axiom,
    ! [X41] : c_Int_OMin != c_Int_OBit0(X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).

fof(f2673,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f1076,f2670]) ).

fof(f2670,plain,
    ( spl0_132
  <=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1076,axiom,
    c_Int_OMin = c_Int_OBit1(c_Int_OMin),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).

fof(f2668,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f932,f2666]) ).

fof(f932,axiom,
    ! [X19] : c_lessequals(X19,X19,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

fof(f2664,plain,
    ~ spl0_130,
    inference(avatar_split_clause,[],[f752,f2661]) ).

fof(f2661,plain,
    ( spl0_130
  <=> c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OMin,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f752,axiom,
    ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OMin,tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I3_J_0) ).

fof(f2659,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f717,f2657]) ).

fof(f2657,plain,
    ( spl0_129
  <=> ! [X19] : ~ c_HOL_Oord__class_Oless(X19,X19,tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f717,axiom,
    ! [X19] : ~ c_HOL_Oord__class_Oless(X19,X19,tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zless__le_1) ).

fof(f2655,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f591,f2652]) ).

fof(f591,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(f2650,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f528,f2647]) ).

fof(f528,axiom,
    c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I6_J_0) ).

fof(f2645,plain,
    ~ spl0_126,
    inference(avatar_split_clause,[],[f154,f2642]) ).

fof(f154,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).

fof(f2640,plain,
    ~ spl0_125,
    inference(avatar_split_clause,[],[f1204,f2637]) ).

fof(f2637,plain,
    ( spl0_125
  <=> c_Int_OMin = c_Int_OPls ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f1204,axiom,
    c_Int_OMin != c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).

fof(f2635,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f1823,f2632]) ).

fof(f2632,plain,
    ( spl0_124
  <=> class_Int_Onumber(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1823,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

fof(f2630,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f1822,f2627]) ).

fof(f2627,plain,
    ( spl0_123
  <=> class_Power_Opower(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1822,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

fof(f2625,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f1821,f2622]) ).

fof(f1821,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(f2620,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f1820,f2617]) ).

fof(f2617,plain,
    ( spl0_121
  <=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1820,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f2615,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f1819,f2612]) ).

fof(f2612,plain,
    ( spl0_120
  <=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1819,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

fof(f2610,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f1818,f2607]) ).

fof(f2607,plain,
    ( spl0_119
  <=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1818,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

fof(f2605,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f1817,f2602]) ).

fof(f2602,plain,
    ( spl0_118
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1817,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f2600,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f1816,f2597]) ).

fof(f2597,plain,
    ( spl0_117
  <=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f1816,axiom,
    class_RealVector_Oreal__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).

fof(f2595,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f1815,f2592]) ).

fof(f2592,plain,
    ( spl0_116
  <=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1815,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(f2590,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f1814,f2587]) ).

fof(f2587,plain,
    ( spl0_115
  <=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1814,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

fof(f2585,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f1813,f2582]) ).

fof(f2582,plain,
    ( spl0_114
  <=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1813,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

fof(f2580,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f1812,f2577]) ).

fof(f2577,plain,
    ( spl0_113
  <=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1812,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

fof(f2575,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f1811,f2572]) ).

fof(f2572,plain,
    ( spl0_112
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1811,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

fof(f2570,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f1810,f2567]) ).

fof(f2567,plain,
    ( spl0_111
  <=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1810,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(f2565,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f1809,f2562]) ).

fof(f2562,plain,
    ( spl0_110
  <=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1809,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

fof(f2560,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f1808,f2557]) ).

fof(f2557,plain,
    ( spl0_109
  <=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1808,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(f2555,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f1807,f2552]) ).

fof(f2552,plain,
    ( spl0_108
  <=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1807,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(f2550,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f1806,f2547]) ).

fof(f2547,plain,
    ( spl0_107
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1806,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(f2545,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f1805,f2542]) ).

fof(f2542,plain,
    ( spl0_106
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1805,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(f2540,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f1804,f2537]) ).

fof(f2537,plain,
    ( spl0_105
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1804,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

fof(f2535,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f1803,f2532]) ).

fof(f2532,plain,
    ( spl0_104
  <=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f1803,axiom,
    class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

fof(f2530,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f1802,f2527]) ).

fof(f2527,plain,
    ( spl0_103
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1802,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(f2525,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f1801,f2522]) ).

fof(f2522,plain,
    ( spl0_102
  <=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1801,axiom,
    class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

fof(f2520,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f1800,f2517]) ).

fof(f2517,plain,
    ( spl0_101
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1800,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

fof(f2515,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f1799,f2512]) ).

fof(f2512,plain,
    ( spl0_100
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1799,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

fof(f2510,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f1798,f2507]) ).

fof(f2507,plain,
    ( spl0_99
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1798,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

fof(f2505,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f1797,f2502]) ).

fof(f2502,plain,
    ( spl0_98
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1797,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f2500,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f1796,f2497]) ).

fof(f1796,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(f2495,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f1795,f2492]) ).

fof(f2492,plain,
    ( spl0_96
  <=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1795,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(f2490,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f1794,f2487]) ).

fof(f2487,plain,
    ( spl0_95
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1794,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(f2485,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f1793,f2482]) ).

fof(f2482,plain,
    ( spl0_94
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1793,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

fof(f2480,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f1792,f2477]) ).

fof(f2477,plain,
    ( spl0_93
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f1792,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(f2475,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f1791,f2472]) ).

fof(f2472,plain,
    ( spl0_92
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f1791,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(f2470,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f1790,f2467]) ).

fof(f2467,plain,
    ( spl0_91
  <=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1790,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(f2465,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f1789,f2462]) ).

fof(f2462,plain,
    ( spl0_90
  <=> class_Int_Onumber(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f1789,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

fof(f2460,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f1788,f2457]) ).

fof(f2457,plain,
    ( spl0_89
  <=> class_Power_Opower(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f1788,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

fof(f2455,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f1787,f2452]) ).

fof(f1787,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

fof(f2450,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f1786,f2447]) ).

fof(f2447,plain,
    ( spl0_87
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f1786,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

fof(f2445,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f1785,f2442]) ).

fof(f2442,plain,
    ( spl0_86
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1785,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

fof(f2440,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f1784,f2437]) ).

fof(f2437,plain,
    ( spl0_85
  <=> class_Divides_Oring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1784,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).

fof(f2435,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f1783,f2432]) ).

fof(f2432,plain,
    ( spl0_84
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f1783,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

fof(f2430,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f1782,f2427]) ).

fof(f1782,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

fof(f2425,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f1781,f2422]) ).

fof(f2422,plain,
    ( spl0_82
  <=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f1781,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

fof(f2420,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f1780,f2417]) ).

fof(f2417,plain,
    ( spl0_81
  <=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1780,axiom,
    class_Ring__and__Field_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).

fof(f2415,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f1779,f2412]) ).

fof(f2412,plain,
    ( spl0_80
  <=> class_Divides_Osemiring__div(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f1779,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).

fof(f2410,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f1778,f2407]) ).

fof(f2407,plain,
    ( spl0_79
  <=> class_Ring__and__Field_Oabs__if(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f1778,axiom,
    class_Ring__and__Field_Oabs__if(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).

fof(f2405,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f1777,f2402]) ).

fof(f2402,plain,
    ( spl0_78
  <=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1777,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(f2400,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f1776,f2397]) ).

fof(f2397,plain,
    ( spl0_77
  <=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1776,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

fof(f2395,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f1775,f2392]) ).

fof(f2392,plain,
    ( spl0_76
  <=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1775,axiom,
    class_OrderedGroup_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).

fof(f2390,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f1774,f2387]) ).

fof(f2387,plain,
    ( spl0_75
  <=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f1774,axiom,
    class_Ring__and__Field_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).

fof(f2385,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f1773,f2382]) ).

fof(f2382,plain,
    ( spl0_74
  <=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f1773,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

fof(f2380,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f1772,f2377]) ).

fof(f2377,plain,
    ( spl0_73
  <=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f1772,axiom,
    class_Ring__and__Field_Omult__mono(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).

fof(f2375,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f1771,f2372]) ).

fof(f2372,plain,
    ( spl0_72
  <=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f1771,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(f2370,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f1770,f2367]) ).

fof(f2367,plain,
    ( spl0_71
  <=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f1770,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

fof(f2365,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f1769,f2362]) ).

fof(f2362,plain,
    ( spl0_70
  <=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f1769,axiom,
    class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).

fof(f2360,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f1768,f2357]) ).

fof(f2357,plain,
    ( spl0_69
  <=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f1768,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(f2355,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f1767,f2352]) ).

fof(f2352,plain,
    ( spl0_68
  <=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f1767,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(f2350,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f1766,f2347]) ).

fof(f2347,plain,
    ( spl0_67
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f1766,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(f2345,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f1765,f2342]) ).

fof(f2342,plain,
    ( spl0_66
  <=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1765,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(f2340,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f1764,f2337]) ).

fof(f2337,plain,
    ( spl0_65
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f1764,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(f2335,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f1763,f2332]) ).

fof(f2332,plain,
    ( spl0_64
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1763,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

fof(f2330,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f1762,f2327]) ).

fof(f2327,plain,
    ( spl0_63
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1762,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(f2325,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f1761,f2322]) ).

fof(f2322,plain,
    ( spl0_62
  <=> class_Ring__and__Field_Olordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1761,axiom,
    class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).

fof(f2320,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f1760,f2317]) ).

fof(f2317,plain,
    ( spl0_61
  <=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f1760,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(f2315,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f1759,f2312]) ).

fof(f2312,plain,
    ( spl0_60
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f1759,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).

fof(f2310,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f1758,f2307]) ).

fof(f2307,plain,
    ( spl0_59
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1758,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).

fof(f2305,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f1757,f2302]) ).

fof(f2302,plain,
    ( spl0_58
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f1757,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).

fof(f2300,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f1756,f2297]) ).

fof(f2297,plain,
    ( spl0_57
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1756,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(f2295,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f1755,f2292]) ).

fof(f2292,plain,
    ( spl0_56
  <=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1755,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(f2290,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f1754,f2287]) ).

fof(f2287,plain,
    ( spl0_55
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f1754,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(f2285,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f1753,f2282]) ).

fof(f2282,plain,
    ( spl0_54
  <=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f1753,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).

fof(f2280,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f1752,f2277]) ).

fof(f2277,plain,
    ( spl0_53
  <=> class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f1752,axiom,
    class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).

fof(f2275,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f1751,f2272]) ).

fof(f2272,plain,
    ( spl0_52
  <=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1751,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).

fof(f2270,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f1750,f2267]) ).

fof(f2267,plain,
    ( spl0_51
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1750,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).

fof(f2265,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f1749,f2262]) ).

fof(f2262,plain,
    ( spl0_50
  <=> class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1749,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(f2260,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f1748,f2257]) ).

fof(f2257,plain,
    ( spl0_49
  <=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1748,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(f2255,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f1747,f2252]) ).

fof(f2252,plain,
    ( spl0_48
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1747,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(f2250,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f1746,f2247]) ).

fof(f2247,plain,
    ( spl0_47
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f1746,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(f2245,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f1745,f2242]) ).

fof(f2242,plain,
    ( spl0_46
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f1745,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(f2240,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f1744,f2237]) ).

fof(f2237,plain,
    ( spl0_45
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1744,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(f2235,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f1743,f2232]) ).

fof(f2232,plain,
    ( spl0_44
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f1743,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(f2230,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f1742,f2227]) ).

fof(f2227,plain,
    ( spl0_43
  <=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f1742,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).

fof(f2225,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f1741,f2222]) ).

fof(f2222,plain,
    ( spl0_42
  <=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1741,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).

fof(f2220,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f1740,f2217]) ).

fof(f2217,plain,
    ( spl0_41
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1740,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f2215,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f1739,f2212]) ).

fof(f2212,plain,
    ( spl0_40
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f1739,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(f2210,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f1738,f2207]) ).

fof(f2207,plain,
    ( spl0_39
  <=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1738,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(f2205,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1737,f2202]) ).

fof(f2202,plain,
    ( spl0_38
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1737,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f2200,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f1736,f2197]) ).

fof(f2197,plain,
    ( spl0_37
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1736,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(f2195,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f1735,f2192]) ).

fof(f2192,plain,
    ( spl0_36
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f1735,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(f2190,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f1734,f2187]) ).

fof(f2187,plain,
    ( spl0_35
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f1734,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(f2185,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f1733,f2182]) ).

fof(f2182,plain,
    ( spl0_34
  <=> class_Int_Onumber(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f1733,axiom,
    class_Int_Onumber(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

fof(f2180,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f1732,f2177]) ).

fof(f2177,plain,
    ( spl0_33
  <=> class_Power_Opower(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f1732,axiom,
    class_Power_Opower(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

fof(f2175,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f1731,f2172]) ).

fof(f1731,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f2170,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f1730,f2167]) ).

fof(f1730,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f2165,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f1729,f2162]) ).

fof(f1729,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f2160,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f1728,f2157]) ).

fof(f2157,plain,
    ( spl0_29
  <=> class_Divides_Osemiring__div(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f1728,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

fof(f2155,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f1727,f2152]) ).

fof(f2152,plain,
    ( spl0_28
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1727,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f2150,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f1726,f2147]) ).

fof(f2147,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f1726,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f2145,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f1725,f2142]) ).

fof(f2142,plain,
    ( spl0_26
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1725,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f2140,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f1724,f2137]) ).

fof(f2137,plain,
    ( spl0_25
  <=> class_Ring__and__Field_Omult__mono(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1724,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(f2135,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f1723,f2132]) ).

fof(f2132,plain,
    ( spl0_24
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f1723,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f2130,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f1722,f2127]) ).

fof(f2127,plain,
    ( spl0_23
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1722,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(f2125,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f1721,f2122]) ).

fof(f2122,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1721,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

fof(f2120,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f1720,f2117]) ).

fof(f1720,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f2115,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f1719,f2112]) ).

fof(f2112,plain,
    ( spl0_20
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f1719,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(f2110,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f1718,f2107]) ).

fof(f2107,plain,
    ( spl0_19
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f1718,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f2105,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f1717,f2102]) ).

fof(f2102,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1717,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f2100,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f1716,f2097]) ).

fof(f2097,plain,
    ( spl0_17
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1716,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f2095,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f1715,f2092]) ).

fof(f2092,plain,
    ( spl0_16
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f1715,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f2090,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f1714,f2087]) ).

fof(f2087,plain,
    ( spl0_15
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f1714,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f2085,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f1713,f2082]) ).

fof(f1713,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(f2080,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f1712,f2077]) ).

fof(f2077,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1712,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f2075,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f1711,f2072]) ).

fof(f2072,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1711,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(f2070,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f1710,f2067]) ).

fof(f2067,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f1710,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(f2065,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1709,f2062]) ).

fof(f2062,plain,
    ( spl0_10
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f1709,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(f2060,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1708,f2057]) ).

fof(f2057,plain,
    ( spl0_9
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1708,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f2055,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f1707,f2052]) ).

fof(f2052,plain,
    ( spl0_8
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f1707,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f2050,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f1706,f2047]) ).

fof(f2047,plain,
    ( spl0_7
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1706,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f2045,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f1705,f2042]) ).

fof(f2042,plain,
    ( spl0_6
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1705,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f2040,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f1704,f2037]) ).

fof(f2037,plain,
    ( spl0_5
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1704,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(f2035,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f1703,f2032]) ).

fof(f2032,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1703,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f2030,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f1702,f2027]) ).

fof(f2027,plain,
    ( spl0_3
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1702,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(f2025,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f1701,f2022]) ).

fof(f2022,plain,
    ( spl0_2
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1701,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(f2020,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f1700,f2017]) ).

fof(f2017,plain,
    ( spl0_1
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f1700,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
% 0.07/0.12  % Problem    : SWV706-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.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   : Fri May  3 20:59:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (3613)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (3616)WARNING: value z3 for option sas not known
% 0.21/0.48  % (3614)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.48  % (3615)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.48  % (3617)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.48  % (3616)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)
% 0.21/0.48  % (3618)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)
% 0.21/0.48  % (3619)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)
% 0.21/0.48  % (3620)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)
% 1.93/0.77  TRYING [1]
% 2.42/0.80  TRYING [2]
% 6.32/1.35  TRYING [3]
% 7.31/1.48  TRYING [1]
% 7.79/1.58  TRYING [2]
% 9.52/1.79  TRYING [1]
% 9.80/1.83  TRYING [2]
% 12.50/2.26  TRYING [3]
% 25.01/4.02  TRYING [3]
% 27.00/4.28  % (3618)First to succeed.
% 27.00/4.33  % (3618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3613"
% 27.00/4.33  % (3618)Refutation found. Thanks to Tanya!
% 27.00/4.33  % SZS status Unsatisfiable for theBenchmark
% 27.00/4.33  % SZS output start Proof for theBenchmark
% See solution above
% 27.00/4.36  % (3618)------------------------------
% 27.00/4.36  % (3618)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 27.00/4.36  % (3618)Termination reason: Refutation
% 27.00/4.36  
% 27.00/4.36  % (3618)Memory used [KB]: 32660
% 27.00/4.36  % (3618)Time elapsed: 3.850 s
% 27.00/4.36  % (3618)Instructions burned: 11403 (million)
% 27.00/4.36  % (3613)Success in time 3.95 s
%------------------------------------------------------------------------------