TSTP Solution File: SWV243-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV243-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 10:47:38 EDT 2024
% Result : Unsatisfiable 11.05s 2.02s
% Output : Refutation 11.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4767
% Syntax : Number of formulae : 8994 (2888 unt; 0 def)
% Number of atoms : 20692 (3921 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 20530 (8832 ~;9051 |; 0 &)
% (2647 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2717 (2715 usr;2648 prp; 0-3 aty)
% Number of functors : 248 ( 248 usr; 49 con; 0-18 aty)
% Number of variables : 12739 (12739 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36319,plain,
$false,
inference(avatar_sat_refutation,[],[f3255,f3260,f3265,f3270,f3275,f3280,f3285,f3290,f3295,f3300,f3305,f3310,f3315,f3320,f3325,f3330,f3335,f3340,f3345,f3350,f3355,f3360,f3365,f3370,f3375,f3380,f3385,f3390,f3395,f3400,f3405,f3410,f3415,f3420,f3425,f3430,f3435,f3440,f3445,f3450,f3455,f3460,f3465,f3470,f3475,f3480,f3485,f3490,f3495,f3500,f3505,f3510,f3515,f3520,f3525,f3530,f3535,f3540,f3545,f3550,f3555,f3560,f3565,f3570,f3575,f3580,f3585,f3590,f3595,f3600,f3605,f3610,f3615,f3620,f3625,f3630,f3635,f3640,f3645,f3650,f3655,f3660,f3665,f3670,f3675,f3680,f3685,f3690,f3695,f3700,f3705,f3710,f3715,f3719,f3724,f3729,f3733,f3737,f3742,f3747,f3751,f3755,f3760,f3765,f3770,f3775,f3780,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f3837,f3841,f3845,f3849,f3853,f3857,f3861,f3865,f3869,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3929,f3933,f3937,f3941,f3945,f3949,f3953,f3957,f3961,f3965,f3969,f3973,f3977,f3981,f3985,f3989,f3993,f3997,f4001,f4005,f4009,f4013,f4017,f4021,f4025,f4029,f4033,f4037,f4041,f4045,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4185,f4189,f4193,f4197,f4201,f4205,f4209,f4213,f4217,f4221,f4225,f4229,f4233,f4237,f4241,f4245,f4249,f4253,f4257,f4261,f4265,f4269,f4273,f4277,f4281,f4285,f4289,f4293,f4297,f4301,f4305,f4309,f4313,f4317,f4321,f4325,f4329,f4333,f4337,f4341,f4345,f4349,f4353,f4357,f4361,f4365,f4369,f4373,f4377,f4381,f4385,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4417,f4421,f4425,f4429,f4433,f4437,f4441,f4445,f4449,f4453,f4457,f4461,f4465,f4469,f4473,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4521,f4525,f4529,f4533,f4537,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4597,f4601,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4653,f4657,f4661,f4665,f4669,f4673,f4677,f4681,f4685,f4689,f4693,f4697,f4701,f4705,f4709,f4713,f4717,f4721,f4725,f4729,f4733,f4737,f4741,f4745,f4749,f4753,f4757,f4761,f4765,f4769,f4773,f4777,f4781,f4785,f4789,f4793,f4797,f4801,f4805,f4809,f4813,f4817,f4821,f4825,f4829,f4833,f4837,f4841,f4845,f4849,f4853,f4857,f4861,f4865,f4869,f4873,f4877,f4881,f4885,f4889,f4893,f4897,f4901,f4905,f4909,f4913,f4917,f4921,f4925,f4929,f4933,f4937,f4941,f4945,f4949,f4953,f4957,f4961,f4965,f4969,f4973,f4977,f4981,f4985,f4989,f4993,f4997,f5001,f5005,f5009,f5013,f5017,f5021,f5025,f5029,f5033,f5037,f5041,f5045,f5049,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5101,f5105,f5109,f5113,f5117,f5121,f5125,f5129,f5133,f5137,f5141,f5145,f5149,f5153,f5157,f5161,f5165,f5169,f5173,f5177,f5181,f5185,f5189,f5193,f5197,f5201,f5205,f5209,f5213,f5217,f5221,f5225,f5229,f5233,f5237,f5241,f5245,f5249,f5253,f5257,f5261,f5265,f5269,f5273,f5277,f5281,f5285,f5289,f5293,f5297,f5301,f5305,f5309,f5313,f5317,f5321,f5325,f5329,f5333,f5337,f5341,f5345,f5349,f5353,f5357,f5361,f5365,f5369,f5373,f5377,f5381,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5453,f5457,f5461,f5465,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5497,f5501,f5505,f5509,f5513,f5517,f5521,f5525,f5529,f5533,f5537,f5541,f5545,f5549,f5553,f5557,f5561,f5565,f5569,f5573,f5577,f5581,f5585,f5589,f5593,f5597,f5601,f5605,f5609,f5613,f5617,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5657,f5661,f5665,f5669,f5673,f5677,f5681,f5685,f5689,f5693,f5697,f5701,f5705,f5709,f5713,f5717,f5721,f5725,f5729,f5733,f5737,f5741,f5745,f5749,f5753,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5793,f5797,f5801,f5805,f5809,f5813,f5817,f5821,f5825,f5829,f5833,f5837,f5841,f5845,f5849,f5853,f5857,f5861,f5865,f5869,f5873,f5877,f5881,f5885,f5889,f5893,f5897,f5901,f5905,f5909,f5914,f5919,f5924,f5928,f5932,f5936,f5941,f5945,f5950,f5954,f5958,f5962,f5967,f5972,f5977,f5982,f5986,f5991,f5996,f6763,f6767,f6771,f6775,f6779,f6784,f6788,f6792,f6796,f6800,f6804,f6808,f6813,f6818,f6823,f6827,f6831,f6835,f6840,f6844,f6848,f6852,f6856,f6860,f6864,f6868,f6873,f6878,f6883,f6888,f6893,f6898,f6903,f6908,f6913,f6918,f6923,f6928,f6933,f6938,f6943,f6948,f6952,f6956,f6960,f6964,f6968,f6972,f6977,f6982,f6987,f6991,f6995,f6999,f7003,f7007,f7011,f7016,f7021,f7025,f7030,f7035,f7039,f7043,f7047,f7051,f7055,f7059,f7063,f7067,f7072,f7077,f7081,f7086,f7090,f7095,f7106,f7111,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7247,f7251,f7255,f7259,f7263,f7267,f7271,f7275,f7279,f7283,f7287,f7291,f7295,f7299,f7303,f7307,f7312,f7316,f7320,f7324,f7328,f7332,f7336,f7340,f7344,f7348,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7392,f7396,f7400,f7404,f7408,f7412,f7416,f7420,f7424,f7428,f7432,f7437,f7441,f7446,f7450,f7455,f7459,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7540,f7544,f7548,f7552,f7556,f7560,f7564,f7568,f7572,f7576,f7580,f7584,f7588,f7592,f7596,f7600,f7604,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7648,f7652,f7656,f7660,f7664,f7668,f7672,f7676,f7680,f7684,f7688,f7692,f7696,f7700,f7704,f7709,f7714,f7718,f7722,f7726,f7742,f7772,f7793,f7805,f7812,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7849,f7853,f7857,f7861,f7865,f7869,f7873,f7878,f7882,f7886,f7890,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f7943,f7947,f7951,f7955,f7959,f7963,f7967,f7971,f7975,f7984,f7988,f7992,f7996,f8000,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8032,f8036,f8040,f8044,f8048,f8052,f8056,f8060,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8100,f8104,f8109,f8113,f8117,f8121,f8125,f8130,f8134,f8138,f8142,f8146,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8196,f8206,f8329,f8333,f8337,f8341,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8398,f8402,f8406,f8410,f8414,f8418,f8422,f8426,f8431,f8435,f8439,f8443,f8447,f8451,f8455,f8459,f8463,f8467,f8471,f8475,f8479,f8483,f8487,f8491,f8495,f8499,f8503,f8507,f8511,f8516,f8520,f8524,f8528,f8532,f8536,f8540,f8544,f8548,f8552,f8556,f8560,f8564,f8568,f8572,f8576,f8580,f8584,f8588,f8592,f8596,f8600,f8604,f8608,f8612,f8616,f8620,f8624,f8628,f8632,f8636,f8640,f8644,f8648,f8652,f8656,f8660,f8664,f8668,f8672,f8676,f8680,f8684,f8688,f8692,f8725,f8774,f8802,f8820,f8866,f8891,f8924,f8928,f8932,f8936,f8941,f8945,f8949,f8953,f8957,f8961,f8965,f8969,f8973,f8977,f8981,f8985,f8989,f8993,f8997,f9001,f9005,f9009,f9013,f9017,f9021,f9026,f9030,f9034,f9038,f9042,f9046,f9050,f9054,f9059,f9063,f9067,f9071,f9075,f9079,f9083,f9087,f9091,f9095,f9099,f9103,f9107,f9111,f9115,f9119,f9123,f9127,f9131,f9135,f9139,f9143,f9147,f9151,f9155,f9159,f9163,f9167,f9171,f9175,f9179,f9183,f9187,f9191,f9195,f9199,f9203,f9207,f9211,f9215,f9219,f9223,f9227,f9231,f9236,f9240,f9245,f9249,f9256,f9260,f9264,f9268,f9272,f9276,f9283,f9340,f9390,f9422,f9464,f9481,f9498,f9513,f9517,f9521,f9525,f9529,f9533,f9537,f9541,f9546,f9550,f9554,f9558,f9562,f9566,f9570,f9574,f9578,f9582,f9586,f9590,f9594,f9598,f9602,f9606,f9610,f9614,f9618,f9622,f9626,f9630,f9634,f9638,f9642,f9646,f9650,f9654,f9658,f9662,f9666,f9670,f9674,f9678,f9682,f9686,f9690,f9694,f9698,f9702,f9706,f9710,f9714,f9718,f9722,f9726,f9730,f9734,f9738,f9742,f9746,f9750,f9754,f9758,f9762,f9766,f9770,f9774,f9778,f9782,f9786,f9790,f9794,f9798,f9802,f9806,f9811,f9819,f9823,f9827,f9831,f9835,f9839,f9844,f9848,f9882,f9889,f10154,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10319,f10323,f10327,f10331,f10335,f10339,f10343,f10347,f10351,f10355,f10359,f10363,f10367,f10371,f10375,f10380,f10385,f10389,f10393,f10397,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10445,f10449,f10453,f10457,f10461,f10465,f10469,f10473,f10477,f10481,f10485,f10490,f10494,f10498,f10502,f10506,f10510,f10514,f10518,f10522,f10526,f10530,f10534,f10538,f10542,f10546,f10550,f10554,f10558,f10562,f10566,f10570,f10577,f10581,f10585,f10589,f10593,f10597,f10601,f10605,f10609,f10613,f10617,f10621,f10625,f10629,f10633,f10637,f10641,f10645,f10649,f10653,f10661,f10665,f10669,f10673,f10677,f10681,f10685,f10689,f10693,f10697,f10702,f10706,f10710,f10714,f10718,f10722,f10726,f10730,f10734,f10738,f10745,f10749,f10753,f10757,f10761,f10765,f10769,f10773,f10777,f10781,f10791,f10795,f10799,f10834,f10971,f11037,f11260,f11431,f11804,f11808,f11812,f11816,f11820,f11824,f11828,f11832,f11836,f11840,f11844,f11848,f11854,f11858,f11862,f11866,f11870,f11874,f11878,f11882,f11886,f11890,f11898,f11902,f11906,f11910,f11914,f11918,f11922,f11926,f11930,f11934,f11943,f11947,f11951,f11955,f11959,f11963,f11967,f11971,f11975,f11979,f11988,f11992,f11996,f12000,f12004,f12008,f12012,f12016,f12020,f12024,f12029,f12033,f12037,f12041,f12045,f12049,f12053,f12057,f12061,f12065,f12069,f12074,f12078,f12082,f12086,f12090,f12094,f12098,f12102,f12106,f12110,f12125,f12129,f12133,f12137,f12141,f12145,f12149,f12153,f12157,f12161,f12171,f12175,f12179,f12183,f12187,f12191,f12195,f12199,f12203,f12207,f12216,f12220,f12224,f12228,f12232,f12236,f12240,f12244,f12248,f12253,f12261,f12268,f12272,f12276,f12280,f12285,f12293,f12297,f12302,f12333,f12337,f12341,f12345,f12349,f12353,f12357,f12580,f13207,f13447,f13568,f13645,f13649,f13653,f13657,f13661,f13665,f13669,f13673,f13677,f13681,f13685,f13689,f13693,f13697,f13701,f13705,f13709,f13713,f13717,f13721,f13725,f13729,f13733,f13737,f13741,f13745,f13749,f13753,f13757,f13761,f13765,f13769,f13773,f13777,f13781,f13785,f13789,f13793,f13797,f13801,f13805,f13809,f13813,f13817,f13821,f13825,f13829,f13833,f13837,f13841,f13845,f13849,f13853,f13857,f13862,f13866,f13870,f13874,f13878,f13882,f13886,f13890,f13894,f13898,f13902,f13906,f13910,f13914,f13918,f13922,f13926,f13930,f13934,f13938,f13942,f13946,f13971,f13976,f13985,f13989,f13993,f13997,f14621,f14753,f15006,f15022,f15026,f15030,f15034,f15038,f15042,f15046,f15050,f15055,f15059,f15063,f15067,f15071,f15075,f15079,f15083,f15087,f15091,f15095,f15100,f15104,f15108,f15112,f15116,f15120,f15124,f15128,f15132,f15136,f15140,f15144,f15148,f15152,f15156,f15160,f15164,f15168,f15172,f15176,f15180,f15193,f15197,f15201,f15205,f15209,f15213,f15217,f15221,f15225,f15229,f15233,f15237,f15241,f15245,f15249,f15253,f15257,f15261,f15265,f15270,f15307,f15312,f15330,f15335,f15355,f15359,f15363,f15367,f15371,f15375,f15379,f15383,f15387,f15391,f15395,f15399,f15406,f15558,f15816,f15976,f16091,f16443,f16447,f16451,f16455,f16459,f16463,f16467,f16471,f16475,f16479,f16483,f16487,f16491,f16495,f16499,f16503,f16522,f16526,f16530,f16534,f16538,f16542,f16547,f16551,f16555,f16559,f16563,f16567,f16571,f16575,f16579,f16583,f16587,f16591,f16595,f16599,f16603,f16607,f16611,f16615,f16619,f16623,f16627,f16631,f16635,f16639,f16643,f16647,f16651,f16655,f16659,f16663,f16667,f16671,f16675,f16679,f16683,f16687,f16691,f16699,f16703,f16707,f16711,f16716,f16744,f16749,f16807,f16812,f16907,f16912,f17011,f17016,f17046,f17051,f17069,f17073,f17078,f17086,f17091,f17099,f17105,f17111,f17115,f17119,f17123,f17129,f17135,f17139,f17143,f17147,f17151,f17157,f17190,f17194,f17208,f17348,f17470,f17648,f17734,f18045,f18317,f18422,f18426,f18430,f18434,f18442,f18446,f18450,f18454,f18458,f18462,f18466,f18470,f18474,f18478,f18482,f18486,f18490,f18494,f18498,f18502,f18506,f18510,f18514,f18518,f18522,f18526,f18530,f18534,f18538,f18542,f18546,f18550,f18554,f18558,f18562,f18566,f18570,f18574,f18578,f18582,f18586,f18590,f18594,f18598,f18602,f18606,f18610,f18614,f18618,f18622,f18626,f18630,f18634,f18638,f18642,f18646,f18652,f18678,f18682,f18688,f18773,f18778,f18803,f18807,f18811,f18816,f18820,f18825,f18830,f18835,f18840,f18845,f18849,f18853,f18857,f18861,f18866,f18888,f18892,f18896,f18900,f18905,f18910,f18915,f18919,f18925,f18930,f18936,f18941,f18954,f18958,f18963,f18967,f18976,f18980,f18984,f18988,f18992,f19034,f19258,f19529,f19656,f19990,f19994,f19998,f20002,f20006,f20010,f20014,f20020,f20037,f20041,f20045,f20049,f20053,f20057,f20061,f20065,f20069,f20073,f20085,f20089,f20093,f20097,f20101,f20105,f20109,f20113,f20117,f20121,f20139,f20143,f20147,f20151,f20155,f20159,f20163,f20167,f20171,f20175,f20183,f20189,f20510,f20519,f20778,f21302,f21306,f21310,f21314,f21318,f21323,f21327,f21332,f21336,f21341,f21345,f21349,f21353,f21357,f21361,f21365,f21369,f21373,f21378,f21382,f21386,f21444,f21480,f21853,f21857,f21861,f21865,f21869,f21874,f21878,f21882,f21886,f21890,f21894,f21898,f21902,f21906,f21910,f21985,f21989,f21993,f21998,f22003,f22009,f22030,f22035,f22049,f22053,f22057,f22061,f22066,f22087,f22092,f22113,f22117,f22158,f22163,f22533,f22537,f22646,f22650,f22655,f22659,f22663,f22667,f22671,f22675,f22679,f22683,f22687,f22691,f22697,f22701,f22705,f22709,f22713,f22717,f22721,f22725,f22729,f22733,f22739,f22743,f22747,f22751,f22755,f22759,f22763,f22767,f22771,f22775,f22785,f22789,f22793,f22797,f22801,f22805,f22809,f22813,f22817,f22821,f22826,f22830,f22834,f22838,f22842,f22846,f22850,f22854,f22858,f22862,f22866,f22871,f22875,f22879,f22883,f22887,f22891,f22895,f22899,f22903,f22910,f22933,f22940,f22963,f22967,f22971,f22975,f22981,f23042,f23050,f23054,f23058,f23062,f23066,f23070,f23074,f23079,f23106,f23112,f24079,f24136,f24140,f24144,f24148,f24152,f24156,f24160,f24164,f24168,f24172,f24176,f24180,f24184,f24188,f24192,f24196,f24200,f24204,f24208,f24212,f24219,f24223,f24227,f24231,f24235,f24239,f24243,f24247,f24251,f24255,f24268,f24658,f25002,f25006,f25010,f25014,f25018,f25022,f25026,f25030,f25034,f25038,f25042,f25046,f25050,f25054,f25058,f25062,f25066,f25070,f25074,f25078,f25083,f25087,f25092,f25117,f25122,f25172,f25176,f25180,f25185,f25505,f25915,f25919,f25923,f25927,f25931,f25935,f25939,f25944,f25949,f25953,f25957,f25961,f25965,f25969,f25973,f25977,f25983,f25989,f26071,f26075,f26079,f26083,f26087,f26092,f26102,f26106,f26146,f26187,f26191,f26338,f26539,f26588,f26592,f26596,f26600,f26604,f26608,f26612,f26757,f26761,f26765,f26769,f26773,f26777,f26781,f26785,f26799,f26803,f26807,f26811,f26815,f26819,f26823,f27223,f27227,f27231,f27235,f27239,f27244,f27404,f27408,f27412,f27416,f27420,f27424,f27428,f27433,f27437,f27441,f27445,f27449,f27453,f27457,f27461,f27465,f27469,f27473,f27477,f27481,f27485,f27489,f27493,f27497,f27501,f27505,f27511,f27541,f27547,f27555,f27561,f27577,f27583,f27632,f27638,f27642,f27655,f27660,f27810,f28195,f28423,f28427,f28472,f28476,f28480,f28484,f28488,f28493,f28504,f28586,f28590,f28594,f28598,f28602,f28606,f28610,f28933,f28937,f28965,f29016,f29020,f29024,f29028,f29032,f29036,f29040,f29046,f29068,f29208,f29212,f29216,f29220,f29224,f29368,f29372,f29376,f29381,f29386,f29404,f29409,f29432,f29436,f29440,f29444,f29478,f29493,f29497,f29501,f29505,f29509,f29513,f29517,f29521,f29674,f29679,f29683,f29687,f29716,f29720,f29724,f29728,f29732,f29737,f29742,f29747,f29752,f29839,f29843,f29847,f29851,f29868,f29888,f29892,f29896,f29902,f29930,f29934,f29969,f29976,f30015,f30021,f30040,f30079,f30086,f30090,f30108,f30112,f30116,f30156,f30160,f30166,f30170,f30301,f30308,f30352,f30369,f30385,f30406,f30429,f30433,f30480,f30503,f30516,f30520,f30533,f30537,f30550,f30554,f30558,f30562,f30566,f30571,f30576,f30580,f30584,f30588,f30600,f30604,f30608,f30612,f30616,f30632,f30639,f30671,f30679,f30697,f30701,f30711,f30715,f30719,f30726,f30730,f30734,f30740,f30744,f30750,f30754,f30758,f30762,f30767,f30824,f30828,f30832,f30836,f30840,f30844,f30848,f30852,f30856,f30860,f30868,f30872,f30876,f30880,f30884,f30888,f30893,f30898,f30902,f30906,f30910,f30914,f30918,f30922,f30965,f30970,f30974,f30978,f30982,f30983,f31008,f31097,f31102,f31278,f31362,f31540,f31567,f31571,f31911,f32006,f32010,f32014,f32018,f32022,f32026,f32030,f32034,f32038,f32043,f32047,f32051,f32055,f32059,f32063,f32067,f32071,f32075,f32079,f32083,f32087,f32092,f32096,f32101,f32105,f32109,f32113,f32117,f32122,f32128,f32147,f32151,f32156,f32160,f32164,f32168,f32172,f32184,f32188,f32192,f32199,f32204,f32208,f32212,f32216,f32220,f32231,f32235,f32240,f32247,f32252,f32256,f32264,f32269,f32273,f32277,f32281,f32285,f32304,f32308,f32312,f32335,f32350,f32355,f32360,f32364,f32368,f32372,f32376,f32380,f32384,f32388,f32393,f32397,f32402,f32407,f32411,f32415,f32419,f32423,f32427,f32431,f32435,f32439,f32444,f32448,f32452,f32456,f32474,f32478,f32482,f32486,f32491,f32496,f32501,f32505,f32509,f32513,f32517,f32521,f32525,f32529,f32533,f32537,f32568,f32659,f32709,f32713,f32852,f32858,f32922,f33104,f33147,f33151,f33287,f33717,f33727,f33731,f34012,f34016,f34020,f34024,f34028,f34032,f34036,f34040,f34044,f34048,f34056,f34061,f34075,f34080,f34096,f34100,f34104,f34108,f34127,f34132,f34137,f34142,f34146,f34150,f34154,f34158,f34163,f34168,f34173,f34177,f34181,f34185,f34194,f34198,f34202,f34206,f34210,f34214,f34218,f34222,f34226,f34230,f34234,f34239,f34243,f34247,f34252,f34257,f34269,f34273,f34277,f34282,f34287,f34291,f34295,f34301,f34306,f34310,f34316,f34321,f34327,f34332,f34337,f34341,f34345,f34349,f34408,f34412,f34441,f34446,f34450,f34454,f34458,f34462,f34466,f34470,f34474,f34478,f34482,f34486,f34490,f34494,f34498,f34502,f34506,f34510,f34514,f34518,f34522,f34526,f34531,f34535,f34539,f34543,f34547,f34551,f34555,f34559,f34563,f34568,f34573,f34815,f35019,f35191,f35195,f35199,f36171,f36311]) ).
fof(f36311,plain,
( spl0_93
| ~ spl0_2627 ),
inference(avatar_contradiction_clause,[],[f36310]) ).
fof(f36310,plain,
( $false
| spl0_93
| ~ spl0_2627 ),
inference(trivial_inequality_removal,[],[f36291]) ).
fof(f36291,plain,
( c_Message_Oanalz(c_Message_Osynth(v_H)) != c_Message_Oanalz(c_Message_Osynth(v_H))
| spl0_93
| ~ spl0_2627 ),
inference(superposition,[],[f3714,f34513]) ).
fof(f34513,plain,
( ! [X0] : c_union(c_Message_Oanalz(X0),c_Message_Osynth(X0),tc_Message_Omsg) = c_Message_Oanalz(c_Message_Osynth(X0))
| ~ spl0_2627 ),
inference(avatar_component_clause,[],[f34512]) ).
fof(f34512,plain,
( spl0_2627
<=> ! [X0] : c_union(c_Message_Oanalz(X0),c_Message_Osynth(X0),tc_Message_Omsg) = c_Message_Oanalz(c_Message_Osynth(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2627])]) ).
fof(f3714,plain,
( c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg)
| spl0_93 ),
inference(avatar_component_clause,[],[f3712]) ).
fof(f3712,plain,
( spl0_93
<=> c_Message_Oanalz(c_Message_Osynth(v_H)) = c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f36171,plain,
( ~ spl0_2647
| ~ spl0_2598
| ~ spl0_2641 ),
inference(avatar_split_clause,[],[f35978,f34570,f34308,f36168]) ).
fof(f36168,plain,
( spl0_2647
<=> c_List_Olist_ONil = c_List_Oupt(c_0,c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2647])]) ).
fof(f34308,plain,
( spl0_2598
<=> ! [X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).
fof(f34570,plain,
( spl0_2641
<=> c_List_Oupt(c_0,c_1) = c_List_Oreplicate(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f35978,plain,
( c_List_Olist_ONil != c_List_Oupt(c_0,c_1)
| ~ spl0_2598
| ~ spl0_2641 ),
inference(superposition,[],[f34309,f34572]) ).
fof(f34572,plain,
( c_List_Oupt(c_0,c_1) = c_List_Oreplicate(c_1,c_0,tc_nat)
| ~ spl0_2641 ),
inference(avatar_component_clause,[],[f34570]) ).
fof(f34309,plain,
( ! [X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_2598 ),
inference(avatar_component_clause,[],[f34308]) ).
fof(f35199,plain,
( spl0_2646
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2568 ),
inference(avatar_split_clause,[],[f34169,f34166,f18552,f9544,f3292,f35197]) ).
fof(f35197,plain,
( spl0_2646
<=> ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2646])]) ).
fof(f3292,plain,
( spl0_9
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f9544,plain,
( spl0_1184
<=> ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f18552,plain,
( spl0_1825
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f34166,plain,
( spl0_2568
<=> ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2568])]) ).
fof(f34169,plain,
( ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2568 ),
inference(forward_demodulation,[],[f34167,f19334]) ).
fof(f19334,plain,
( ! [X0,X1] : c_uminus(c_plus(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f19333,f9545]) ).
fof(f9545,plain,
( ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint)
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f9544]) ).
fof(f19333,plain,
( ! [X0,X1] : c_uminus(c_plus(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_uminus(X0,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1825 ),
inference(resolution,[],[f18553,f3294]) ).
fof(f3294,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f3292]) ).
fof(f18553,plain,
( ! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) )
| ~ spl0_1825 ),
inference(avatar_component_clause,[],[f18552]) ).
fof(f34167,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_2568 ),
inference(avatar_component_clause,[],[f34166]) ).
fof(f35195,plain,
( spl0_2645
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2567 ),
inference(avatar_split_clause,[],[f34164,f34161,f18552,f9544,f3292,f35193]) ).
fof(f35193,plain,
( spl0_2645
<=> ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2645])]) ).
fof(f34161,plain,
( spl0_2567
<=> ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2567])]) ).
fof(f34164,plain,
( ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2567 ),
inference(forward_demodulation,[],[f34162,f19334]) ).
fof(f34162,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_2567 ),
inference(avatar_component_clause,[],[f34161]) ).
fof(f35191,plain,
( spl0_2644
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2566 ),
inference(avatar_split_clause,[],[f34159,f34156,f18552,f9544,f3292,f35189]) ).
fof(f35189,plain,
( spl0_2644
<=> ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2644])]) ).
fof(f34156,plain,
( spl0_2566
<=> ! [X0] : c_less(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2566])]) ).
fof(f34159,plain,
( ! [X0] : c_less(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2566 ),
inference(forward_demodulation,[],[f34157,f19334]) ).
fof(f34157,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_2566 ),
inference(avatar_component_clause,[],[f34156]) ).
fof(f35019,plain,
( spl0_2643
| ~ spl0_801
| ~ spl0_2540 ),
inference(avatar_split_clause,[],[f33956,f33729,f7374,f35016]) ).
fof(f35016,plain,
( spl0_2643
<=> c_Message_Oanalz(c_IntDef_ONats) = c_Message_Oanalz(c_Message_Osynth(c_IntDef_ONats)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f7374,plain,
( spl0_801
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f33729,plain,
( spl0_2540
<=> ! [X0] : c_Message_Oanalz(c_IntDef_ONats) = c_Message_Oanalz(c_union(c_Message_Osynth(c_IntDef_ONats),X0,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f33956,plain,
( c_Message_Oanalz(c_IntDef_ONats) = c_Message_Oanalz(c_Message_Osynth(c_IntDef_ONats))
| ~ spl0_801
| ~ spl0_2540 ),
inference(superposition,[],[f33730,f7375]) ).
fof(f7375,plain,
( ! [X3,X1] : c_union(X3,X3,X1) = X3
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7374]) ).
fof(f33730,plain,
( ! [X0] : c_Message_Oanalz(c_IntDef_ONats) = c_Message_Oanalz(c_union(c_Message_Osynth(c_IntDef_ONats),X0,tc_Message_Omsg))
| ~ spl0_2540 ),
inference(avatar_component_clause,[],[f33729]) ).
fof(f34815,plain,
( spl0_2642
| ~ spl0_803
| ~ spl0_2538 ),
inference(avatar_split_clause,[],[f33898,f33715,f7382,f34813]) ).
fof(f34813,plain,
( spl0_2642
<=> ! [X0] : c_IntDef_ONats = c_uminus(c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f7382,plain,
( spl0_803
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f33715,plain,
( spl0_2538
<=> ! [X0,X1] : c_IntDef_ONats = c_union(c_uminus(X0,tc_set(X1)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f33898,plain,
( ! [X0] : c_IntDef_ONats = c_uminus(c_emptyset,tc_set(X0))
| ~ spl0_803
| ~ spl0_2538 ),
inference(superposition,[],[f33716,f7383]) ).
fof(f7383,plain,
( ! [X3,X1] : c_union(X3,c_emptyset,X1) = X3
| ~ spl0_803 ),
inference(avatar_component_clause,[],[f7382]) ).
fof(f33716,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_2538 ),
inference(avatar_component_clause,[],[f33715]) ).
fof(f34573,plain,
( ~ spl0_86
| spl0_2641
| ~ spl0_675
| ~ spl0_706
| ~ spl0_774
| ~ spl0_817
| ~ spl0_934
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f23036,f22979,f7994,f7439,f7265,f6970,f6829,f34570,f3677]) ).
fof(f3677,plain,
( spl0_86
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f6829,plain,
( spl0_675
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f6970,plain,
( spl0_706
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f7265,plain,
( spl0_774
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f7439,plain,
( spl0_817
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f7994,plain,
( spl0_934
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f22979,plain,
( spl0_2067
<=> ! [X59,X43] :
( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
| ~ c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f23036,plain,
( c_List_Oupt(c_0,c_1) = c_List_Oreplicate(c_1,c_0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_675
| ~ spl0_706
| ~ spl0_774
| ~ spl0_817
| ~ spl0_934
| ~ spl0_2067 ),
inference(forward_demodulation,[],[f23035,f6830]) ).
fof(f6830,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f6829]) ).
fof(f23035,plain,
( c_List_Oreplicate(c_1,c_0,tc_nat) = c_List_Oupt(c_NatArith_Oof__nat(c_0,tc_nat),c_1)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_706
| ~ spl0_774
| ~ spl0_817
| ~ spl0_934
| ~ spl0_2067 ),
inference(forward_demodulation,[],[f23034,f7266]) ).
fof(f7266,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7265]) ).
fof(f23034,plain,
( c_List_Oreplicate(c_1,c_0,tc_nat) = c_List_Oupt(c_NatArith_Oof__nat(c_0,tc_nat),c_plus(c_1,c_0,tc_nat))
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_706
| ~ spl0_817
| ~ spl0_934
| ~ spl0_2067 ),
inference(forward_demodulation,[],[f23033,f7440]) ).
fof(f7440,plain,
( ! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7439]) ).
fof(f23033,plain,
( c_List_Oupt(c_NatArith_Oof__nat(c_0,tc_nat),c_plus(c_1,c_0,tc_nat)) = c_append(c_List_Olist_ONil,c_List_Oreplicate(c_1,c_0,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_706
| ~ spl0_934
| ~ spl0_2067 ),
inference(forward_demodulation,[],[f23019,f6971]) ).
fof(f6971,plain,
( ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0)
| ~ spl0_706 ),
inference(avatar_component_clause,[],[f6970]) ).
fof(f23019,plain,
( c_List_Oupt(c_NatArith_Oof__nat(c_0,tc_nat),c_plus(c_1,c_0,tc_nat)) = c_append(c_List_Oupt(c_NatArith_Oof__nat(c_0,tc_nat),c_0),c_List_Oreplicate(c_1,c_0,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_934
| ~ spl0_2067 ),
inference(resolution,[],[f22980,f7995]) ).
fof(f7995,plain,
( ! [X1] :
( c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_934 ),
inference(avatar_component_clause,[],[f7994]) ).
fof(f22980,plain,
( ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat) )
| ~ spl0_2067 ),
inference(avatar_component_clause,[],[f22979]) ).
fof(f34568,plain,
( spl0_2640
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935 ),
inference(avatar_split_clause,[],[f20270,f20187,f7301,f7265,f34565]) ).
fof(f34565,plain,
( spl0_2640
<=> c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f7301,plain,
( spl0_783
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f20187,plain,
( spl0_1935
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f20270,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_1,tc_nat)
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935 ),
inference(forward_demodulation,[],[f20191,f7266]) ).
fof(f20191,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_plus(c_1,c_0,tc_nat),tc_nat)
| ~ spl0_783
| ~ spl0_1935 ),
inference(superposition,[],[f20188,f7302]) ).
fof(f7302,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f7301]) ).
fof(f20188,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_1935 ),
inference(avatar_component_clause,[],[f20187]) ).
fof(f34563,plain,
( spl0_2639
| ~ spl0_1052
| ~ spl0_2526 ),
inference(avatar_split_clause,[],[f33833,f32535,f8598,f34561]) ).
fof(f34561,plain,
( spl0_2639
<=> ! [X0,X1] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2639])]) ).
fof(f8598,plain,
( spl0_1052
<=> ! [X12,X1] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f32535,plain,
( spl0_2526
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f33833,plain,
( ! [X0,X1] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X1)
| ~ spl0_1052
| ~ spl0_2526 ),
inference(resolution,[],[f32536,f8599]) ).
fof(f8599,plain,
( ! [X1,X12] :
( c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1)
| c_emptyset = X12 )
| ~ spl0_1052 ),
inference(avatar_component_clause,[],[f8598]) ).
fof(f32536,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
| ~ spl0_2526 ),
inference(avatar_component_clause,[],[f32535]) ).
fof(f34559,plain,
( spl0_100
| spl0_2638
| ~ spl0_1033
| ~ spl0_1871 ),
inference(avatar_split_clause,[],[f19845,f18890,f8522,f34557,f3744]) ).
fof(f3744,plain,
( spl0_100
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f34557,plain,
( spl0_2638
<=> ! [X0,X1] : c_0 != c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2638])]) ).
fof(f8522,plain,
( spl0_1033
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f18890,plain,
( spl0_1871
<=> ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f19845,plain,
( ! [X0,X1] :
( c_0 != c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg)
| c_0 = c_1 )
| ~ spl0_1033
| ~ spl0_1871 ),
inference(superposition,[],[f8523,f18891]) ).
fof(f18891,plain,
( ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat)
| ~ spl0_1871 ),
inference(avatar_component_clause,[],[f18890]) ).
fof(f8523,plain,
( ! [X21,X15] :
( c_0 != c_plus(X15,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_1033 ),
inference(avatar_component_clause,[],[f8522]) ).
fof(f34555,plain,
( spl0_2637
| ~ spl0_1483
| ~ spl0_1856 ),
inference(avatar_split_clause,[],[f19636,f18805,f12173,f34553]) ).
fof(f34553,plain,
( spl0_2637
<=> ! [X0,X1] : ~ c_Wellfounded__Recursion_Owf(c_Transitive__Closure_Otrancl(c_union(X0,c_Relation_OId,tc_prod(X1,X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2637])]) ).
fof(f12173,plain,
( spl0_1483
<=> ! [X18,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f18805,plain,
( spl0_1856
<=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f19636,plain,
( ! [X0,X1] : ~ c_Wellfounded__Recursion_Owf(c_Transitive__Closure_Otrancl(c_union(X0,c_Relation_OId,tc_prod(X1,X1)),X1),X1)
| ~ spl0_1483
| ~ spl0_1856 ),
inference(resolution,[],[f18806,f12174]) ).
fof(f12174,plain,
( ! [X18,X1,X5] :
( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
| ~ c_Wellfounded__Recursion_Owf(X5,X1) )
| ~ spl0_1483 ),
inference(avatar_component_clause,[],[f12173]) ).
fof(f18806,plain,
( ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1))
| ~ spl0_1856 ),
inference(avatar_component_clause,[],[f18805]) ).
fof(f34551,plain,
( spl0_2636
| ~ spl0_774
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f18796,f18776,f7265,f34549]) ).
fof(f34549,plain,
( spl0_2636
<=> ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(X0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2636])]) ).
fof(f18776,plain,
( spl0_1854
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f18796,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(X0,c_1,tc_nat)
| ~ spl0_774
| ~ spl0_1854 ),
inference(forward_demodulation,[],[f18779,f7266]) ).
fof(f18779,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(X0,c_plus(c_1,c_0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_1854 ),
inference(superposition,[],[f18777,f7266]) ).
fof(f18777,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_1854 ),
inference(avatar_component_clause,[],[f18776]) ).
fof(f34547,plain,
( spl0_2635
| ~ spl0_979
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f18788,f18776,f8177,f34545]) ).
fof(f34545,plain,
( spl0_2635
<=> ! [X0,X1] : c_less(c_0,c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2635])]) ).
fof(f8177,plain,
( spl0_979
<=> ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f18788,plain,
( ! [X0,X1] : c_less(c_0,c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_979
| ~ spl0_1854 ),
inference(superposition,[],[f8178,f18777]) ).
fof(f8178,plain,
( ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8177]) ).
fof(f34543,plain,
( spl0_2634
| ~ spl0_856
| ~ spl0_1852 ),
inference(avatar_split_clause,[],[f18695,f18686,f7606,f34541]) ).
fof(f34541,plain,
( spl0_2634
<=> ! [X0,X1] : ~ c_less(c_plus(c_1,c_plus(X0,X1,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2634])]) ).
fof(f7606,plain,
( spl0_856
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f18686,plain,
( spl0_1852
<=> ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f18695,plain,
( ! [X0,X1] : ~ c_less(c_plus(c_1,c_plus(X0,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_856
| ~ spl0_1852 ),
inference(superposition,[],[f7607,f18687]) ).
fof(f18687,plain,
( ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat)
| ~ spl0_1852 ),
inference(avatar_component_clause,[],[f18686]) ).
fof(f7607,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_856 ),
inference(avatar_component_clause,[],[f7606]) ).
fof(f34539,plain,
( spl0_2633
| ~ spl0_852
| ~ spl0_1849 ),
inference(avatar_split_clause,[],[f18666,f18650,f7590,f34537]) ).
fof(f34537,plain,
( spl0_2633
<=> ! [X0,X1] : c_lessequals(c_minus(X0,X1,tc_nat),c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2633])]) ).
fof(f7590,plain,
( spl0_852
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f18650,plain,
( spl0_1849
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f18666,plain,
( ! [X0,X1] : c_lessequals(c_minus(X0,X1,tc_nat),c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_852
| ~ spl0_1849 ),
inference(superposition,[],[f7591,f18651]) ).
fof(f18651,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_1849 ),
inference(avatar_component_clause,[],[f18650]) ).
fof(f7591,plain,
( ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_852 ),
inference(avatar_component_clause,[],[f7590]) ).
fof(f34535,plain,
( spl0_2632
| ~ spl0_1385
| ~ spl0_1779 ),
inference(avatar_split_clause,[],[f18398,f17141,f10759,f34533]) ).
fof(f34533,plain,
( spl0_2632
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X2,c_emptyset,tc_set(X1))
| c_lessequals(X2,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2632])]) ).
fof(f10759,plain,
( spl0_1385
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f17141,plain,
( spl0_1779
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f18398,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,c_emptyset,tc_set(X1))
| c_lessequals(X2,X0,tc_set(X1)) )
| ~ spl0_1385
| ~ spl0_1779 ),
inference(superposition,[],[f17142,f10760]) ).
fof(f10760,plain,
( ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1)
| ~ spl0_1385 ),
inference(avatar_component_clause,[],[f10759]) ).
fof(f17142,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1))
| c_lessequals(X32,X12,tc_set(X1)) )
| ~ spl0_1779 ),
inference(avatar_component_clause,[],[f17141]) ).
fof(f34531,plain,
( spl0_2631
| ~ spl0_1386
| ~ spl0_1772 ),
inference(avatar_split_clause,[],[f18340,f17109,f10763,f34529]) ).
fof(f34529,plain,
( spl0_2631
<=> ! [X2,X0,X1] : ~ c_in(X0,c_uminus(c_insert(X0,X1,X2),tc_set(X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2631])]) ).
fof(f10763,plain,
( spl0_1386
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f17109,plain,
( spl0_1772
<=> ! [X13,X12,X27,X1] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f18340,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_uminus(c_insert(X0,X1,X2),tc_set(X2)),X2)
| ~ spl0_1386
| ~ spl0_1772 ),
inference(trivial_inequality_removal,[],[f18338]) ).
fof(f18338,plain,
( ! [X2,X0,X1] :
( c_emptyset != c_emptyset
| ~ c_in(X0,c_uminus(c_insert(X0,X1,X2),tc_set(X2)),X2) )
| ~ spl0_1386
| ~ spl0_1772 ),
inference(superposition,[],[f17110,f10764]) ).
fof(f10764,plain,
( ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1)
| ~ spl0_1386 ),
inference(avatar_component_clause,[],[f10763]) ).
fof(f17110,plain,
( ! [X1,X27,X12,X13] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1)
| ~ c_in(X27,X12,X1) )
| ~ spl0_1772 ),
inference(avatar_component_clause,[],[f17109]) ).
fof(f34526,plain,
( spl0_2630
| ~ spl0_1069
| ~ spl0_1752 ),
inference(avatar_split_clause,[],[f18263,f16705,f8666,f34524]) ).
fof(f34524,plain,
( spl0_2630
<=> ! [X0,X1] : c_minus(c_UNIV,c_uminus(X1,tc_set(X0)),tc_set(X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2630])]) ).
fof(f8666,plain,
( spl0_1069
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f16705,plain,
( spl0_1752
<=> ! [X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f18263,plain,
( ! [X0,X1] : c_minus(c_UNIV,c_uminus(X1,tc_set(X0)),tc_set(X0)) = X1
| ~ spl0_1069
| ~ spl0_1752 ),
inference(superposition,[],[f16706,f8667]) ).
fof(f8667,plain,
( ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3
| ~ spl0_1069 ),
inference(avatar_component_clause,[],[f8666]) ).
fof(f16706,plain,
( ! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1))
| ~ spl0_1752 ),
inference(avatar_component_clause,[],[f16705]) ).
fof(f34522,plain,
( spl0_2629
| ~ spl0_1070
| ~ spl0_1752 ),
inference(avatar_split_clause,[],[f18257,f16705,f8670,f34520]) ).
fof(f34520,plain,
( spl0_2629
<=> ! [X0,X1] : c_minus(X0,c_uminus(X0,tc_set(X1)),tc_set(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2629])]) ).
fof(f8670,plain,
( spl0_1070
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f18257,plain,
( ! [X0,X1] : c_minus(X0,c_uminus(X0,tc_set(X1)),tc_set(X1)) = X0
| ~ spl0_1070
| ~ spl0_1752 ),
inference(superposition,[],[f16706,f8671]) ).
fof(f8671,plain,
( ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f8670]) ).
fof(f34518,plain,
( spl0_2628
| ~ spl0_783
| ~ spl0_2517 ),
inference(avatar_split_clause,[],[f33735,f32499,f7301,f34516]) ).
fof(f34516,plain,
( spl0_2628
<=> ! [X0] : c_0 != c_plus(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2628])]) ).
fof(f32499,plain,
( spl0_2517
<=> ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f33735,plain,
( ! [X0] : c_0 != c_plus(c_1,X0,tc_nat)
| ~ spl0_783
| ~ spl0_2517 ),
inference(superposition,[],[f32500,f7302]) ).
fof(f32500,plain,
( ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat)
| ~ spl0_2517 ),
inference(avatar_component_clause,[],[f32499]) ).
fof(f34514,plain,
( spl0_2627
| ~ spl0_803
| ~ spl0_1751 ),
inference(avatar_split_clause,[],[f18252,f16701,f7382,f34512]) ).
fof(f16701,plain,
( spl0_1751
<=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f18252,plain,
( ! [X0] : c_union(c_Message_Oanalz(X0),c_Message_Osynth(X0),tc_Message_Omsg) = c_Message_Oanalz(c_Message_Osynth(X0))
| ~ spl0_803
| ~ spl0_1751 ),
inference(forward_demodulation,[],[f18226,f7383]) ).
fof(f18226,plain,
( ! [X0] : c_union(c_Message_Oanalz(X0),c_Message_Osynth(X0),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(X0),c_emptyset,tc_Message_Omsg))
| ~ spl0_803
| ~ spl0_1751 ),
inference(superposition,[],[f16702,f7383]) ).
fof(f16702,plain,
( ! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg)
| ~ spl0_1751 ),
inference(avatar_component_clause,[],[f16701]) ).
fof(f34510,plain,
( spl0_2626
| ~ spl0_1736
| ~ spl0_1737 ),
inference(avatar_split_clause,[],[f17977,f16645,f16641,f34508]) ).
fof(f34508,plain,
( spl0_2626
<=> ! [X2,X0,X1] :
( c_less(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2626])]) ).
fof(f16641,plain,
( spl0_1736
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f16645,plain,
( spl0_1737
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f17977,plain,
( ! [X2,X0,X1] :
( c_less(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X2,X2,X1) )
| ~ spl0_1736
| ~ spl0_1737 ),
inference(duplicate_literal_removal,[],[f17955]) ).
fof(f17955,plain,
( ! [X2,X0,X1] :
( c_less(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1736
| ~ spl0_1737 ),
inference(resolution,[],[f16646,f16642]) ).
fof(f16642,plain,
( ! [X18,X1,X27,X4] :
( c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1)
| ~ c_less(X18,X27,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1736 ),
inference(avatar_component_clause,[],[f16641]) ).
fof(f16646,plain,
( ! [X18,X1,X27,X4] :
( ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1)
| c_less(X18,X27,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1737 ),
inference(avatar_component_clause,[],[f16645]) ).
fof(f34506,plain,
( spl0_2625
| ~ spl0_1732
| ~ spl0_1733 ),
inference(avatar_split_clause,[],[f17840,f16629,f16625,f34504]) ).
fof(f34504,plain,
( spl0_2625
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2625])]) ).
fof(f16625,plain,
( spl0_1732
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f16629,plain,
( spl0_1733
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f17840,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X2,X1) )
| ~ spl0_1732
| ~ spl0_1733 ),
inference(duplicate_literal_removal,[],[f17814]) ).
fof(f17814,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1732
| ~ spl0_1733 ),
inference(resolution,[],[f16630,f16626]) ).
fof(f16626,plain,
( ! [X18,X1,X27,X4] :
( c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1)
| ~ c_lessequals(X18,X27,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1732 ),
inference(avatar_component_clause,[],[f16625]) ).
fof(f16630,plain,
( ! [X18,X1,X27,X4] :
( ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1)
| c_lessequals(X18,X27,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_1733 ),
inference(avatar_component_clause,[],[f16629]) ).
fof(f34502,plain,
( spl0_2624
| ~ spl0_1201
| ~ spl0_1710 ),
inference(avatar_split_clause,[],[f17521,f16536,f9612,f34500]) ).
fof(f34500,plain,
( spl0_2624
<=> ! [X2,X0,X1] : c_List_Olast(c_List_Orev(c_List_Olist_OCons(X2,X0,X1),X1),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2624])]) ).
fof(f9612,plain,
( spl0_1201
<=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f16536,plain,
( spl0_1710
<=> ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f17521,plain,
( ! [X2,X0,X1] : c_List_Olast(c_List_Orev(c_List_Olist_OCons(X2,X0,X1),X1),X1) = X2
| ~ spl0_1201
| ~ spl0_1710 ),
inference(superposition,[],[f9613,f16537]) ).
fof(f16537,plain,
( ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41)
| ~ spl0_1710 ),
inference(avatar_component_clause,[],[f16536]) ).
fof(f9613,plain,
( ! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3
| ~ spl0_1201 ),
inference(avatar_component_clause,[],[f9612]) ).
fof(f34498,plain,
( spl0_2623
| ~ spl0_846
| ~ spl0_1762 ),
inference(avatar_split_clause,[],[f17021,f17014,f7566,f34496]) ).
fof(f34496,plain,
( spl0_2623
<=> ! [X2,X0,X1] : c_List_Oop_Amem(X0,c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2623])]) ).
fof(f7566,plain,
( spl0_846
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f17014,plain,
( spl0_1762
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f17021,plain,
( ! [X2,X0,X1] : c_List_Oop_Amem(X0,c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_846
| ~ spl0_1762 ),
inference(superposition,[],[f7567,f17015]) ).
fof(f17015,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_1762 ),
inference(avatar_component_clause,[],[f17014]) ).
fof(f7567,plain,
( ! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1)
| ~ spl0_846 ),
inference(avatar_component_clause,[],[f7566]) ).
fof(f34494,plain,
( spl0_2622
| ~ spl0_823
| ~ spl0_1760 ),
inference(avatar_split_clause,[],[f16956,f16910,f7474,f34492]) ).
fof(f34492,plain,
( spl0_2622
<=> ! [X0,X1] : c_Divides_Oop_Advd(X1,c_plus(X1,c_times(X0,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2622])]) ).
fof(f7474,plain,
( spl0_823
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f16910,plain,
( spl0_1760
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f16956,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X1,c_plus(X1,c_times(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_823
| ~ spl0_1760 ),
inference(superposition,[],[f7475,f16911]) ).
fof(f16911,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_1760 ),
inference(avatar_component_clause,[],[f16910]) ).
fof(f7475,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat)
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f7474]) ).
fof(f34490,plain,
( spl0_2621
| ~ spl0_855
| ~ spl0_1760 ),
inference(avatar_split_clause,[],[f16925,f16910,f7602,f34488]) ).
fof(f34488,plain,
( spl0_2621
<=> ! [X0,X1] : ~ c_less(c_times(c_plus(c_1,X1,tc_nat),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f7602,plain,
( spl0_855
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f16925,plain,
( ! [X0,X1] : ~ c_less(c_times(c_plus(c_1,X1,tc_nat),X0,tc_nat),X0,tc_nat)
| ~ spl0_855
| ~ spl0_1760 ),
inference(superposition,[],[f7603,f16911]) ).
fof(f7603,plain,
( ! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat)
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f7602]) ).
fof(f34486,plain,
( spl0_2620
| ~ spl0_822
| ~ spl0_1758 ),
inference(avatar_split_clause,[],[f16852,f16810,f7470,f34484]) ).
fof(f34484,plain,
( spl0_2620
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_plus(X0,c_times(X0,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2620])]) ).
fof(f7470,plain,
( spl0_822
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f16810,plain,
( spl0_1758
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f16852,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_plus(X0,c_times(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_822
| ~ spl0_1758 ),
inference(superposition,[],[f7471,f16811]) ).
fof(f16811,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_1758 ),
inference(avatar_component_clause,[],[f16810]) ).
fof(f7471,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat)
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7470]) ).
fof(f34482,plain,
( spl0_2619
| ~ spl0_855
| ~ spl0_1758 ),
inference(avatar_split_clause,[],[f16822,f16810,f7602,f34480]) ).
fof(f34480,plain,
( spl0_2619
<=> ! [X0,X1] : ~ c_less(c_times(X0,c_plus(c_1,X1,tc_nat),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2619])]) ).
fof(f16822,plain,
( ! [X0,X1] : ~ c_less(c_times(X0,c_plus(c_1,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_855
| ~ spl0_1758 ),
inference(superposition,[],[f7603,f16811]) ).
fof(f34478,plain,
( spl0_2618
| ~ spl0_822
| ~ spl0_1756 ),
inference(avatar_split_clause,[],[f16755,f16747,f7470,f34476]) ).
fof(f34476,plain,
( spl0_2618
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_Nat_Opower(X0,c_plus(c_1,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2618])]) ).
fof(f16747,plain,
( spl0_1756
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f16755,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_Nat_Opower(X0,c_plus(c_1,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_822
| ~ spl0_1756 ),
inference(superposition,[],[f7471,f16748]) ).
fof(f16748,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_1756 ),
inference(avatar_component_clause,[],[f16747]) ).
fof(f34474,plain,
( spl0_2617
| ~ spl0_774
| ~ spl0_2517 ),
inference(avatar_split_clause,[],[f33733,f32499,f7265,f34472]) ).
fof(f34472,plain,
( spl0_2617
<=> ! [X0] : c_0 != c_plus(X0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2617])]) ).
fof(f33733,plain,
( ! [X0] : c_0 != c_plus(X0,c_1,tc_nat)
| ~ spl0_774
| ~ spl0_2517 ),
inference(superposition,[],[f32500,f7266]) ).
fof(f34470,plain,
( spl0_2616
| ~ spl0_824
| ~ spl0_1754 ),
inference(avatar_split_clause,[],[f16722,f16714,f7478,f34468]) ).
fof(f34468,plain,
( spl0_2616
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_Nat_Opower(X0,c_plus(c_1,X1,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2616])]) ).
fof(f7478,plain,
( spl0_824
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f16714,plain,
( spl0_1754
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f16722,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_Nat_Opower(X0,c_plus(c_1,X1,tc_nat),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_824
| ~ spl0_1754 ),
inference(superposition,[],[f7479,f16715]) ).
fof(f16715,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint)
| ~ spl0_1754 ),
inference(avatar_component_clause,[],[f16714]) ).
fof(f7479,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_824 ),
inference(avatar_component_clause,[],[f7478]) ).
fof(f34466,plain,
( spl0_2615
| ~ spl0_856
| ~ spl0_1675 ),
inference(avatar_split_clause,[],[f16290,f15361,f7606,f34464]) ).
fof(f34464,plain,
( spl0_2615
<=> ! [X2,X0,X1] : ~ c_less(c_Nat_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2615])]) ).
fof(f15361,plain,
( spl0_1675
<=> ! [X18,X64,X1] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f16290,plain,
( ! [X2,X0,X1] : ~ c_less(c_Nat_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),c_1,tc_nat)
| ~ spl0_856
| ~ spl0_1675 ),
inference(superposition,[],[f7607,f15362]) ).
fof(f15362,plain,
( ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat)
| ~ spl0_1675 ),
inference(avatar_component_clause,[],[f15361]) ).
fof(f34462,plain,
( spl0_2614
| ~ spl0_878
| ~ spl0_1663 ),
inference(avatar_split_clause,[],[f16105,f15247,f7694,f34460]) ).
fof(f34460,plain,
( spl0_2614
<=> ! [X0,X3,X2,X1] : c_in(X0,c_union(X1,c_insert(X0,X2,X3),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2614])]) ).
fof(f7694,plain,
( spl0_878
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f15247,plain,
( spl0_1663
<=> ! [X18,X13,X12,X1] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f16105,plain,
( ! [X2,X3,X0,X1] : c_in(X0,c_union(X1,c_insert(X0,X2,X3),X3),X3)
| ~ spl0_878
| ~ spl0_1663 ),
inference(superposition,[],[f7695,f15248]) ).
fof(f15248,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_1663 ),
inference(avatar_component_clause,[],[f15247]) ).
fof(f7695,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f7694]) ).
fof(f34458,plain,
( spl0_2613
| ~ spl0_801
| ~ spl0_1631 ),
inference(avatar_split_clause,[],[f15771,f15110,f7374,f34456]) ).
fof(f34456,plain,
( spl0_2613
<=> ! [X0,X1] : c_List_Oset(X0,X1) = c_List_Oset(c_append(X0,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2613])]) ).
fof(f15110,plain,
( spl0_1631
<=> ! [X25,X1,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f15771,plain,
( ! [X0,X1] : c_List_Oset(X0,X1) = c_List_Oset(c_append(X0,X0,X1),X1)
| ~ spl0_801
| ~ spl0_1631 ),
inference(superposition,[],[f15111,f7375]) ).
fof(f15111,plain,
( ! [X1,X25,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1)
| ~ spl0_1631 ),
inference(avatar_component_clause,[],[f15110]) ).
fof(f34454,plain,
( spl0_2612
| ~ spl0_846
| ~ spl0_1627 ),
inference(avatar_split_clause,[],[f15689,f15093,f7566,f34452]) ).
fof(f34452,plain,
( spl0_2612
<=> ! [X0,X3,X2,X1] : c_List_Oop_Amem(X0,c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2612])]) ).
fof(f15093,plain,
( spl0_1627
<=> ! [X41,X0,X23,X25] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f15689,plain,
( ! [X2,X3,X0,X1] : c_List_Oop_Amem(X0,c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_846
| ~ spl0_1627 ),
inference(superposition,[],[f7567,f15094]) ).
fof(f15094,plain,
( ! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41)
| ~ spl0_1627 ),
inference(avatar_component_clause,[],[f15093]) ).
fof(f34450,plain,
( spl0_2611
| ~ spl0_881
| ~ spl0_1597 ),
inference(avatar_split_clause,[],[f14942,f13936,f7706,f34448]) ).
fof(f34448,plain,
( spl0_2611
<=> ! [X0] :
( c_1 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2611])]) ).
fof(f7706,plain,
( spl0_881
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f13936,plain,
( spl0_1597
<=> ! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f14942,plain,
( ! [X0] :
( c_1 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_881
| ~ spl0_1597 ),
inference(superposition,[],[f13937,f7708]) ).
fof(f7708,plain,
( c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_881 ),
inference(avatar_component_clause,[],[f7706]) ).
fof(f13937,plain,
( ! [X21,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)
| X15 = X21 )
| ~ spl0_1597 ),
inference(avatar_component_clause,[],[f13936]) ).
fof(f34446,plain,
( spl0_2610
| ~ spl0_708
| ~ spl0_883
| ~ spl0_1071
| ~ spl0_1569 ),
inference(avatar_split_clause,[],[f14613,f13823,f8674,f7716,f6979,f34444]) ).
fof(f34444,plain,
( spl0_2610
<=> ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(X0)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f6979,plain,
( spl0_708
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f7716,plain,
( spl0_883
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f8674,plain,
( spl0_1071
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f13823,plain,
( spl0_1569
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f14613,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(X0)),c_Numeral_Obit_OB0)
| ~ spl0_708
| ~ spl0_883
| ~ spl0_1071
| ~ spl0_1569 ),
inference(forward_demodulation,[],[f14605,f8903]) ).
fof(f8903,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X0,c_Numeral_Obit_OB1))
| ~ spl0_883
| ~ spl0_1071 ),
inference(superposition,[],[f8675,f7717]) ).
fof(f7717,plain,
( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f7716]) ).
fof(f8675,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f8674]) ).
fof(f14605,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X0,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(X0)),c_Numeral_Obit_OB0)
| ~ spl0_708
| ~ spl0_1569 ),
inference(superposition,[],[f13824,f6981]) ).
fof(f6981,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f6979]) ).
fof(f13824,plain,
( ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0)
| ~ spl0_1569 ),
inference(avatar_component_clause,[],[f13823]) ).
fof(f34441,plain,
( spl0_2609
| ~ spl0_800
| ~ spl0_1478 ),
inference(avatar_split_clause,[],[f13267,f12147,f7370,f34439]) ).
fof(f34439,plain,
( spl0_2609
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_UNIV,X2,tc_set(X1))
| c_lessequals(X0,X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f7370,plain,
( spl0_800
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f12147,plain,
( spl0_1478
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f13267,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_UNIV,X2,tc_set(X1))
| c_lessequals(X0,X2,tc_set(X1)) )
| ~ spl0_800
| ~ spl0_1478 ),
inference(superposition,[],[f12148,f7371]) ).
fof(f7371,plain,
( ! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1)
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7370]) ).
fof(f12148,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X12,X32,tc_set(X1)) )
| ~ spl0_1478 ),
inference(avatar_component_clause,[],[f12147]) ).
fof(f34412,plain,
( ~ spl0_91
| spl0_2608
| ~ spl0_780
| ~ spl0_1453 ),
inference(avatar_split_clause,[],[f13023,f12035,f7289,f34410,f3702]) ).
fof(f3702,plain,
( spl0_91
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f34410,plain,
( spl0_2608
<=> ! [X0,X1] :
( ~ c_lessequals(X1,c_0,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f7289,plain,
( spl0_780
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f12035,plain,
( spl0_1453
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f13023,plain,
( ! [X0,X1] :
( ~ c_lessequals(X1,c_0,tc_nat)
| c_lessequals(X1,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_780
| ~ spl0_1453 ),
inference(superposition,[],[f12036,f7290]) ).
fof(f7290,plain,
( ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat)
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f7289]) ).
fof(f12036,plain,
( ! [X2,X3,X48,X0] :
( ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2)
| c_lessequals(X0,X3,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_1453 ),
inference(avatar_component_clause,[],[f12035]) ).
fof(f34408,plain,
( spl0_2607
| ~ spl0_774
| ~ spl0_2508 ),
inference(avatar_split_clause,[],[f33433,f32446,f7265,f34406]) ).
fof(f34406,plain,
( spl0_2607
<=> ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_1,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2607])]) ).
fof(f32446,plain,
( spl0_2508
<=> ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f33433,plain,
( ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_1,X0,X1),X1)
| ~ spl0_774
| ~ spl0_2508 ),
inference(superposition,[],[f32447,f7266]) ).
fof(f32447,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_2508 ),
inference(avatar_component_clause,[],[f32446]) ).
fof(f34349,plain,
( ~ spl0_91
| spl0_2606
| ~ spl0_777
| ~ spl0_1448 ),
inference(avatar_split_clause,[],[f12977,f12014,f7277,f34347,f3702]) ).
fof(f34347,plain,
( spl0_2606
<=> ! [X0,X1] :
( ~ c_less(X0,X1,tc_nat)
| c_less(c_0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2606])]) ).
fof(f7277,plain,
( spl0_777
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f12014,plain,
( spl0_1448
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f12977,plain,
( ! [X0,X1] :
( ~ c_less(X0,X1,tc_nat)
| c_less(c_0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_777
| ~ spl0_1448 ),
inference(superposition,[],[f12015,f7278]) ).
fof(f7278,plain,
( ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3
| ~ spl0_777 ),
inference(avatar_component_clause,[],[f7277]) ).
fof(f12015,plain,
( ! [X3,X48,X0,X1] :
( ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1)
| c_less(X0,X48,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1448 ),
inference(avatar_component_clause,[],[f12014]) ).
fof(f34345,plain,
( spl0_2605
| ~ spl0_710
| ~ spl0_785
| ~ spl0_1434 ),
inference(avatar_split_clause,[],[f12791,f11953,f7309,f6989,f34343]) ).
fof(f34343,plain,
( spl0_2605
<=> ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OBit(X0,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2605])]) ).
fof(f6989,plain,
( spl0_710
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f7309,plain,
( spl0_785
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f11953,plain,
( spl0_1434
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f12791,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OBit(X0,c_Numeral_Obit_OB0))
| ~ spl0_710
| ~ spl0_785
| ~ spl0_1434 ),
inference(forward_demodulation,[],[f12784,f6990]) ).
fof(f6990,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f6989]) ).
fof(f12784,plain,
( ! [X0] : c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OPls,X0),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OBit(X0,c_Numeral_Obit_OB0))
| ~ spl0_785
| ~ spl0_1434 ),
inference(superposition,[],[f11954,f7311]) ).
fof(f7311,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7309]) ).
fof(f11954,plain,
( ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1)
| ~ spl0_1434 ),
inference(avatar_component_clause,[],[f11953]) ).
fof(f34341,plain,
( spl0_2604
| ~ spl0_711
| ~ spl0_785
| ~ spl0_1433 ),
inference(avatar_split_clause,[],[f12782,f11949,f7309,f6993,f34339]) ).
fof(f34339,plain,
( spl0_2604
<=> ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OBit(X0,c_Numeral_Obit_OB0),c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2604])]) ).
fof(f6993,plain,
( spl0_711
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f11949,plain,
( spl0_1433
<=> ! [X11,X3,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f12782,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OBit(X0,c_Numeral_Obit_OB0),c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_711
| ~ spl0_785
| ~ spl0_1433 ),
inference(forward_demodulation,[],[f12774,f6994]) ).
fof(f6994,plain,
( ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f6993]) ).
fof(f12774,plain,
( ! [X0] : c_Numeral_OBit(c_Numeral_Obin__add(X0,c_Numeral_OPls),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OBit(X0,c_Numeral_Obit_OB0),c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_785
| ~ spl0_1433 ),
inference(superposition,[],[f11950,f7311]) ).
fof(f11950,plain,
( ! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3)
| ~ spl0_1433 ),
inference(avatar_component_clause,[],[f11949]) ).
fof(f34337,plain,
( spl0_2603
| ~ spl0_761
| ~ spl0_1417 ),
inference(avatar_split_clause,[],[f12532,f11876,f7213,f34335]) ).
fof(f34335,plain,
( spl0_2603
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_lessequals(c_Nat_Osize(X0,tc_List_Olist(X1)),c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2603])]) ).
fof(f7213,plain,
( spl0_761
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f11876,plain,
( spl0_1417
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f12532,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_lessequals(c_Nat_Osize(X0,tc_List_Olist(X1)),c_0,tc_nat) )
| ~ spl0_761
| ~ spl0_1417 ),
inference(superposition,[],[f11877,f7214]) ).
fof(f7214,plain,
( ! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3
| ~ spl0_761 ),
inference(avatar_component_clause,[],[f7213]) ).
fof(f11877,plain,
( ! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) )
| ~ spl0_1417 ),
inference(avatar_component_clause,[],[f11876]) ).
fof(f34332,plain,
( spl0_2602
| ~ spl0_800
| ~ spl0_1410 ),
inference(avatar_split_clause,[],[f12471,f11846,f7370,f34330]) ).
fof(f34330,plain,
( spl0_2602
<=> ! [X0,X1] :
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(X1))
| c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f11846,plain,
( spl0_1410
<=> ! [X20,X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f12471,plain,
( ! [X0,X1] :
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(X1))
| c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) )
| ~ spl0_800
| ~ spl0_1410 ),
inference(superposition,[],[f11847,f7371]) ).
fof(f11847,plain,
( ! [X1,X19,X20] :
( ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(X19,c_Finite__Set_OFinites,tc_set(X1)) )
| ~ spl0_1410 ),
inference(avatar_component_clause,[],[f11846]) ).
fof(f34327,plain,
( spl0_2601
| ~ spl0_87
| ~ spl0_1392 ),
inference(avatar_split_clause,[],[f11795,f10793,f3682,f34324]) ).
fof(f34324,plain,
( spl0_2601
<=> c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2601])]) ).
fof(f3682,plain,
( spl0_87
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f10793,plain,
( spl0_1392
<=> ! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f11795,plain,
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_87
| ~ spl0_1392 ),
inference(resolution,[],[f10794,f3684]) ).
fof(f3684,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f3682]) ).
fof(f10794,plain,
( ! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1) )
| ~ spl0_1392 ),
inference(avatar_component_clause,[],[f10793]) ).
fof(f34321,plain,
( spl0_2600
| ~ spl0_53
| ~ spl0_1392 ),
inference(avatar_split_clause,[],[f11794,f10793,f3512,f34318]) ).
fof(f34318,plain,
( spl0_2600
<=> c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2600])]) ).
fof(f3512,plain,
( spl0_53
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f11794,plain,
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1392 ),
inference(resolution,[],[f10794,f3514]) ).
fof(f3514,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f3512]) ).
fof(f34316,plain,
( spl0_2599
| ~ spl0_52
| ~ spl0_1391 ),
inference(avatar_split_clause,[],[f11793,f10789,f3507,f34313]) ).
fof(f34313,plain,
( spl0_2599
<=> c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint) = c_plus(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).
fof(f3507,plain,
( spl0_52
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f10789,plain,
( spl0_1391
<=> ! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f11793,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint) = c_plus(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1391 ),
inference(resolution,[],[f10790,f3509]) ).
fof(f3509,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f3507]) ).
fof(f10790,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1) )
| ~ spl0_1391 ),
inference(avatar_component_clause,[],[f10789]) ).
fof(f34310,plain,
( spl0_2598
| ~ spl0_774
| ~ spl0_2507 ),
inference(avatar_split_clause,[],[f33431,f32442,f7265,f34308]) ).
fof(f32442,plain,
( spl0_2507
<=> ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f33431,plain,
( ! [X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_774
| ~ spl0_2507 ),
inference(superposition,[],[f32443,f7266]) ).
fof(f32443,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2)
| ~ spl0_2507 ),
inference(avatar_component_clause,[],[f32442]) ).
fof(f34306,plain,
( spl0_2597
| ~ spl0_2249
| ~ spl0_2596 ),
inference(avatar_split_clause,[],[f34302,f34299,f28501,f34304]) ).
fof(f34304,plain,
( spl0_2597
<=> ! [X0,X1] : c_IntDef_ONats != c_Relation_OImage(c_emptyset,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).
fof(f28501,plain,
( spl0_2249
<=> c_UNIV = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f34299,plain,
( spl0_2596
<=> ! [X0,X1] : c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).
fof(f34302,plain,
( ! [X0,X1] : c_IntDef_ONats != c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_2249
| ~ spl0_2596 ),
inference(forward_demodulation,[],[f34300,f28503]) ).
fof(f28503,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_2249 ),
inference(avatar_component_clause,[],[f28501]) ).
fof(f34300,plain,
( ! [X0,X1] : c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_2596 ),
inference(avatar_component_clause,[],[f34299]) ).
fof(f34301,plain,
( spl0_107
| spl0_2596
| ~ spl0_718
| ~ spl0_1390 ),
inference(avatar_split_clause,[],[f11786,f10779,f7023,f34299,f3777]) ).
fof(f3777,plain,
( spl0_107
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f7023,plain,
( spl0_718
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f10779,plain,
( spl0_1390
<=> ! [X13,X12,X1] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f11786,plain,
( ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_emptyset = c_UNIV )
| ~ spl0_718
| ~ spl0_1390 ),
inference(superposition,[],[f10780,f7024]) ).
fof(f7024,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f7023]) ).
fof(f10780,plain,
( ! [X1,X12,X13] :
( c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_UNIV = X12 )
| ~ spl0_1390 ),
inference(avatar_component_clause,[],[f10779]) ).
fof(f34295,plain,
( spl0_2595
| ~ spl0_718
| ~ spl0_1389 ),
inference(avatar_split_clause,[],[f11779,f10775,f7023,f34293]) ).
fof(f34293,plain,
( spl0_2595
<=> ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_UNIV = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).
fof(f10775,plain,
( spl0_1389
<=> ! [X13,X12,X1] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f11779,plain,
( ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_UNIV = X1 )
| ~ spl0_718
| ~ spl0_1389 ),
inference(superposition,[],[f10776,f7024]) ).
fof(f10776,plain,
( ! [X1,X12,X13] :
( c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_UNIV = X13 )
| ~ spl0_1389 ),
inference(avatar_component_clause,[],[f10775]) ).
fof(f34291,plain,
( spl0_2594
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387 ),
inference(avatar_split_clause,[],[f11726,f10767,f10447,f6846,f5911,f34289]) ).
fof(f34289,plain,
( spl0_2594
<=> ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).
fof(f5911,plain,
( spl0_640
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f6846,plain,
( spl0_679
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f10447,plain,
( spl0_1310
<=> ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f10767,plain,
( spl0_1387
<=> ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f11726,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387 ),
inference(forward_demodulation,[],[f11725,f6847]) ).
fof(f6847,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_679 ),
inference(avatar_component_clause,[],[f6846]) ).
fof(f11725,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_IntDef_Onat(c_IntDef_Oint(c_plus(c_1,X0,tc_nat)))
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387 ),
inference(forward_demodulation,[],[f11687,f11073]) ).
fof(f11073,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_640
| ~ spl0_1310 ),
inference(superposition,[],[f10448,f5913]) ).
fof(f5913,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f5911]) ).
fof(f10448,plain,
( ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1310 ),
inference(avatar_component_clause,[],[f10447]) ).
fof(f11687,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_IntDef_Onat(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint))
| ~ spl0_679
| ~ spl0_1387 ),
inference(superposition,[],[f6847,f10768]) ).
fof(f10768,plain,
( ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat))
| ~ spl0_1387 ),
inference(avatar_component_clause,[],[f10767]) ).
fof(f34287,plain,
( spl0_2593
| ~ spl0_967
| ~ spl0_1372 ),
inference(avatar_split_clause,[],[f11545,f10704,f8127,f34284]) ).
fof(f34284,plain,
( spl0_2593
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f8127,plain,
( spl0_967
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f10704,plain,
( spl0_1372
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f11545,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_967
| ~ spl0_1372 ),
inference(superposition,[],[f10705,f8129]) ).
fof(f8129,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_967 ),
inference(avatar_component_clause,[],[f8127]) ).
fof(f10705,plain,
( ! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_1372 ),
inference(avatar_component_clause,[],[f10704]) ).
fof(f34282,plain,
( spl0_2592
| ~ spl0_796
| ~ spl0_1363 ),
inference(avatar_split_clause,[],[f11466,f10667,f7354,f34280]) ).
fof(f34280,plain,
( spl0_2592
<=> ! [X0] :
( c_emptyset = c_minus(c_0,c_1,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).
fof(f7354,plain,
( spl0_796
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f10667,plain,
( spl0_1363
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f11466,plain,
( ! [X0] :
( c_emptyset = c_minus(c_0,c_1,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) )
| ~ spl0_796
| ~ spl0_1363 ),
inference(resolution,[],[f10668,f7355]) ).
fof(f7355,plain,
( ! [X1] :
( c_lessequals(c_0,c_1,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7354]) ).
fof(f10668,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) )
| ~ spl0_1363 ),
inference(avatar_component_clause,[],[f10667]) ).
fof(f34277,plain,
( ~ spl0_91
| spl0_2591
| ~ spl0_720
| ~ spl0_1358 ),
inference(avatar_split_clause,[],[f11437,f10643,f7032,f34275,f3702]) ).
fof(f34275,plain,
( spl0_2591
<=> ! [X0] :
( c_emptyset != c_SetInterval_OlessThan(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f7032,plain,
( spl0_720
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f10643,plain,
( spl0_1358
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f11437,plain,
( ! [X0] :
( c_emptyset != c_SetInterval_OlessThan(X0,tc_nat)
| c_0 = X0
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_720
| ~ spl0_1358 ),
inference(superposition,[],[f10644,f7034]) ).
fof(f7034,plain,
( c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat)
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f7032]) ).
fof(f10644,plain,
( ! [X3,X0,X1] :
( c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1)
| X0 = X3
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1358 ),
inference(avatar_component_clause,[],[f10643]) ).
fof(f34273,plain,
( spl0_2590
| ~ spl0_662
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11413,f10627,f6773,f34271]) ).
fof(f34271,plain,
( spl0_2590
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).
fof(f6773,plain,
( spl0_662
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f10627,plain,
( spl0_1354
<=> ! [X16,X1,X26] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f11413,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,c_emptyset,tc_set(X0)) )
| ~ spl0_662
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f6774]) ).
fof(f6774,plain,
( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f6773]) ).
fof(f10628,plain,
( ! [X1,X26,X16] :
( ~ c_lessequals(X26,X16,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
| ~ spl0_1354 ),
inference(avatar_component_clause,[],[f10627]) ).
fof(f34269,plain,
( spl0_2589
| ~ spl0_796
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11405,f10627,f7354,f34267]) ).
fof(f34267,plain,
( spl0_2589
<=> ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).
fof(f11405,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_796
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f7355]) ).
fof(f34257,plain,
( spl0_2588
| ~ spl0_727
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11394,f10627,f7061,f34255]) ).
fof(f34255,plain,
( spl0_2588
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_UNIV,X1,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).
fof(f7061,plain,
( spl0_727
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f11394,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_UNIV,X1,tc_set(X0)) )
| ~ spl0_727
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f7062]) ).
fof(f7062,plain,
( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f7061]) ).
fof(f34252,plain,
( spl0_2587
| ~ spl0_2249
| ~ spl0_2586 ),
inference(avatar_split_clause,[],[f34248,f34245,f28501,f34250]) ).
fof(f34250,plain,
( spl0_2587
<=> ! [X0] :
( c_IntDef_ONats != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2587])]) ).
fof(f34245,plain,
( spl0_2586
<=> ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2586])]) ).
fof(f34248,plain,
( ! [X0] :
( c_IntDef_ONats != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 )
| ~ spl0_2249
| ~ spl0_2586 ),
inference(forward_demodulation,[],[f34246,f28503]) ).
fof(f34246,plain,
( ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 )
| ~ spl0_2586 ),
inference(avatar_component_clause,[],[f34245]) ).
fof(f34247,plain,
( ~ spl0_91
| spl0_2586
| ~ spl0_719
| ~ spl0_1346 ),
inference(avatar_split_clause,[],[f11376,f10595,f7027,f34245,f3702]) ).
fof(f7027,plain,
( spl0_719
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f10595,plain,
( spl0_1346
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f11376,plain,
( ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_719
| ~ spl0_1346 ),
inference(superposition,[],[f10596,f7029]) ).
fof(f7029,plain,
( c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat)
| ~ spl0_719 ),
inference(avatar_component_clause,[],[f7027]) ).
fof(f10596,plain,
( ! [X3,X0,X1] :
( c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1)
| X0 = X3
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1346 ),
inference(avatar_component_clause,[],[f10595]) ).
fof(f34243,plain,
( spl0_2585
| ~ spl0_662
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11348,f10591,f6773,f34241]) ).
fof(f34241,plain,
( spl0_2585
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).
fof(f10591,plain,
( spl0_1345
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f11348,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,c_emptyset,tc_set(X0)) )
| ~ spl0_662
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f6774]) ).
fof(f10592,plain,
( ! [X21,X1,X15] :
( ~ c_lessequals(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f10591]) ).
fof(f34239,plain,
( spl0_2584
| ~ spl0_796
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11340,f10591,f7354,f34237]) ).
fof(f34237,plain,
( spl0_2584
<=> ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).
fof(f11340,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_796
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f7355]) ).
fof(f34234,plain,
( spl0_2583
| ~ spl0_727
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11329,f10591,f7061,f34232]) ).
fof(f34232,plain,
( spl0_2583
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_UNIV,X1,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f11329,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_UNIV,X1,tc_set(X0)) )
| ~ spl0_727
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f7062]) ).
fof(f34230,plain,
( spl0_2582
| ~ spl0_795
| ~ spl0_1344 ),
inference(avatar_split_clause,[],[f11309,f10587,f7350,f34228]) ).
fof(f34228,plain,
( spl0_2582
<=> ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f7350,plain,
( spl0_795
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f10587,plain,
( spl0_1344
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f11309,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_795
| ~ spl0_1344 ),
inference(resolution,[],[f10588,f7351]) ).
fof(f7351,plain,
( ! [X1] :
( c_less(c_0,c_1,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_795 ),
inference(avatar_component_clause,[],[f7350]) ).
fof(f10588,plain,
( ! [X21,X1,X15] :
( ~ c_less(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
| ~ spl0_1344 ),
inference(avatar_component_clause,[],[f10587]) ).
fof(f34226,plain,
( spl0_2581
| ~ spl0_91
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f11296,f10583,f3702,f34224]) ).
fof(f34224,plain,
( spl0_2581
<=> ! [X0] : c_SetInterval_OatLeast(X0,tc_nat) = c_uminus(c_SetInterval_OlessThan(X0,tc_nat),tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).
fof(f10583,plain,
( spl0_1343
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f11296,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,tc_nat) = c_uminus(c_SetInterval_OlessThan(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_91
| ~ spl0_1343 ),
inference(resolution,[],[f10584,f3704]) ).
fof(f3704,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f3702]) ).
fof(f10584,plain,
( ! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) )
| ~ spl0_1343 ),
inference(avatar_component_clause,[],[f10583]) ).
fof(f34222,plain,
( spl0_2580
| ~ spl0_27
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f11295,f10583,f3382,f34220]) ).
fof(f34220,plain,
( spl0_2580
<=> ! [X0] : c_SetInterval_OatLeast(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OlessThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2580])]) ).
fof(f3382,plain,
( spl0_27
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f11295,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OlessThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint))
| ~ spl0_27
| ~ spl0_1343 ),
inference(resolution,[],[f10584,f3384]) ).
fof(f3384,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3382]) ).
fof(f34218,plain,
( spl0_2579
| ~ spl0_804
| ~ spl0_2472 ),
inference(avatar_split_clause,[],[f32981,f32245,f7386,f34216]) ).
fof(f34216,plain,
( spl0_2579
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2579])]) ).
fof(f7386,plain,
( spl0_804
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f32245,plain,
( spl0_2472
<=> ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f32981,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_804
| ~ spl0_2472 ),
inference(superposition,[],[f7387,f32246]) ).
fof(f32246,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_2472 ),
inference(avatar_component_clause,[],[f32245]) ).
fof(f7387,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f7386]) ).
fof(f34214,plain,
( spl0_2578
| ~ spl0_91
| ~ spl0_1342 ),
inference(avatar_split_clause,[],[f11294,f10579,f3702,f34212]) ).
fof(f34212,plain,
( spl0_2578
<=> ! [X0] : c_SetInterval_OatMost(X0,tc_nat) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_nat),tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).
fof(f10579,plain,
( spl0_1342
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f11294,plain,
( ! [X0] : c_SetInterval_OatMost(X0,tc_nat) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_91
| ~ spl0_1342 ),
inference(resolution,[],[f10580,f3704]) ).
fof(f10580,plain,
( ! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) )
| ~ spl0_1342 ),
inference(avatar_component_clause,[],[f10579]) ).
fof(f34210,plain,
( spl0_2577
| ~ spl0_27
| ~ spl0_1342 ),
inference(avatar_split_clause,[],[f11293,f10579,f3382,f34208]) ).
fof(f34208,plain,
( spl0_2577
<=> ! [X0] : c_SetInterval_OatMost(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).
fof(f11293,plain,
( ! [X0] : c_SetInterval_OatMost(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint))
| ~ spl0_27
| ~ spl0_1342 ),
inference(resolution,[],[f10580,f3384]) ).
fof(f34206,plain,
( spl0_2576
| ~ spl0_91
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11292,f10575,f3702,f34204]) ).
fof(f34204,plain,
( spl0_2576
<=> ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2576])]) ).
fof(f10575,plain,
( spl0_1341
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f11292,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(X0,tc_nat)
| ~ spl0_91
| ~ spl0_1341 ),
inference(resolution,[],[f10576,f3704]) ).
fof(f10576,plain,
( ! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) )
| ~ spl0_1341 ),
inference(avatar_component_clause,[],[f10575]) ).
fof(f34202,plain,
( spl0_2575
| ~ spl0_27
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11291,f10575,f3382,f34200]) ).
fof(f34200,plain,
( spl0_2575
<=> ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2575])]) ).
fof(f11291,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_1341 ),
inference(resolution,[],[f10576,f3384]) ).
fof(f34198,plain,
( spl0_2574
| ~ spl0_91
| ~ spl0_1340 ),
inference(avatar_split_clause,[],[f11290,f10568,f3702,f34196]) ).
fof(f34196,plain,
( spl0_2574
<=> ! [X0] : c_SetInterval_OlessThan(X0,tc_nat) = c_uminus(c_SetInterval_OatLeast(X0,tc_nat),tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).
fof(f10568,plain,
( spl0_1340
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f11290,plain,
( ! [X0] : c_SetInterval_OlessThan(X0,tc_nat) = c_uminus(c_SetInterval_OatLeast(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_91
| ~ spl0_1340 ),
inference(resolution,[],[f10569,f3704]) ).
fof(f10569,plain,
( ! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) )
| ~ spl0_1340 ),
inference(avatar_component_clause,[],[f10568]) ).
fof(f34194,plain,
( spl0_2573
| ~ spl0_27
| ~ spl0_1340 ),
inference(avatar_split_clause,[],[f11289,f10568,f3382,f34192]) ).
fof(f34192,plain,
( spl0_2573
<=> ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).
fof(f11289,plain,
( ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(X0,tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_1340 ),
inference(resolution,[],[f10569,f3384]) ).
fof(f34185,plain,
( ~ spl0_39
| spl0_2572
| ~ spl0_640
| ~ spl0_1250
| ~ spl0_1310
| ~ spl0_1317 ),
inference(avatar_split_clause,[],[f11134,f10475,f10447,f9809,f5911,f34183,f3442]) ).
fof(f3442,plain,
( spl0_39
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f34183,plain,
( spl0_2572
<=> ! [X0] : ~ c_lessequals(c_IntDef_Oint(c_plus(c_1,X0,tc_nat)),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2572])]) ).
fof(f9809,plain,
( spl0_1250
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f10475,plain,
( spl0_1317
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f11134,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(c_plus(c_1,X0,tc_nat)),c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) )
| ~ spl0_640
| ~ spl0_1250
| ~ spl0_1310
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f11121,f11073]) ).
fof(f11121,plain,
( ! [X0] :
( ~ c_lessequals(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) )
| ~ spl0_1250
| ~ spl0_1317 ),
inference(resolution,[],[f10476,f9810]) ).
fof(f9810,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1250 ),
inference(avatar_component_clause,[],[f9809]) ).
fof(f10476,plain,
( ! [X18,X1] :
( c_lessequals(c_0,c_uminus(X18,X1),X1)
| ~ c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1317 ),
inference(avatar_component_clause,[],[f10475]) ).
fof(f34181,plain,
( spl0_2571
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1315 ),
inference(avatar_split_clause,[],[f11114,f10467,f8526,f3507,f34179]) ).
fof(f34179,plain,
( spl0_2571
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2571])]) ).
fof(f8526,plain,
( spl0_1034
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f10467,plain,
( spl0_1315
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f11114,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1315 ),
inference(forward_demodulation,[],[f11113,f8847]) ).
fof(f8847,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034 ),
inference(resolution,[],[f8527,f3509]) ).
fof(f8527,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f8526]) ).
fof(f11113,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(X0,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1315 ),
inference(resolution,[],[f10468,f3509]) ).
fof(f10468,plain,
( ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) )
| ~ spl0_1315 ),
inference(avatar_component_clause,[],[f10467]) ).
fof(f34177,plain,
( spl0_2570
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1314 ),
inference(avatar_split_clause,[],[f11098,f10463,f8526,f3507,f34175]) ).
fof(f34175,plain,
( spl0_2570
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2570])]) ).
fof(f10463,plain,
( spl0_1314
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f11098,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1314 ),
inference(forward_demodulation,[],[f11097,f8847]) ).
fof(f11097,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1314 ),
inference(resolution,[],[f10464,f3509]) ).
fof(f10464,plain,
( ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) )
| ~ spl0_1314 ),
inference(avatar_component_clause,[],[f10463]) ).
fof(f34173,plain,
( spl0_2569
| ~ spl0_804
| ~ spl0_2471 ),
inference(avatar_split_clause,[],[f32936,f32238,f7386,f34171]) ).
fof(f34171,plain,
( spl0_2569
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2569])]) ).
fof(f32238,plain,
( spl0_2471
<=> ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2471])]) ).
fof(f32936,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_804
| ~ spl0_2471 ),
inference(superposition,[],[f7387,f32239]) ).
fof(f32239,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_2471 ),
inference(avatar_component_clause,[],[f32238]) ).
fof(f34168,plain,
( spl0_2568
| ~ spl0_641
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10229,f9825,f5916,f34166]) ).
fof(f5916,plain,
( spl0_641
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f9825,plain,
( spl0_1253
<=> ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f10229,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1253 ),
inference(superposition,[],[f9826,f5918]) ).
fof(f5918,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5916]) ).
fof(f9826,plain,
( ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1253 ),
inference(avatar_component_clause,[],[f9825]) ).
fof(f34163,plain,
( spl0_2567
| ~ spl0_640
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10228,f9825,f5911,f34161]) ).
fof(f10228,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1253 ),
inference(superposition,[],[f9826,f5913]) ).
fof(f34158,plain,
( spl0_2566
| ~ spl0_640
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10226,f9825,f5911,f34156]) ).
fof(f10226,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1253 ),
inference(superposition,[],[f9826,f5913]) ).
fof(f34154,plain,
( spl0_2565
| ~ spl0_785
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f10046,f9684,f7309,f34152]) ).
fof(f34152,plain,
( spl0_2565
<=> ! [X0] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2565])]) ).
fof(f9684,plain,
( spl0_1219
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f10046,plain,
( ! [X0] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_785
| ~ spl0_1219 ),
inference(superposition,[],[f9685,f7311]) ).
fof(f9685,plain,
( ! [X11,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1219 ),
inference(avatar_component_clause,[],[f9684]) ).
fof(f34150,plain,
( spl0_2564
| ~ spl0_857
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f10017,f9672,f7610,f34148]) ).
fof(f34148,plain,
( spl0_2564
<=> ! [X0,X1] :
( c_less(X0,X1,tc_nat)
| c_0 = c_minus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2564])]) ).
fof(f7610,plain,
( spl0_857
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f9672,plain,
( spl0_1216
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f10017,plain,
( ! [X0,X1] :
( c_less(X0,X1,tc_nat)
| c_0 = c_minus(X1,X0,tc_nat) )
| ~ spl0_857
| ~ spl0_1216 ),
inference(resolution,[],[f9673,f7611]) ).
fof(f7611,plain,
( ! [X21] :
( c_less(c_0,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7610]) ).
fof(f9673,plain,
( ! [X21,X15] :
( ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat)
| c_less(X15,X21,tc_nat) )
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9672]) ).
fof(f34146,plain,
( spl0_2563
| ~ spl0_857
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f10014,f9668,f7610,f34144]) ).
fof(f34144,plain,
( spl0_2563
<=> ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).
fof(f9668,plain,
( spl0_1215
<=> ! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f10014,plain,
( ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X1,X0,tc_nat) )
| ~ spl0_857
| ~ spl0_1215 ),
inference(resolution,[],[f9669,f7611]) ).
fof(f9669,plain,
( ! [X21,X15] :
( ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat)
| c_less(c_0,X21,tc_nat) )
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f9668]) ).
fof(f34142,plain,
( spl0_2562
| ~ spl0_857
| ~ spl0_1213 ),
inference(avatar_split_clause,[],[f10011,f9660,f7610,f34140]) ).
fof(f34140,plain,
( spl0_2562
<=> ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).
fof(f9660,plain,
( spl0_1213
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f10011,plain,
( ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X0,X1,tc_nat) )
| ~ spl0_857
| ~ spl0_1213 ),
inference(resolution,[],[f9661,f7611]) ).
fof(f9661,plain,
( ! [X21,X15] :
( ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat)
| c_less(c_0,X15,tc_nat) )
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f9660]) ).
fof(f34137,plain,
( ~ spl0_52
| ~ spl0_50
| spl0_2561
| ~ spl0_1035
| ~ spl0_1210 ),
inference(avatar_split_clause,[],[f9997,f9648,f8530,f34134,f3497,f3507]) ).
fof(f3497,plain,
( spl0_50
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f34134,plain,
( spl0_2561
<=> c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).
fof(f8530,plain,
( spl0_1035
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f9648,plain,
( spl0_1210
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f9997,plain,
( c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat))
| ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_1035
| ~ spl0_1210 ),
inference(resolution,[],[f9649,f8531]) ).
fof(f8531,plain,
( ! [X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1035 ),
inference(avatar_component_clause,[],[f8530]) ).
fof(f9649,plain,
( ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) )
| ~ spl0_1210 ),
inference(avatar_component_clause,[],[f9648]) ).
fof(f34132,plain,
( spl0_2560
| ~ spl0_857
| ~ spl0_1198 ),
inference(avatar_split_clause,[],[f9942,f9600,f7610,f34130]) ).
fof(f34130,plain,
( spl0_2560
<=> ! [X0] :
( c_0 = c_List_Ohd(c_List_Oupt(c_0,X0),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2560])]) ).
fof(f9600,plain,
( spl0_1198
<=> ! [X59,X3] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f9942,plain,
( ! [X0] :
( c_0 = c_List_Ohd(c_List_Oupt(c_0,X0),tc_nat)
| c_0 = X0 )
| ~ spl0_857
| ~ spl0_1198 ),
inference(resolution,[],[f9601,f7611]) ).
fof(f9601,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f9600]) ).
fof(f34127,plain,
( spl0_2559
| ~ spl0_1003
| ~ spl0_1171 ),
inference(avatar_split_clause,[],[f9506,f9388,f8400,f34125]) ).
fof(f34125,plain,
( spl0_2559
<=> ! [X0] : c_0 = c_uminus(c_Divides_Oop_Amod(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2559])]) ).
fof(f8400,plain,
( spl0_1003
<=> ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f9388,plain,
( spl0_1171
<=> ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f9506,plain,
( ! [X0] : c_0 = c_uminus(c_Divides_Oop_Amod(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1003
| ~ spl0_1171 ),
inference(superposition,[],[f9389,f8401]) ).
fof(f8401,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1003 ),
inference(avatar_component_clause,[],[f8400]) ).
fof(f9389,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1171 ),
inference(avatar_component_clause,[],[f9388]) ).
fof(f34108,plain,
( spl0_2558
| ~ spl0_847
| ~ spl0_1123 ),
inference(avatar_split_clause,[],[f9408,f9089,f7570,f34106]) ).
fof(f34106,plain,
( spl0_2558
<=> ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2558])]) ).
fof(f7570,plain,
( spl0_847
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f9089,plain,
( spl0_1123
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f9408,plain,
( ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 )
| ~ spl0_847
| ~ spl0_1123 ),
inference(superposition,[],[f9090,f7571]) ).
fof(f7571,plain,
( ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f7570]) ).
fof(f9090,plain,
( ! [X1,X25,X23] :
( c_List_Orev(X23,X1) != c_List_Orev(X25,X1)
| X23 = X25 )
| ~ spl0_1123 ),
inference(avatar_component_clause,[],[f9089]) ).
fof(f34104,plain,
( spl0_2557
| ~ spl0_1021
| ~ spl0_1122 ),
inference(avatar_split_clause,[],[f9406,f9085,f8473,f34102]) ).
fof(f34102,plain,
( spl0_2557
<=> ! [X2,X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).
fof(f8473,plain,
( spl0_1021
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f9085,plain,
( spl0_1122
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f9406,plain,
( ! [X2,X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_1021
| ~ spl0_1122 ),
inference(superposition,[],[f9086,f8474]) ).
fof(f8474,plain,
( ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3
| ~ spl0_1021 ),
inference(avatar_component_clause,[],[f8473]) ).
fof(f9086,plain,
( ! [X1,X23] :
( c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olist_ONil = X23 )
| ~ spl0_1122 ),
inference(avatar_component_clause,[],[f9085]) ).
fof(f34100,plain,
( spl0_2556
| ~ spl0_679
| ~ spl0_1111 ),
inference(avatar_split_clause,[],[f9377,f9040,f6846,f34098]) ).
fof(f34098,plain,
( spl0_2556
<=> ! [X0,X1] :
( ~ c_less(c_IntDef_Onat(X1),X0,tc_nat)
| c_less(X1,c_IntDef_Oint(X0),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).
fof(f9040,plain,
( spl0_1111
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f9377,plain,
( ! [X0,X1] :
( ~ c_less(c_IntDef_Onat(X1),X0,tc_nat)
| c_less(X1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_679
| ~ spl0_1111 ),
inference(superposition,[],[f9041,f6847]) ).
fof(f9041,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(X11,X48,tc_IntDef_Oint) )
| ~ spl0_1111 ),
inference(avatar_component_clause,[],[f9040]) ).
fof(f34096,plain,
( spl0_2555
| ~ spl0_679
| ~ spl0_1111 ),
inference(avatar_split_clause,[],[f9372,f9040,f6846,f34094]) ).
fof(f34094,plain,
( spl0_2555
<=> ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_IntDef_Oint(X0),X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f9372,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_IntDef_Oint(X0),X1,tc_IntDef_Oint) )
| ~ spl0_679
| ~ spl0_1111 ),
inference(superposition,[],[f9041,f6847]) ).
fof(f34080,plain,
( spl0_2554
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2553 ),
inference(avatar_split_clause,[],[f34076,f34073,f10767,f10447,f6846,f5911,f34078]) ).
fof(f34078,plain,
( spl0_2554
<=> ! [X0] : c_Divides_Oop_Amod(X0,c_plus(c_1,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).
fof(f34073,plain,
( spl0_2553
<=> ! [X0] : c_Divides_Oop_Amod(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).
fof(f34076,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_plus(c_1,X0,tc_nat),tc_nat) = X0
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2553 ),
inference(forward_demodulation,[],[f34074,f11726]) ).
fof(f34074,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_2553 ),
inference(avatar_component_clause,[],[f34073]) ).
fof(f34075,plain,
( spl0_2553
| ~ spl0_978
| ~ spl0_1097 ),
inference(avatar_split_clause,[],[f9319,f8983,f8173,f34073]) ).
fof(f8173,plain,
( spl0_978
<=> ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f8983,plain,
( spl0_1097
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f9319,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_978
| ~ spl0_1097 ),
inference(resolution,[],[f8984,f8174]) ).
fof(f8174,plain,
( ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_978 ),
inference(avatar_component_clause,[],[f8173]) ).
fof(f8984,plain,
( ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 )
| ~ spl0_1097 ),
inference(avatar_component_clause,[],[f8983]) ).
fof(f34061,plain,
( spl0_2552
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2551 ),
inference(avatar_split_clause,[],[f34057,f34054,f10767,f10447,f6846,f5911,f34059]) ).
fof(f34059,plain,
( spl0_2552
<=> ! [X0] : c_0 = c_div(X0,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f34054,plain,
( spl0_2551
<=> ! [X0] : c_0 = c_div(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f34057,plain,
( ! [X0] : c_0 = c_div(X0,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2551 ),
inference(forward_demodulation,[],[f34055,f11726]) ).
fof(f34055,plain,
( ! [X0] : c_0 = c_div(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_2551 ),
inference(avatar_component_clause,[],[f34054]) ).
fof(f34056,plain,
( spl0_2551
| ~ spl0_978
| ~ spl0_1094 ),
inference(avatar_split_clause,[],[f9306,f8971,f8173,f34054]) ).
fof(f8971,plain,
( spl0_1094
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f9306,plain,
( ! [X0] : c_0 = c_div(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_978
| ~ spl0_1094 ),
inference(resolution,[],[f8972,f8174]) ).
fof(f8972,plain,
( ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f8971]) ).
fof(f34048,plain,
( spl0_2550
| ~ spl0_830
| ~ spl0_1086 ),
inference(avatar_split_clause,[],[f9293,f8939,f7502,f34046]) ).
fof(f34046,plain,
( spl0_2550
<=> ! [X0,X1] :
( c_Main_Onot__Some__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f7502,plain,
( spl0_830
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f8939,plain,
( spl0_1086
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f9293,plain,
( ! [X0,X1] :
( c_Main_Onot__Some__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_830
| ~ spl0_1086 ),
inference(superposition,[],[f7503,f8940]) ).
fof(f8940,plain,
( ! [X0,X1] :
( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_1086 ),
inference(avatar_component_clause,[],[f8939]) ).
fof(f7503,plain,
( ! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3
| ~ spl0_830 ),
inference(avatar_component_clause,[],[f7502]) ).
fof(f34044,plain,
( spl0_2549
| ~ spl0_830
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f9290,f8934,f7502,f34042]) ).
fof(f34042,plain,
( spl0_2549
<=> ! [X0,X1] :
( c_Main_Onot__None__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f8934,plain,
( spl0_1085
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f9290,plain,
( ! [X0,X1] :
( c_Main_Onot__None__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_830
| ~ spl0_1085 ),
inference(superposition,[],[f7503,f8935]) ).
fof(f8935,plain,
( ! [X0,X1] :
( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f8934]) ).
fof(f34040,plain,
( spl0_2548
| ~ spl0_1049
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f9288,f8930,f8586,f34038]) ).
fof(f34038,plain,
( spl0_2548
<=> ! [X0,X1] :
( ~ c_in(X1,c_Pow(c_emptyset,X0),tc_set(X0))
| c_emptyset = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).
fof(f8586,plain,
( spl0_1049
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f8930,plain,
( spl0_1084
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f9288,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_Pow(c_emptyset,X0),tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_1049
| ~ spl0_1084 ),
inference(superposition,[],[f8931,f8587]) ).
fof(f8587,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f8586]) ).
fof(f8931,plain,
( ! [X18,X1,X27] :
( ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1)
| X18 = X27 )
| ~ spl0_1084 ),
inference(avatar_component_clause,[],[f8930]) ).
fof(f34036,plain,
( spl0_2547
| ~ spl0_1022
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f9287,f8930,f8477,f34034]) ).
fof(f34034,plain,
( spl0_2547
<=> ! [X0,X1] :
( ~ c_in(X1,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| c_List_Olist_ONil = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2547])]) ).
fof(f8477,plain,
( spl0_1022
<=> ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f9287,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| c_List_Olist_ONil = X1 )
| ~ spl0_1022
| ~ spl0_1084 ),
inference(superposition,[],[f8931,f8478]) ).
fof(f8478,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f8477]) ).
fof(f34032,plain,
( spl0_2546
| ~ spl0_814
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f8893,f8642,f7426,f34030]) ).
fof(f34030,plain,
( spl0_2546
<=> ! [X0,X1] :
( c_in(X1,c_Message_Oparts(X0),tc_Message_Omsg)
| ~ c_in(X1,c_Message_Oanalz(X0),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).
fof(f7426,plain,
( spl0_814
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f8642,plain,
( spl0_1063
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f8893,plain,
( ! [X0,X1] :
( c_in(X1,c_Message_Oparts(X0),tc_Message_Omsg)
| ~ c_in(X1,c_Message_Oanalz(X0),tc_Message_Omsg) )
| ~ spl0_814
| ~ spl0_1063 ),
inference(superposition,[],[f8643,f7427]) ).
fof(f7427,plain,
( ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88))
| ~ spl0_814 ),
inference(avatar_component_clause,[],[f7426]) ).
fof(f8643,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1063 ),
inference(avatar_component_clause,[],[f8642]) ).
fof(f34028,plain,
( spl0_2545
| ~ spl0_937
| ~ spl0_1037 ),
inference(avatar_split_clause,[],[f8852,f8538,f8006,f34026]) ).
fof(f34026,plain,
( spl0_2545
<=> ! [X0] : c_Numeral_OBit(c_Numeral_Obin__succ(X0),c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OBit(X0,c_Numeral_Obit_OB1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).
fof(f8006,plain,
( spl0_937
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f8538,plain,
( spl0_1037
<=> ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f8852,plain,
( ! [X0] : c_Numeral_OBit(c_Numeral_Obin__succ(X0),c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OBit(X0,c_Numeral_Obit_OB1)))
| ~ spl0_937
| ~ spl0_1037 ),
inference(superposition,[],[f8007,f8539]) ).
fof(f8539,plain,
( ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0)
| ~ spl0_1037 ),
inference(avatar_component_clause,[],[f8538]) ).
fof(f8007,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_937 ),
inference(avatar_component_clause,[],[f8006]) ).
fof(f34024,plain,
( spl0_2544
| ~ spl0_929
| ~ spl0_1029 ),
inference(avatar_split_clause,[],[f8828,f8505,f7973,f34022]) ).
fof(f34022,plain,
( spl0_2544
<=> ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orotate1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f7973,plain,
( spl0_929
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f8505,plain,
( spl0_1029
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f8828,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orotate1(X0,X1) )
| ~ spl0_929
| ~ spl0_1029 ),
inference(superposition,[],[f7974,f8506]) ).
fof(f8506,plain,
( ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1)
| ~ spl0_1029 ),
inference(avatar_component_clause,[],[f8505]) ).
fof(f7974,plain,
( ! [X1,X23] :
( c_emptyset != c_List_Oset(X23,X1)
| c_List_Olist_ONil = X23 )
| ~ spl0_929 ),
inference(avatar_component_clause,[],[f7973]) ).
fof(f34020,plain,
( spl0_2543
| ~ spl0_929
| ~ spl0_1028 ),
inference(avatar_split_clause,[],[f8826,f8501,f7973,f34018]) ).
fof(f34018,plain,
( spl0_2543
<=> ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).
fof(f8501,plain,
( spl0_1028
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f8826,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_929
| ~ spl0_1028 ),
inference(superposition,[],[f7974,f8502]) ).
fof(f8502,plain,
( ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1)
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8501]) ).
fof(f34016,plain,
( spl0_2542
| ~ spl0_929
| ~ spl0_1027 ),
inference(avatar_split_clause,[],[f8823,f8497,f7973,f34014]) ).
fof(f34014,plain,
( spl0_2542
<=> ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f8497,plain,
( spl0_1027
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f8823,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Oremdups(X0,X1) )
| ~ spl0_929
| ~ spl0_1027 ),
inference(superposition,[],[f7974,f8498]) ).
fof(f8498,plain,
( ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1)
| ~ spl0_1027 ),
inference(avatar_component_clause,[],[f8497]) ).
fof(f34012,plain,
( spl0_2541
| ~ spl0_997
| ~ spl0_998 ),
inference(avatar_split_clause,[],[f8744,f8380,f8376,f34010]) ).
fof(f34010,plain,
( spl0_2541
<=> ! [X0] :
( c_0 = c_IntDef_Oint(c_IntDef_Onat(X0))
| c_IntDef_Oint(c_IntDef_Onat(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f8376,plain,
( spl0_997
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f8380,plain,
( spl0_998
<=> ! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f8744,plain,
( ! [X0] :
( c_0 = c_IntDef_Oint(c_IntDef_Onat(X0))
| c_IntDef_Oint(c_IntDef_Onat(X0)) = X0 )
| ~ spl0_997
| ~ spl0_998 ),
inference(resolution,[],[f8381,f8377]) ).
fof(f8377,plain,
( ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 )
| ~ spl0_997 ),
inference(avatar_component_clause,[],[f8376]) ).
fof(f8381,plain,
( ! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) )
| ~ spl0_998 ),
inference(avatar_component_clause,[],[f8380]) ).
fof(f33731,plain,
( spl0_2540
| ~ spl0_2249
| ~ spl0_2516 ),
inference(avatar_split_clause,[],[f32497,f32494,f28501,f33729]) ).
fof(f32494,plain,
( spl0_2516
<=> ! [X0] : c_Message_Oanalz(c_UNIV) = c_Message_Oanalz(c_union(c_Message_Osynth(c_UNIV),X0,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f32497,plain,
( ! [X0] : c_Message_Oanalz(c_IntDef_ONats) = c_Message_Oanalz(c_union(c_Message_Osynth(c_IntDef_ONats),X0,tc_Message_Omsg))
| ~ spl0_2249
| ~ spl0_2516 ),
inference(forward_demodulation,[],[f32495,f28503]) ).
fof(f32495,plain,
( ! [X0] : c_Message_Oanalz(c_UNIV) = c_Message_Oanalz(c_union(c_Message_Osynth(c_UNIV),X0,tc_Message_Omsg))
| ~ spl0_2516 ),
inference(avatar_component_clause,[],[f32494]) ).
fof(f33727,plain,
( spl0_2539
| ~ spl0_2249
| ~ spl0_2515 ),
inference(avatar_split_clause,[],[f32492,f32489,f28501,f33725]) ).
fof(f33725,plain,
( spl0_2539
<=> ! [X0] : c_Message_Oanalz(c_IntDef_ONats) = c_union(c_Message_Oanalz(c_IntDef_ONats),c_Message_Osynth(X0),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f32489,plain,
( spl0_2515
<=> ! [X0] : c_Message_Oanalz(c_UNIV) = c_union(c_Message_Oanalz(c_UNIV),c_Message_Osynth(X0),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f32492,plain,
( ! [X0] : c_Message_Oanalz(c_IntDef_ONats) = c_union(c_Message_Oanalz(c_IntDef_ONats),c_Message_Osynth(X0),tc_Message_Omsg)
| ~ spl0_2249
| ~ spl0_2515 ),
inference(forward_demodulation,[],[f32490,f28503]) ).
fof(f32490,plain,
( ! [X0] : c_Message_Oanalz(c_UNIV) = c_union(c_Message_Oanalz(c_UNIV),c_Message_Osynth(X0),tc_Message_Omsg)
| ~ spl0_2515 ),
inference(avatar_component_clause,[],[f32489]) ).
fof(f33717,plain,
( spl0_2538
| ~ spl0_2249
| ~ spl0_2514 ),
inference(avatar_split_clause,[],[f32487,f32484,f28501,f33715]) ).
fof(f32484,plain,
( spl0_2514
<=> ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f32487,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_2249
| ~ spl0_2514 ),
inference(forward_demodulation,[],[f32485,f28503]) ).
fof(f32485,plain,
( ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_2514 ),
inference(avatar_component_clause,[],[f32484]) ).
fof(f33287,plain,
( spl0_2537
| ~ spl0_2249
| ~ spl0_2494 ),
inference(avatar_split_clause,[],[f32389,f32386,f28501,f33285]) ).
fof(f33285,plain,
( spl0_2537
<=> ! [X0] :
( c_IntDef_ONats = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).
fof(f32386,plain,
( spl0_2494
<=> ! [X0] :
( c_UNIV = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f32389,plain,
( ! [X0] :
( c_IntDef_ONats = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_2249
| ~ spl0_2494 ),
inference(forward_demodulation,[],[f32387,f28503]) ).
fof(f32387,plain,
( ! [X0] :
( c_UNIV = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_2494 ),
inference(avatar_component_clause,[],[f32386]) ).
fof(f33151,plain,
( spl0_2536
| ~ spl0_2249
| ~ spl0_2486 ),
inference(avatar_split_clause,[],[f32356,f32353,f28501,f33149]) ).
fof(f33149,plain,
( spl0_2536
<=> ! [X0,X1] :
( c_IntDef_ONats = X1
| c_emptyset != c_uminus(X1,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).
fof(f32353,plain,
( spl0_2486
<=> ! [X0,X1] :
( c_emptyset != c_uminus(X1,tc_set(X0))
| c_UNIV = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f32356,plain,
( ! [X0,X1] :
( c_IntDef_ONats = X1
| c_emptyset != c_uminus(X1,tc_set(X0)) )
| ~ spl0_2249
| ~ spl0_2486 ),
inference(forward_demodulation,[],[f32354,f28503]) ).
fof(f32354,plain,
( ! [X0,X1] :
( c_emptyset != c_uminus(X1,tc_set(X0))
| c_UNIV = X1 )
| ~ spl0_2486 ),
inference(avatar_component_clause,[],[f32353]) ).
fof(f33147,plain,
( spl0_2535
| ~ spl0_2249
| ~ spl0_2485 ),
inference(avatar_split_clause,[],[f32351,f32348,f28501,f33145]) ).
fof(f33145,plain,
( spl0_2535
<=> ! [X0,X1] :
( c_IntDef_ONats != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).
fof(f32348,plain,
( spl0_2485
<=> ! [X0,X1] :
( c_UNIV != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f32351,plain,
( ! [X0,X1] :
( c_IntDef_ONats != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_2249
| ~ spl0_2485 ),
inference(forward_demodulation,[],[f32349,f28503]) ).
fof(f32349,plain,
( ! [X0,X1] :
( c_UNIV != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_2485 ),
inference(avatar_component_clause,[],[f32348]) ).
fof(f33104,plain,
( spl0_2534
| ~ spl0_640
| ~ spl0_2484 ),
inference(avatar_split_clause,[],[f32336,f32333,f5911,f33101]) ).
fof(f33101,plain,
( spl0_2534
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).
fof(f32333,plain,
( spl0_2484
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f32336,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_2484 ),
inference(superposition,[],[f32334,f5913]) ).
fof(f32334,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ spl0_2484 ),
inference(avatar_component_clause,[],[f32333]) ).
fof(f32922,plain,
( spl0_2533
| ~ spl0_640
| ~ spl0_2483 ),
inference(avatar_split_clause,[],[f32313,f32310,f5911,f32919]) ).
fof(f32919,plain,
( spl0_2533
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2533])]) ).
fof(f32310,plain,
( spl0_2483
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f32313,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_2483 ),
inference(superposition,[],[f32311,f5913]) ).
fof(f32311,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ spl0_2483 ),
inference(avatar_component_clause,[],[f32310]) ).
fof(f32858,plain,
( ~ spl0_2532
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| spl0_2449 ),
inference(avatar_split_clause,[],[f32123,f32119,f18552,f9544,f3292,f32855]) ).
fof(f32855,plain,
( spl0_2532
<=> c_lessequals(c_0,c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f32119,plain,
( spl0_2449
<=> c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).
fof(f32123,plain,
( ~ c_lessequals(c_0,c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| spl0_2449 ),
inference(forward_demodulation,[],[f32121,f19334]) ).
fof(f32121,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_2449 ),
inference(avatar_component_clause,[],[f32119]) ).
fof(f32852,plain,
( spl0_2531
| ~ spl0_1242
| ~ spl0_2419 ),
inference(avatar_split_clause,[],[f31997,f31569,f9776,f32850]) ).
fof(f32850,plain,
( spl0_2531
<=> ! [X0] : c_IntDef_ONats = c_Relation_ODomain(c_IntDef_ONats,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f9776,plain,
( spl0_1242
<=> ! [X5,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f31569,plain,
( spl0_2419
<=> ! [X0] : c_IntDef_ONats = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f31997,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ODomain(c_IntDef_ONats,X0,X0)
| ~ spl0_1242
| ~ spl0_2419 ),
inference(superposition,[],[f31570,f9777]) ).
fof(f9777,plain,
( ! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1)
| ~ spl0_1242 ),
inference(avatar_component_clause,[],[f9776]) ).
fof(f31570,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0)
| ~ spl0_2419 ),
inference(avatar_component_clause,[],[f31569]) ).
fof(f32713,plain,
( spl0_2530
| ~ spl0_11
| ~ spl0_1649
| ~ spl0_2443 ),
inference(avatar_split_clause,[],[f32097,f32094,f15191,f3302,f32711]) ).
fof(f32711,plain,
( spl0_2530
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f3302,plain,
( spl0_11
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f15191,plain,
( spl0_1649
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f32094,plain,
( spl0_2443
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f32097,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_1649
| ~ spl0_2443 ),
inference(forward_demodulation,[],[f32095,f15956]) ).
fof(f15956,plain,
( ! [X0,X1] : c_uminus(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_1649 ),
inference(resolution,[],[f15192,f3304]) ).
fof(f3304,plain,
( class_Ring__and__Field_Oring(tc_IntDef_Oint)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f3302]) ).
fof(f15192,plain,
( ! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) )
| ~ spl0_1649 ),
inference(avatar_component_clause,[],[f15191]) ).
fof(f32095,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2443 ),
inference(avatar_component_clause,[],[f32094]) ).
fof(f32709,plain,
( spl0_2529
| ~ spl0_11
| ~ spl0_1648
| ~ spl0_2441 ),
inference(avatar_split_clause,[],[f32088,f32085,f15178,f3302,f32707]) ).
fof(f32707,plain,
( spl0_2529
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f15178,plain,
( spl0_1648
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f32085,plain,
( spl0_2441
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).
fof(f32088,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_1648
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f32086,f15955]) ).
fof(f15955,plain,
( ! [X0,X1] : c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_uminus(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_1648 ),
inference(resolution,[],[f15179,f3304]) ).
fof(f15179,plain,
( ! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) )
| ~ spl0_1648 ),
inference(avatar_component_clause,[],[f15178]) ).
fof(f32086,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2441 ),
inference(avatar_component_clause,[],[f32085]) ).
fof(f32659,plain,
( spl0_2528
| ~ spl0_1243
| ~ spl0_2418 ),
inference(avatar_split_clause,[],[f31995,f31565,f9780,f32657]) ).
fof(f32657,plain,
( spl0_2528
<=> ! [X0] : c_IntDef_ONats = c_Relation_ORange(c_IntDef_ONats,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).
fof(f9780,plain,
( spl0_1243
<=> ! [X5,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f31565,plain,
( spl0_2418
<=> ! [X0] : c_IntDef_ONats = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f31995,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ORange(c_IntDef_ONats,X0,X0)
| ~ spl0_1243
| ~ spl0_2418 ),
inference(superposition,[],[f31566,f9781]) ).
fof(f9781,plain,
( ! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1)
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f9780]) ).
fof(f31566,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0)
| ~ spl0_2418 ),
inference(avatar_component_clause,[],[f31565]) ).
fof(f32568,plain,
( spl0_2527
| ~ spl0_825
| ~ spl0_2405 ),
inference(avatar_split_clause,[],[f31914,f30916,f7482,f32566]) ).
fof(f32566,plain,
( spl0_2527
<=> ! [X0] : c_Divides_Oop_Advd(c_Main_Ozmod__eq__0D__dest__1(X0,X0),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).
fof(f7482,plain,
( spl0_825
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f30916,plain,
( spl0_2405
<=> ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2405])]) ).
fof(f31914,plain,
( ! [X0] : c_Divides_Oop_Advd(c_Main_Ozmod__eq__0D__dest__1(X0,X0),X0,tc_IntDef_Oint)
| ~ spl0_825
| ~ spl0_2405 ),
inference(superposition,[],[f7483,f30917]) ).
fof(f30917,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_2405 ),
inference(avatar_component_clause,[],[f30916]) ).
fof(f7483,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f7482]) ).
fof(f32537,plain,
( spl0_2526
| ~ spl0_649
| ~ spl0_2195 ),
inference(avatar_split_clause,[],[f27275,f27221,f5952,f32535]) ).
fof(f5952,plain,
( spl0_649
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f27221,plain,
( spl0_2195
<=> ! [X5,X29,X2,X1] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f27275,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
| ~ spl0_649
| ~ spl0_2195 ),
inference(resolution,[],[f27222,f5953]) ).
fof(f5953,plain,
( ! [X1,X4] : ~ c_in(X4,c_emptyset,X1)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f5952]) ).
fof(f27222,plain,
( ! [X2,X29,X1,X5] :
( c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) )
| ~ spl0_2195 ),
inference(avatar_component_clause,[],[f27221]) ).
fof(f32533,plain,
( spl0_2525
| ~ spl0_804
| ~ spl0_2058 ),
inference(avatar_split_clause,[],[f23780,f22897,f7386,f32531]) ).
fof(f32531,plain,
( spl0_2525
<=> ! [X2,X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X0,X1),X2,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f22897,plain,
( spl0_2058
<=> ! [X87,X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f23780,plain,
( ! [X2,X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X0,X1),X2,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_2058 ),
inference(superposition,[],[f7387,f22898]) ).
fof(f22898,plain,
( ! [X88,X86,X87] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg)
| ~ spl0_2058 ),
inference(avatar_component_clause,[],[f22897]) ).
fof(f32529,plain,
( spl0_2524
| ~ spl0_804
| ~ spl0_2057 ),
inference(avatar_split_clause,[],[f23694,f22893,f7386,f32527]) ).
fof(f32527,plain,
( spl0_2524
<=> ! [X2,X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X0,X1),X2,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f22893,plain,
( spl0_2057
<=> ! [X87,X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f23694,plain,
( ! [X2,X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X0,X1),X2,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_2057 ),
inference(superposition,[],[f7387,f22894]) ).
fof(f22894,plain,
( ! [X88,X86,X87] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg)
| ~ spl0_2057 ),
inference(avatar_component_clause,[],[f22893]) ).
fof(f32525,plain,
( spl0_2523
| ~ spl0_774
| ~ spl0_779
| ~ spl0_2062 ),
inference(avatar_split_clause,[],[f22954,f22938,f7285,f7265,f32523]) ).
fof(f32523,plain,
( spl0_2523
<=> ! [X0] : c_1 = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f7285,plain,
( spl0_779
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f22938,plain,
( spl0_2062
<=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f22954,plain,
( ! [X0] : c_1 = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_779
| ~ spl0_2062 ),
inference(forward_demodulation,[],[f22953,f7266]) ).
fof(f22953,plain,
( ! [X0] : c_plus(c_1,c_0,tc_nat) = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_779
| ~ spl0_2062 ),
inference(forward_demodulation,[],[f22941,f7286]) ).
fof(f7286,plain,
( ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat)
| ~ spl0_779 ),
inference(avatar_component_clause,[],[f7285]) ).
fof(f22941,plain,
( ! [X0] : c_plus(c_1,c_Orderings_Omin(c_0,X0,tc_nat),tc_nat) = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_2062 ),
inference(superposition,[],[f22939,f7266]) ).
fof(f22939,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_2062 ),
inference(avatar_component_clause,[],[f22938]) ).
fof(f32521,plain,
( spl0_2522
| ~ spl0_804
| ~ spl0_1928 ),
inference(avatar_split_clause,[],[f21147,f20153,f7386,f32519]) ).
fof(f32519,plain,
( spl0_2522
<=> ! [X2,X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X0,X1),X2,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f20153,plain,
( spl0_1928
<=> ! [X86,X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f21147,plain,
( ! [X2,X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X0,X1),X2,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1928 ),
inference(superposition,[],[f7387,f20154]) ).
fof(f20154,plain,
( ! [X91,X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg)
| ~ spl0_1928 ),
inference(avatar_component_clause,[],[f20153]) ).
fof(f32517,plain,
( spl0_2521
| ~ spl0_823
| ~ spl0_2402 ),
inference(avatar_split_clause,[],[f31763,f30904,f7474,f32515]) ).
fof(f32515,plain,
( spl0_2521
<=> ! [X0] : c_Divides_Oop_Advd(c_Main_Omod__eq__0D__dest__1(X0,X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f30904,plain,
( spl0_2402
<=> ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2402])]) ).
fof(f31763,plain,
( ! [X0] : c_Divides_Oop_Advd(c_Main_Omod__eq__0D__dest__1(X0,X0),X0,tc_nat)
| ~ spl0_823
| ~ spl0_2402 ),
inference(superposition,[],[f7475,f30905]) ).
fof(f30905,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_2402 ),
inference(avatar_component_clause,[],[f30904]) ).
fof(f32513,plain,
( spl0_2520
| ~ spl0_1021
| ~ spl0_1865
| ~ spl0_1866 ),
inference(avatar_split_clause,[],[f19719,f18851,f18847,f8473,f32511]) ).
fof(f32511,plain,
( spl0_2520
<=> ! [X0,X3] : c_Orderings_Omin(X0,X3,tc_nat) = c_Orderings_Omin(X3,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).
fof(f18847,plain,
( spl0_1865
<=> ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f18851,plain,
( spl0_1866
<=> ! [X43,X0,X16,X1] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f19719,plain,
( ! [X3,X0] : c_Orderings_Omin(X0,X3,tc_nat) = c_Orderings_Omin(X3,X0,tc_nat)
| ~ spl0_1021
| ~ spl0_1865
| ~ spl0_1866 ),
inference(forward_demodulation,[],[f19718,f8474]) ).
fof(f19718,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Omin(X3,X0,tc_nat) = c_Orderings_Omin(c_Nat_Osize(c_List_Oreplicate(X0,X1,X2),tc_List_Olist(X2)),X3,tc_nat)
| ~ spl0_1021
| ~ spl0_1865
| ~ spl0_1866 ),
inference(forward_demodulation,[],[f19709,f8474]) ).
fof(f19709,plain,
( ! [X2,X3,X0,X1] : c_Orderings_Omin(c_Nat_Osize(c_List_Oreplicate(X0,X1,X2),tc_List_Olist(X2)),X3,tc_nat) = c_Nat_Osize(c_List_Oreplicate(c_Orderings_Omin(X3,X0,tc_nat),X1,X2),tc_List_Olist(X2))
| ~ spl0_1865
| ~ spl0_1866 ),
inference(superposition,[],[f18848,f18852]) ).
fof(f18852,plain,
( ! [X0,X1,X16,X43] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1)
| ~ spl0_1866 ),
inference(avatar_component_clause,[],[f18851]) ).
fof(f18848,plain,
( ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1))
| ~ spl0_1865 ),
inference(avatar_component_clause,[],[f18847]) ).
fof(f32509,plain,
( spl0_2519
| ~ spl0_722
| ~ spl0_1068
| ~ spl0_1864 ),
inference(avatar_split_clause,[],[f19681,f18843,f8662,f7041,f32507]) ).
fof(f32507,plain,
( spl0_2519
<=> ! [X0,X1] : c_Inter(c_insert(X1,c_emptyset,tc_set(X0)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f7041,plain,
( spl0_722
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f8662,plain,
( spl0_1068
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f18843,plain,
( spl0_1864
<=> ! [X13,X18,X1] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f19681,plain,
( ! [X0,X1] : c_Inter(c_insert(X1,c_emptyset,tc_set(X0)),X0) = X1
| ~ spl0_722
| ~ spl0_1068
| ~ spl0_1864 ),
inference(forward_demodulation,[],[f19659,f8663]) ).
fof(f8663,plain,
( ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f8662]) ).
fof(f19659,plain,
( ! [X0,X1] : c_Relation_OImage(c_Relation_Odiag(X1,X0),c_UNIV,X0,X0) = c_Inter(c_insert(X1,c_emptyset,tc_set(X0)),X0)
| ~ spl0_722
| ~ spl0_1864 ),
inference(superposition,[],[f18844,f7042]) ).
fof(f7042,plain,
( ! [X1] : c_UNIV = c_Inter(c_emptyset,X1)
| ~ spl0_722 ),
inference(avatar_component_clause,[],[f7041]) ).
fof(f18844,plain,
( ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1)
| ~ spl0_1864 ),
inference(avatar_component_clause,[],[f18843]) ).
fof(f32505,plain,
( spl0_2518
| ~ spl0_718
| ~ spl0_884
| ~ spl0_1864 ),
inference(avatar_split_clause,[],[f19678,f18843,f7720,f7023,f32503]) ).
fof(f32503,plain,
( spl0_2518
<=> ! [X0,X1] : c_emptyset = c_Inter(c_insert(c_emptyset,X1,tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f7720,plain,
( spl0_884
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f19678,plain,
( ! [X0,X1] : c_emptyset = c_Inter(c_insert(c_emptyset,X1,tc_set(X0)),X0)
| ~ spl0_718
| ~ spl0_884
| ~ spl0_1864 ),
inference(forward_demodulation,[],[f19657,f7721]) ).
fof(f7721,plain,
( ! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1)
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7720]) ).
fof(f19657,plain,
( ! [X0,X1] : c_Inter(c_insert(c_emptyset,X1,tc_set(X0)),X0) = c_Relation_OImage(c_emptyset,c_Inter(X1,X0),X0,X0)
| ~ spl0_718
| ~ spl0_1864 ),
inference(superposition,[],[f18844,f7024]) ).
fof(f32501,plain,
( spl0_2517
| ~ spl0_880
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f18786,f18776,f7702,f32499]) ).
fof(f7702,plain,
( spl0_880
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f18786,plain,
( ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat)
| ~ spl0_880
| ~ spl0_1854 ),
inference(superposition,[],[f7703,f18777]) ).
fof(f7703,plain,
( ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f7702]) ).
fof(f32496,plain,
( spl0_2516
| ~ spl0_799
| ~ spl0_800
| ~ spl0_1751 ),
inference(avatar_split_clause,[],[f18253,f16701,f7370,f7366,f32494]) ).
fof(f7366,plain,
( spl0_799
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f18253,plain,
( ! [X0] : c_Message_Oanalz(c_UNIV) = c_Message_Oanalz(c_union(c_Message_Osynth(c_UNIV),X0,tc_Message_Omsg))
| ~ spl0_799
| ~ spl0_800
| ~ spl0_1751 ),
inference(forward_demodulation,[],[f18230,f18251]) ).
fof(f18251,plain,
( ! [X0] : c_Message_Oanalz(c_UNIV) = c_union(c_Message_Oanalz(c_UNIV),c_Message_Osynth(X0),tc_Message_Omsg)
| ~ spl0_800
| ~ spl0_1751 ),
inference(forward_demodulation,[],[f18224,f7371]) ).
fof(f18224,plain,
( ! [X0] : c_Message_Oanalz(c_union(c_Message_Osynth(X0),c_UNIV,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_UNIV),c_Message_Osynth(X0),tc_Message_Omsg)
| ~ spl0_800
| ~ spl0_1751 ),
inference(superposition,[],[f16702,f7371]) ).
fof(f18230,plain,
( ! [X0] : c_Message_Oanalz(c_union(c_Message_Osynth(c_UNIV),X0,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_UNIV),c_Message_Osynth(c_UNIV),tc_Message_Omsg)
| ~ spl0_799
| ~ spl0_1751 ),
inference(superposition,[],[f16702,f7367]) ).
fof(f7367,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7366]) ).
fof(f32491,plain,
( spl0_2515
| ~ spl0_800
| ~ spl0_1751 ),
inference(avatar_split_clause,[],[f18251,f16701,f7370,f32489]) ).
fof(f32486,plain,
( spl0_2514
| ~ spl0_798
| ~ spl0_874
| ~ spl0_1742 ),
inference(avatar_split_clause,[],[f18111,f16665,f7678,f7362,f32484]) ).
fof(f7362,plain,
( spl0_798
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f7678,plain,
( spl0_874
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f16665,plain,
( spl0_1742
<=> ! [X13,X12,X1] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f18111,plain,
( ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_798
| ~ spl0_874
| ~ spl0_1742 ),
inference(forward_demodulation,[],[f18072,f7363]) ).
fof(f7363,plain,
( ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1))
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7362]) ).
fof(f18072,plain,
( ! [X0,X1] : c_uminus(c_emptyset,tc_set(X1)) = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_874
| ~ spl0_1742 ),
inference(superposition,[],[f16666,f7679]) ).
fof(f7679,plain,
( ! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1))
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f7678]) ).
fof(f16666,plain,
( ! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1)
| ~ spl0_1742 ),
inference(avatar_component_clause,[],[f16665]) ).
fof(f32482,plain,
( spl0_2513
| ~ spl0_1483
| ~ spl0_1691 ),
inference(avatar_split_clause,[],[f17240,f16445,f12173,f32480]) ).
fof(f32480,plain,
( spl0_2513
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Wellfounded__Recursion_Owf(c_Relation_Odiag(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f16445,plain,
( spl0_1691
<=> ! [X12,X1,X18] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f17240,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Wellfounded__Recursion_Owf(c_Relation_Odiag(X1,X2),X2) )
| ~ spl0_1483
| ~ spl0_1691 ),
inference(resolution,[],[f16446,f12174]) ).
fof(f16446,plain,
( ! [X18,X1,X12] :
( c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
| ~ c_in(X18,X12,X1) )
| ~ spl0_1691 ),
inference(avatar_component_clause,[],[f16445]) ).
fof(f32478,plain,
( spl0_2512
| ~ spl0_1526
| ~ spl0_1690 ),
inference(avatar_split_clause,[],[f17239,f16441,f13651,f32476]) ).
fof(f32476,plain,
( spl0_2512
<=> ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f13651,plain,
( spl0_1526
<=> ! [X12,X1,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f16441,plain,
( spl0_1690
<=> ! [X12,X1,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f17239,plain,
( ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
| ~ spl0_1526
| ~ spl0_1690 ),
inference(duplicate_literal_removal,[],[f17229]) ).
fof(f17229,plain,
( ! [X0,X1] :
( c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
| c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) )
| ~ spl0_1526
| ~ spl0_1690 ),
inference(resolution,[],[f16442,f13652]) ).
fof(f13652,plain,
( ! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) )
| ~ spl0_1526 ),
inference(avatar_component_clause,[],[f13651]) ).
fof(f16442,plain,
( ! [X1,X12,X23] :
( c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) )
| ~ spl0_1690 ),
inference(avatar_component_clause,[],[f16441]) ).
fof(f32474,plain,
( spl0_2511
| ~ spl0_761
| ~ spl0_774
| ~ spl0_1764 ),
inference(avatar_split_clause,[],[f17063,f17049,f7265,f7213,f32472]) ).
fof(f32472,plain,
( spl0_2511
<=> ! [X2,X0,X1] : c_List_Odrop(c_1,c_List_Olist_OCons(X2,X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f17049,plain,
( spl0_1764
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f17063,plain,
( ! [X2,X0,X1] : c_List_Odrop(c_1,c_List_Olist_OCons(X2,X0,X1),X1) = X0
| ~ spl0_761
| ~ spl0_774
| ~ spl0_1764 ),
inference(forward_demodulation,[],[f17052,f7214]) ).
fof(f17052,plain,
( ! [X2,X0,X1] : c_List_Odrop(c_0,X0,X1) = c_List_Odrop(c_1,c_List_Olist_OCons(X2,X0,X1),X1)
| ~ spl0_774
| ~ spl0_1764 ),
inference(superposition,[],[f17050,f7266]) ).
fof(f17050,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_1764 ),
inference(avatar_component_clause,[],[f17049]) ).
fof(f32456,plain,
( spl0_2510
| ~ spl0_1021
| ~ spl0_1675
| ~ spl0_1762 ),
inference(avatar_split_clause,[],[f17042,f17014,f15361,f8473,f32454]) ).
fof(f32454,plain,
( spl0_2510
<=> ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f17042,plain,
( ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat)
| ~ spl0_1021
| ~ spl0_1675
| ~ spl0_1762 ),
inference(forward_demodulation,[],[f17041,f8474]) ).
fof(f17041,plain,
( ! [X2,X0,X1] : c_plus(c_1,X1,tc_nat) = c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat)
| ~ spl0_1021
| ~ spl0_1675
| ~ spl0_1762 ),
inference(forward_demodulation,[],[f17037,f8474]) ).
fof(f17037,plain,
( ! [X2,X0,X1] : c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat) = c_Nat_Osize(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),tc_List_Olist(X2))
| ~ spl0_1675
| ~ spl0_1762 ),
inference(superposition,[],[f15362,f17015]) ).
fof(f32452,plain,
( spl0_2509
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762 ),
inference(avatar_split_clause,[],[f17040,f17014,f7265,f7245,f32450]) ).
fof(f32450,plain,
( spl0_2509
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f7245,plain,
( spl0_769
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f17040,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762 ),
inference(forward_demodulation,[],[f17017,f7266]) ).
fof(f17017,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_plus(c_1,c_0,tc_nat),X0,X1)
| ~ spl0_769
| ~ spl0_1762 ),
inference(superposition,[],[f17015,f7246]) ).
fof(f7246,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f7245]) ).
fof(f32448,plain,
( spl0_2508
| ~ spl0_767
| ~ spl0_1762 ),
inference(avatar_split_clause,[],[f17020,f17014,f7237,f32446]) ).
fof(f7237,plain,
( spl0_767
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f17020,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_767
| ~ spl0_1762 ),
inference(superposition,[],[f7238,f17015]) ).
fof(f7238,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_767 ),
inference(avatar_component_clause,[],[f7237]) ).
fof(f32444,plain,
( spl0_2507
| ~ spl0_764
| ~ spl0_1762 ),
inference(avatar_split_clause,[],[f17018,f17014,f7225,f32442]) ).
fof(f7225,plain,
( spl0_764
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f17018,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2)
| ~ spl0_764
| ~ spl0_1762 ),
inference(superposition,[],[f7226,f17015]) ).
fof(f7226,plain,
( ! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1)
| ~ spl0_764 ),
inference(avatar_component_clause,[],[f7225]) ).
fof(f32439,plain,
( spl0_2506
| ~ spl0_762
| ~ spl0_783
| ~ spl0_1675 ),
inference(avatar_split_clause,[],[f16320,f15361,f7301,f7217,f32437]) ).
fof(f32437,plain,
( spl0_2506
<=> ! [X0,X1] : c_1 = c_Nat_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f7217,plain,
( spl0_762
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f16320,plain,
( ! [X0,X1] : c_1 = c_Nat_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_762
| ~ spl0_783
| ~ spl0_1675 ),
inference(forward_demodulation,[],[f16265,f7302]) ).
fof(f16265,plain,
( ! [X0,X1] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_762
| ~ spl0_1675 ),
inference(superposition,[],[f15362,f7218]) ).
fof(f7218,plain,
( ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1))
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f7217]) ).
fof(f32435,plain,
( spl0_2505
| ~ spl0_804
| ~ spl0_1663 ),
inference(avatar_split_clause,[],[f16104,f15247,f7386,f32433]) ).
fof(f32433,plain,
( spl0_2505
<=> ! [X2,X0,X1,X3] : c_emptyset != c_union(X1,c_insert(X0,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f16104,plain,
( ! [X2,X3,X0,X1] : c_emptyset != c_union(X1,c_insert(X0,X2,X3),X3)
| ~ spl0_804
| ~ spl0_1663 ),
inference(superposition,[],[f7387,f15248]) ).
fof(f32431,plain,
( spl0_2504
| ~ spl0_775
| ~ spl0_776
| ~ spl0_1638 ),
inference(avatar_split_clause,[],[f15868,f15138,f7273,f7269,f32429]) ).
fof(f32429,plain,
( spl0_2504
<=> ! [X0,X1] : c_0 = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).
fof(f7269,plain,
( spl0_775
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f7273,plain,
( spl0_776
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f15138,plain,
( spl0_1638
<=> ! [X16,X59,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f15868,plain,
( ! [X0,X1] : c_0 = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat)
| ~ spl0_775
| ~ spl0_776
| ~ spl0_1638 ),
inference(forward_demodulation,[],[f15843,f7270]) ).
fof(f7270,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_775 ),
inference(avatar_component_clause,[],[f7269]) ).
fof(f15843,plain,
( ! [X0,X1] : c_minus(c_0,X1,tc_nat) = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat)
| ~ spl0_776
| ~ spl0_1638 ),
inference(superposition,[],[f15139,f7274]) ).
fof(f7274,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_776 ),
inference(avatar_component_clause,[],[f7273]) ).
fof(f15139,plain,
( ! [X59,X16,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat)
| ~ spl0_1638 ),
inference(avatar_component_clause,[],[f15138]) ).
fof(f32427,plain,
( spl0_2503
| ~ spl0_746
| ~ spl0_1630 ),
inference(avatar_split_clause,[],[f15757,f15106,f7152,f32425]) ).
fof(f32425,plain,
( spl0_2503
<=> ! [X0,X1] : c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).
fof(f7152,plain,
( spl0_746
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f15106,plain,
( spl0_1630
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f15757,plain,
( ! [X0,X1] : c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0
| ~ spl0_746
| ~ spl0_1630 ),
inference(trivial_inequality_removal,[],[f15745]) ).
fof(f15745,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 )
| ~ spl0_746
| ~ spl0_1630 ),
inference(superposition,[],[f15107,f7153]) ).
fof(f7153,plain,
( ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat)
| ~ spl0_746 ),
inference(avatar_component_clause,[],[f7152]) ).
fof(f15107,plain,
( ! [X21,X3,X1] :
( c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Orotate(X21,X3,X1) = X3 )
| ~ spl0_1630 ),
inference(avatar_component_clause,[],[f15106]) ).
fof(f32423,plain,
( spl0_2502
| ~ spl0_767
| ~ spl0_1627 ),
inference(avatar_split_clause,[],[f15688,f15093,f7237,f32421]) ).
fof(f32421,plain,
( spl0_2502
<=> ! [X2,X0,X1,X3] : ~ c_List_Onull(c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).
fof(f15688,plain,
( ! [X2,X3,X0,X1] : ~ c_List_Onull(c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_767
| ~ spl0_1627 ),
inference(superposition,[],[f7238,f15094]) ).
fof(f32419,plain,
( spl0_2501
| ~ spl0_764
| ~ spl0_1627 ),
inference(avatar_split_clause,[],[f15686,f15093,f7225,f32417]) ).
fof(f32417,plain,
( spl0_2501
<=> ! [X2,X0,X1,X3] : c_List_Olist_ONil != c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).
fof(f15686,plain,
( ! [X2,X3,X0,X1] : c_List_Olist_ONil != c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3)
| ~ spl0_764
| ~ spl0_1627 ),
inference(superposition,[],[f7226,f15094]) ).
fof(f32415,plain,
( spl0_2500
| ~ spl0_71
| ~ spl0_2369 ),
inference(avatar_split_clause,[],[f31280,f30709,f3602,f32413]) ).
fof(f32413,plain,
( spl0_2500
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f3602,plain,
( spl0_71
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f30709,plain,
( spl0_2369
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f31280,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_nat)
| ~ spl0_71
| ~ spl0_2369 ),
inference(resolution,[],[f30710,f3604]) ).
fof(f3604,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f3602]) ).
fof(f30710,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_2369 ),
inference(avatar_component_clause,[],[f30709]) ).
fof(f32411,plain,
( spl0_2499
| ~ spl0_852
| ~ spl0_1670 ),
inference(avatar_split_clause,[],[f15321,f15310,f7590,f32409]) ).
fof(f32409,plain,
( spl0_2499
<=> ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X0,tc_nat),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f15310,plain,
( spl0_1670
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f15321,plain,
( ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X0,tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_852
| ~ spl0_1670 ),
inference(superposition,[],[f7591,f15311]) ).
fof(f15311,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_1670 ),
inference(avatar_component_clause,[],[f15310]) ).
fof(f32407,plain,
( spl0_2498
| ~ spl0_1009
| ~ spl0_1596 ),
inference(avatar_split_clause,[],[f14925,f13932,f8424,f32405]) ).
fof(f32405,plain,
( spl0_2498
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Odrop(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f8424,plain,
( spl0_1009
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f13932,plain,
( spl0_1596
<=> ! [X21,X1,X3] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f14925,plain,
( ! [X2,X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Odrop(X1,X0,X2) )
| ~ spl0_1009
| ~ spl0_1596 ),
inference(superposition,[],[f8425,f13933]) ).
fof(f13933,plain,
( ! [X21,X3,X1] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3
| ~ spl0_1596 ),
inference(avatar_component_clause,[],[f13932]) ).
fof(f8425,plain,
( ! [X1,X25,X23] :
( c_List_Olist_ONil != c_append(X23,X25,X1)
| c_List_Olist_ONil = X25 )
| ~ spl0_1009 ),
inference(avatar_component_clause,[],[f8424]) ).
fof(f32402,plain,
( ~ spl0_2497
| spl0_659
| ~ spl0_816
| ~ spl0_1260
| ~ spl0_1513 ),
inference(avatar_split_clause,[],[f13593,f12335,f9886,f7434,f6760,f32399]) ).
fof(f32399,plain,
( spl0_2497
<=> c_less(c_0,c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f6760,plain,
( spl0_659
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f7434,plain,
( spl0_816
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f9886,plain,
( spl0_1260
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f12335,plain,
( spl0_1513
<=> ! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f13593,plain,
( c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat)
| ~ spl0_816
| ~ spl0_1260
| ~ spl0_1513 ),
inference(forward_demodulation,[],[f13590,f9888]) ).
fof(f9888,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1260 ),
inference(avatar_component_clause,[],[f9886]) ).
fof(f13590,plain,
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat)
| ~ spl0_816
| ~ spl0_1513 ),
inference(superposition,[],[f12336,f7436]) ).
fof(f7436,plain,
( c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7434]) ).
fof(f12336,plain,
( ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) )
| ~ spl0_1513 ),
inference(avatar_component_clause,[],[f12335]) ).
fof(f32397,plain,
( spl0_2496
| ~ spl0_1143
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f13150,f12080,f9169,f32395]) ).
fof(f32395,plain,
( spl0_2496
<=> ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f9169,plain,
( spl0_1143
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f12080,plain,
( spl0_1464
<=> ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f13150,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1143
| ~ spl0_1464 ),
inference(superposition,[],[f9170,f12081]) ).
fof(f12081,plain,
( ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48
| ~ spl0_1464 ),
inference(avatar_component_clause,[],[f12080]) ).
fof(f9170,plain,
( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f9169]) ).
fof(f32393,plain,
( spl0_2495
| ~ spl0_1144
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f13149,f12080,f9173,f32391]) ).
fof(f32391,plain,
( spl0_2495
<=> ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f9173,plain,
( spl0_1144
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f13149,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1144
| ~ spl0_1464 ),
inference(superposition,[],[f9174,f12081]) ).
fof(f9174,plain,
( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
| ~ spl0_1144 ),
inference(avatar_component_clause,[],[f9173]) ).
fof(f32388,plain,
( spl0_2494
| ~ spl0_662
| ~ spl0_798
| ~ spl0_1435 ),
inference(avatar_split_clause,[],[f12815,f11957,f7362,f6773,f32386]) ).
fof(f11957,plain,
( spl0_1435
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f12815,plain,
( ! [X0] :
( c_UNIV = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_662
| ~ spl0_798
| ~ spl0_1435 ),
inference(forward_demodulation,[],[f12803,f7363]) ).
fof(f12803,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_uminus(c_emptyset,tc_set(X0)) = c_HOL_Oabs(c_emptyset,tc_set(X0)) )
| ~ spl0_662
| ~ spl0_1435 ),
inference(resolution,[],[f11958,f6774]) ).
fof(f11958,plain,
( ! [X18,X1] :
( ~ c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) )
| ~ spl0_1435 ),
inference(avatar_component_clause,[],[f11957]) ).
fof(f32384,plain,
( spl0_2493
| ~ spl0_878
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f12633,f11920,f7694,f32382]) ).
fof(f32382,plain,
( spl0_2493
<=> ! [X2,X0,X1] : c_in(X0,c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).
fof(f11920,plain,
( spl0_1427
<=> ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f12633,plain,
( ! [X2,X0,X1] : c_in(X0,c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2),X2)
| ~ spl0_878
| ~ spl0_1427 ),
inference(superposition,[],[f7695,f11921]) ).
fof(f11921,plain,
( ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41)
| ~ spl0_1427 ),
inference(avatar_component_clause,[],[f11920]) ).
fof(f32380,plain,
( spl0_2492
| ~ spl0_646
| ~ spl0_1425 ),
inference(avatar_split_clause,[],[f12602,f11912,f5938,f32378]) ).
fof(f32378,plain,
( spl0_2492
<=> ! [X0,X1] : c_List_Onth(c_List_Oreplicate(c_1,X0,X1),c_0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f5938,plain,
( spl0_646
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f11912,plain,
( spl0_1425
<=> ! [X43,X3,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f12602,plain,
( ! [X0,X1] : c_List_Onth(c_List_Oreplicate(c_1,X0,X1),c_0,X1) = X0
| ~ spl0_646
| ~ spl0_1425 ),
inference(resolution,[],[f11913,f5940]) ).
fof(f5940,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f5938]) ).
fof(f11913,plain,
( ! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 )
| ~ spl0_1425 ),
inference(avatar_component_clause,[],[f11912]) ).
fof(f32376,plain,
( spl0_2491
| ~ spl0_846
| ~ spl0_1420 ),
inference(avatar_split_clause,[],[f12563,f11888,f7566,f32374]) ).
fof(f32374,plain,
( spl0_2491
<=> ! [X0,X1] :
( c_List_Oop_Amem(c_List_Ohd(X0,X1),X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f11888,plain,
( spl0_1420
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f12563,plain,
( ! [X0,X1] :
( c_List_Oop_Amem(c_List_Ohd(X0,X1),X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_846
| ~ spl0_1420 ),
inference(superposition,[],[f7567,f11889]) ).
fof(f11889,plain,
( ! [X3,X1] :
( c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3
| c_List_Olist_ONil = X3 )
| ~ spl0_1420 ),
inference(avatar_component_clause,[],[f11888]) ).
fof(f32372,plain,
( spl0_2490
| ~ spl0_87
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f11778,f10771,f10767,f10447,f6846,f5911,f3682,f32370]) ).
fof(f32370,plain,
( spl0_2490
<=> ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f10771,plain,
( spl0_1388
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f11778,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_87
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1388 ),
inference(forward_demodulation,[],[f11776,f11726]) ).
fof(f11776,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_87
| ~ spl0_1388 ),
inference(resolution,[],[f10772,f3684]) ).
fof(f10772,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) )
| ~ spl0_1388 ),
inference(avatar_component_clause,[],[f10771]) ).
fof(f32368,plain,
( spl0_2489
| ~ spl0_23
| ~ spl0_2369 ),
inference(avatar_split_clause,[],[f31279,f30709,f3362,f32366]) ).
fof(f32366,plain,
( spl0_2489
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f3362,plain,
( spl0_23
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f31279,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_2369 ),
inference(resolution,[],[f30710,f3364]) ).
fof(f3364,plain,
( class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3362]) ).
fof(f32364,plain,
( spl0_2488
| ~ spl0_53
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f11777,f10771,f10767,f10447,f6846,f5911,f3512,f32362]) ).
fof(f32362,plain,
( spl0_2488
<=> ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f11777,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1388 ),
inference(forward_demodulation,[],[f11775,f11726]) ).
fof(f11775,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1388 ),
inference(resolution,[],[f10772,f3514]) ).
fof(f32360,plain,
( spl0_2487
| ~ spl0_801
| ~ spl0_812
| ~ spl0_1384 ),
inference(avatar_split_clause,[],[f11670,f10755,f7418,f7374,f32358]) ).
fof(f32358,plain,
( spl0_2487
<=> ! [X0] : c_Message_Oanalz(X0) = c_Message_Oanalz(c_union(X0,c_Message_Oanalz(X0),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f7418,plain,
( spl0_812
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f10755,plain,
( spl0_1384
<=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f11670,plain,
( ! [X0] : c_Message_Oanalz(X0) = c_Message_Oanalz(c_union(X0,c_Message_Oanalz(X0),tc_Message_Omsg))
| ~ spl0_801
| ~ spl0_812
| ~ spl0_1384 ),
inference(forward_demodulation,[],[f11661,f7419]) ).
fof(f7419,plain,
( ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88))
| ~ spl0_812 ),
inference(avatar_component_clause,[],[f7418]) ).
fof(f11661,plain,
( ! [X0] : c_Message_Oanalz(c_Message_Oanalz(X0)) = c_Message_Oanalz(c_union(X0,c_Message_Oanalz(X0),tc_Message_Omsg))
| ~ spl0_801
| ~ spl0_1384 ),
inference(superposition,[],[f10756,f7375]) ).
fof(f10756,plain,
( ! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg))
| ~ spl0_1384 ),
inference(avatar_component_clause,[],[f10755]) ).
fof(f32355,plain,
( spl0_2486
| ~ spl0_797
| ~ spl0_1361 ),
inference(avatar_split_clause,[],[f11449,f10659,f7358,f32353]) ).
fof(f7358,plain,
( spl0_797
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f10659,plain,
( spl0_1361
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f11449,plain,
( ! [X0,X1] :
( c_emptyset != c_uminus(X1,tc_set(X0))
| c_UNIV = X1 )
| ~ spl0_797
| ~ spl0_1361 ),
inference(superposition,[],[f10660,f7359]) ).
fof(f7359,plain,
( ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1))
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7358]) ).
fof(f10660,plain,
( ! [X1,X12,X13] :
( c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1361 ),
inference(avatar_component_clause,[],[f10659]) ).
fof(f32350,plain,
( spl0_2485
| ~ spl0_798
| ~ spl0_1361 ),
inference(avatar_split_clause,[],[f11447,f10659,f7362,f32348]) ).
fof(f11447,plain,
( ! [X0,X1] :
( c_UNIV != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_798
| ~ spl0_1361 ),
inference(superposition,[],[f10660,f7363]) ).
fof(f32335,plain,
( spl0_2484
| ~ spl0_23
| ~ spl0_680
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11402,f10627,f6850,f3362,f32333]) ).
fof(f6850,plain,
( spl0_680
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f11402,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) )
| ~ spl0_680
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f6851]) ).
fof(f6851,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f6850]) ).
fof(f32312,plain,
( spl0_2483
| ~ spl0_23
| ~ spl0_680
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11337,f10591,f6850,f3362,f32310]) ).
fof(f11337,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) )
| ~ spl0_680
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f6851]) ).
fof(f32308,plain,
( spl0_2482
| ~ spl0_783
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f11091,f10459,f7301,f32306]) ).
fof(f32306,plain,
( spl0_2482
<=> ! [X0,X1] :
( c_plus(X1,X0,tc_nat) != X0
| c_0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).
fof(f10459,plain,
( spl0_1313
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f11091,plain,
( ! [X0,X1] :
( c_plus(X1,X0,tc_nat) != X0
| c_0 = X1 )
| ~ spl0_783
| ~ spl0_1313 ),
inference(superposition,[],[f10460,f7302]) ).
fof(f10460,plain,
( ! [X21,X16,X15] :
( c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat)
| X15 = X21 )
| ~ spl0_1313 ),
inference(avatar_component_clause,[],[f10459]) ).
fof(f32304,plain,
( spl0_2481
| ~ spl0_774
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f11090,f10459,f7265,f32302]) ).
fof(f32302,plain,
( spl0_2481
<=> ! [X0,X1] :
( c_plus(X1,c_0,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f11090,plain,
( ! [X0,X1] :
( c_plus(X1,c_0,tc_nat) != X0
| X0 = X1 )
| ~ spl0_774
| ~ spl0_1313 ),
inference(superposition,[],[f10460,f7266]) ).
fof(f32285,plain,
( spl0_2480
| ~ spl0_783
| ~ spl0_1312 ),
inference(avatar_split_clause,[],[f11084,f10455,f7301,f32283]) ).
fof(f32283,plain,
( spl0_2480
<=> ! [X0,X1] :
( c_plus(c_0,X1,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f10455,plain,
( spl0_1312
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f11084,plain,
( ! [X0,X1] :
( c_plus(c_0,X1,tc_nat) != X0
| X0 = X1 )
| ~ spl0_783
| ~ spl0_1312 ),
inference(superposition,[],[f10456,f7302]) ).
fof(f10456,plain,
( ! [X21,X16,X15] :
( c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat)
| X15 = X21 )
| ~ spl0_1312 ),
inference(avatar_component_clause,[],[f10455]) ).
fof(f32281,plain,
( spl0_2479
| ~ spl0_774
| ~ spl0_1312 ),
inference(avatar_split_clause,[],[f11083,f10455,f7265,f32279]) ).
fof(f32279,plain,
( spl0_2479
<=> ! [X0,X1] :
( c_plus(X0,X1,tc_nat) != X0
| c_0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f11083,plain,
( ! [X0,X1] :
( c_plus(X0,X1,tc_nat) != X0
| c_0 = X1 )
| ~ spl0_774
| ~ spl0_1312 ),
inference(superposition,[],[f10456,f7266]) ).
fof(f32277,plain,
( spl0_2478
| ~ spl0_817
| ~ spl0_1305 ),
inference(avatar_split_clause,[],[f11039,f10427,f7439,f32275]) ).
fof(f32275,plain,
( spl0_2478
<=> ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f10427,plain,
( spl0_1305
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f11039,plain,
( ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 )
| ~ spl0_817
| ~ spl0_1305 ),
inference(superposition,[],[f10428,f7440]) ).
fof(f10428,plain,
( ! [X51,X1,X25,X23] :
( c_append(X23,X25,X1) != c_append(X23,X51,X1)
| X25 = X51 )
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f10427]) ).
fof(f32273,plain,
( spl0_2477
| ~ spl0_771
| ~ spl0_1297 ),
inference(avatar_split_clause,[],[f11018,f10395,f7253,f32271]) ).
fof(f32271,plain,
( spl0_2477
<=> ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f7253,plain,
( spl0_771
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f10395,plain,
( spl0_1297
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f11018,plain,
( ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 )
| ~ spl0_771
| ~ spl0_1297 ),
inference(superposition,[],[f10396,f7254]) ).
fof(f7254,plain,
( ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23
| ~ spl0_771 ),
inference(avatar_component_clause,[],[f7253]) ).
fof(f10396,plain,
( ! [X51,X1,X25,X23] :
( c_append(X25,X23,X1) != c_append(X51,X23,X1)
| X25 = X51 )
| ~ spl0_1297 ),
inference(avatar_component_clause,[],[f10395]) ).
fof(f32269,plain,
( spl0_2476
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1259 ),
inference(avatar_split_clause,[],[f10255,f9880,f8526,f3507,f32266]) ).
fof(f32266,plain,
( spl0_2476
<=> c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).
fof(f9880,plain,
( spl0_1259
<=> ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f10255,plain,
( c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1259 ),
inference(forward_demodulation,[],[f10254,f8847]) ).
fof(f10254,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1259 ),
inference(resolution,[],[f9881,f3509]) ).
fof(f9881,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1) )
| ~ spl0_1259 ),
inference(avatar_component_clause,[],[f9880]) ).
fof(f32264,plain,
( spl0_2475
| ~ spl0_855
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10241,f9829,f7602,f32262]) ).
fof(f32262,plain,
( spl0_2475
<=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_Nat_Osize(X0,tc_Message_Omsg),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f9829,plain,
( spl0_1254
<=> ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f10241,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_Nat_Osize(X0,tc_Message_Omsg),tc_nat)
| ~ spl0_855
| ~ spl0_1254 ),
inference(superposition,[],[f7603,f9830]) ).
fof(f9830,plain,
( ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_1254 ),
inference(avatar_component_clause,[],[f9829]) ).
fof(f32256,plain,
( spl0_100
| spl0_2474
| ~ spl0_1033
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10238,f9829,f8522,f32254,f3744]) ).
fof(f32254,plain,
( spl0_2474
<=> ! [X0] : c_0 != c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f10238,plain,
( ! [X0] :
( c_0 != c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg)
| c_0 = c_1 )
| ~ spl0_1033
| ~ spl0_1254 ),
inference(superposition,[],[f8523,f9830]) ).
fof(f32252,plain,
( spl0_2473
| ~ spl0_785
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1251 ),
inference(avatar_split_clause,[],[f10216,f9817,f8538,f7711,f7434,f7309,f32249]) ).
fof(f32249,plain,
( spl0_2473
<=> c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f7711,plain,
( spl0_882
<=> c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f9817,plain,
( spl0_1251
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f10216,plain,
( c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_785
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1251 ),
inference(forward_demodulation,[],[f10215,f7311]) ).
fof(f10215,plain,
( c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1251 ),
inference(forward_demodulation,[],[f10214,f8539]) ).
fof(f10214,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1251 ),
inference(forward_demodulation,[],[f10209,f7713]) ).
fof(f7713,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_882 ),
inference(avatar_component_clause,[],[f7711]) ).
fof(f10209,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0))
| ~ spl0_816
| ~ spl0_1251 ),
inference(superposition,[],[f9818,f7436]) ).
fof(f9818,plain,
( ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0)
| ~ spl0_1251 ),
inference(avatar_component_clause,[],[f9817]) ).
fof(f32247,plain,
( spl0_2472
| ~ spl0_71
| ~ spl0_1233 ),
inference(avatar_split_clause,[],[f10175,f9740,f3602,f32245]) ).
fof(f9740,plain,
( spl0_1233
<=> ! [X18,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f10175,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_71
| ~ spl0_1233 ),
inference(resolution,[],[f9741,f3604]) ).
fof(f9741,plain,
( ! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) )
| ~ spl0_1233 ),
inference(avatar_component_clause,[],[f9740]) ).
fof(f32240,plain,
( spl0_2471
| ~ spl0_23
| ~ spl0_1233 ),
inference(avatar_split_clause,[],[f10174,f9740,f3362,f32238]) ).
fof(f10174,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_1233 ),
inference(resolution,[],[f9741,f3364]) ).
fof(f32235,plain,
( spl0_2470
| ~ spl0_727
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f10143,f9724,f7061,f32233]) ).
fof(f32233,plain,
( spl0_2470
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).
fof(f9724,plain,
( spl0_1229
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f10143,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) )
| ~ spl0_727
| ~ spl0_1229 ),
inference(resolution,[],[f9725,f7062]) ).
fof(f9725,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 )
| ~ spl0_1229 ),
inference(avatar_component_clause,[],[f9724]) ).
fof(f32231,plain,
( spl0_2469
| ~ spl0_796
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f10136,f9724,f7354,f32229]) ).
fof(f32229,plain,
( spl0_2469
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).
fof(f10136,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_796
| ~ spl0_1229 ),
inference(resolution,[],[f9725,f7355]) ).
fof(f32220,plain,
( spl0_2468
| ~ spl0_40
| ~ spl0_680
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f10134,f9724,f6850,f3447,f32218]) ).
fof(f32218,plain,
( spl0_2468
<=> ! [X0] : c_IntDef_Oint(X0) = c_OrderedGroup_Opprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).
fof(f3447,plain,
( spl0_40
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f10134,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_IntDef_Oint(X0) = c_OrderedGroup_Opprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_680
| ~ spl0_1229 ),
inference(resolution,[],[f9725,f6851]) ).
fof(f32216,plain,
( spl0_2467
| ~ spl0_947
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f10127,f9720,f8046,f32214]) ).
fof(f32214,plain,
( spl0_2467
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f8046,plain,
( spl0_947
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f9720,plain,
( spl0_1228
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f10127,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) )
| ~ spl0_947
| ~ spl0_1228 ),
inference(duplicate_literal_removal,[],[f10126]) ).
fof(f10126,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) )
| ~ spl0_947
| ~ spl0_1228 ),
inference(resolution,[],[f9721,f8047]) ).
fof(f8047,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f8046]) ).
fof(f9721,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) )
| ~ spl0_1228 ),
inference(avatar_component_clause,[],[f9720]) ).
fof(f32212,plain,
( spl0_2466
| ~ spl0_662
| ~ spl0_1228 ),
inference(avatar_split_clause,[],[f10121,f9720,f6773,f32210]) ).
fof(f32210,plain,
( spl0_2466
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).
fof(f10121,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) )
| ~ spl0_662
| ~ spl0_1228 ),
inference(resolution,[],[f9721,f6774]) ).
fof(f32208,plain,
( spl0_2465
| ~ spl0_662
| ~ spl0_1227 ),
inference(avatar_split_clause,[],[f10104,f9716,f6773,f32206]) ).
fof(f32206,plain,
( spl0_2465
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).
fof(f9716,plain,
( spl0_1227
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f10104,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) )
| ~ spl0_662
| ~ spl0_1227 ),
inference(resolution,[],[f9717,f6774]) ).
fof(f9717,plain,
( ! [X3,X1] :
( ~ c_lessequals(X3,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 )
| ~ spl0_1227 ),
inference(avatar_component_clause,[],[f9716]) ).
fof(f32204,plain,
( spl0_2464
| ~ spl0_948
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f10095,f9712,f8050,f32202]) ).
fof(f32202,plain,
( spl0_2464
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).
fof(f8050,plain,
( spl0_948
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f9712,plain,
( spl0_1226
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f10095,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) )
| ~ spl0_948
| ~ spl0_1226 ),
inference(duplicate_literal_removal,[],[f10089]) ).
fof(f10089,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) )
| ~ spl0_948
| ~ spl0_1226 ),
inference(resolution,[],[f9713,f8051]) ).
fof(f8051,plain,
( ! [X18,X1] :
( c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_948 ),
inference(avatar_component_clause,[],[f8050]) ).
fof(f9713,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_0,X0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) )
| ~ spl0_1226 ),
inference(avatar_component_clause,[],[f9712]) ).
fof(f32199,plain,
( spl0_2463
| ~ spl0_727
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f10092,f9712,f7061,f32197]) ).
fof(f32197,plain,
( spl0_2463
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).
fof(f10092,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) )
| ~ spl0_727
| ~ spl0_1226 ),
inference(resolution,[],[f9713,f7062]) ).
fof(f32192,plain,
( spl0_2462
| ~ spl0_796
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f10085,f9712,f7354,f32190]) ).
fof(f32190,plain,
( spl0_2462
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).
fof(f10085,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_796
| ~ spl0_1226 ),
inference(resolution,[],[f9713,f7355]) ).
fof(f32188,plain,
( spl0_2458
| spl0_2461
| ~ spl0_875
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f10076,f9704,f7682,f32186,f32175]) ).
fof(f32175,plain,
( spl0_2458
<=> ! [X1] : ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(f32186,plain,
( spl0_2461
<=> ! [X0] :
( c_0 != X0
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f7682,plain,
( spl0_875
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f9704,plain,
( spl0_1224
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f10076,plain,
( ! [X0,X1] :
( c_0 != X0
| c_emptyset = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_875
| ~ spl0_1224 ),
inference(superposition,[],[f9705,f7683]) ).
fof(f7683,plain,
( ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f7682]) ).
fof(f9705,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1224 ),
inference(avatar_component_clause,[],[f9704]) ).
fof(f32184,plain,
( spl0_2458
| spl0_2459
| ~ spl0_2460
| ~ spl0_873
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f10074,f9704,f7674,f32181,f32178,f32175]) ).
fof(f32178,plain,
( spl0_2459
<=> ! [X0] : c_UNIV = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(f32181,plain,
( spl0_2460
<=> c_0 = c_emptyset ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(f7674,plain,
( spl0_873
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f10074,plain,
( ! [X0,X1] :
( c_0 != c_emptyset
| c_UNIV = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_873
| ~ spl0_1224 ),
inference(superposition,[],[f9705,f7675]) ).
fof(f7675,plain,
( ! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1))
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f7674]) ).
fof(f32172,plain,
( spl0_2457
| ~ spl0_727
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f10067,f9700,f7061,f32170]) ).
fof(f32170,plain,
( spl0_2457
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).
fof(f9700,plain,
( spl0_1223
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f10067,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) )
| ~ spl0_727
| ~ spl0_1223 ),
inference(resolution,[],[f9701,f7062]) ).
fof(f9701,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1223 ),
inference(avatar_component_clause,[],[f9700]) ).
fof(f32168,plain,
( spl0_2456
| ~ spl0_796
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f10060,f9700,f7354,f32166]) ).
fof(f32166,plain,
( spl0_2456
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_1 = c_HOL_Oabs(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).
fof(f10060,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_1 = c_HOL_Oabs(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_796
| ~ spl0_1223 ),
inference(resolution,[],[f9701,f7355]) ).
fof(f32164,plain,
( spl0_2455
| ~ spl0_43
| ~ spl0_1222 ),
inference(avatar_split_clause,[],[f10053,f9696,f3462,f32162]) ).
fof(f32162,plain,
( spl0_2455
<=> ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).
fof(f3462,plain,
( spl0_43
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f9696,plain,
( spl0_1222
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f10053,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_43
| ~ spl0_1222 ),
inference(resolution,[],[f9697,f3464]) ).
fof(f3464,plain,
( class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f3462]) ).
fof(f9697,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) )
| ~ spl0_1222 ),
inference(avatar_component_clause,[],[f9696]) ).
fof(f32160,plain,
( spl0_2454
| ~ spl0_43
| ~ spl0_1220 ),
inference(avatar_split_clause,[],[f10047,f9688,f3462,f32158]) ).
fof(f32158,plain,
( spl0_2454
<=> ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).
fof(f9688,plain,
( spl0_1220
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f10047,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_43
| ~ spl0_1220 ),
inference(resolution,[],[f9689,f3464]) ).
fof(f9689,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) )
| ~ spl0_1220 ),
inference(avatar_component_clause,[],[f9688]) ).
fof(f32156,plain,
( spl0_2453
| ~ spl0_785
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1218 ),
inference(avatar_split_clause,[],[f10038,f9680,f8538,f7711,f7434,f7309,f32153]) ).
fof(f32153,plain,
( spl0_2453
<=> c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).
fof(f9680,plain,
( spl0_1218
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f10038,plain,
( c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_785
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f10037,f7311]) ).
fof(f10037,plain,
( c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1037
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f10036,f8539]) ).
fof(f10036,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_816
| ~ spl0_882
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f10031,f7713]) ).
fof(f10031,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OMin)
| ~ spl0_816
| ~ spl0_1218 ),
inference(superposition,[],[f9681,f7436]) ).
fof(f9681,plain,
( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0)
| ~ spl0_1218 ),
inference(avatar_component_clause,[],[f9680]) ).
fof(f32151,plain,
( spl0_2452
| ~ spl0_1161
| ~ spl0_2404 ),
inference(avatar_split_clause,[],[f31882,f30912,f9243,f32149]) ).
fof(f32149,plain,
( spl0_2452
<=> ! [X0] : c_Main_Ozmod__eq__0D__dest__1(c_1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).
fof(f9243,plain,
( spl0_1161
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f30912,plain,
( spl0_2404
<=> ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).
fof(f31882,plain,
( ! [X0] : c_Main_Ozmod__eq__0D__dest__1(c_1,X0) = X0
| ~ spl0_1161
| ~ spl0_2404 ),
inference(superposition,[],[f30913,f9244]) ).
fof(f9244,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f9243]) ).
fof(f30913,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_2404 ),
inference(avatar_component_clause,[],[f30912]) ).
fof(f32147,plain,
( spl0_2451
| ~ spl0_22
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f9896,f9564,f3357,f32145]) ).
fof(f32145,plain,
( spl0_2451
<=> ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2451])]) ).
fof(f3357,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f9564,plain,
( spl0_1189
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f9896,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_1189 ),
inference(resolution,[],[f9565,f3359]) ).
fof(f3359,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f3357]) ).
fof(f9565,plain,
( ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9564]) ).
fof(f32128,plain,
( ~ spl0_50
| spl0_2450
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9878,f9535,f8526,f3507,f32125,f3497]) ).
fof(f32125,plain,
( spl0_2450
<=> c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).
fof(f9535,plain,
( spl0_1182
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f9878,plain,
( c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1182 ),
inference(forward_demodulation,[],[f9877,f8847]) ).
fof(f9877,plain,
( ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1182 ),
inference(resolution,[],[f9536,f3509]) ).
fof(f9536,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f9535]) ).
fof(f32122,plain,
( ~ spl0_2449
| ~ spl0_640
| ~ spl0_1250 ),
inference(avatar_split_clause,[],[f9813,f9809,f5911,f32119]) ).
fof(f9813,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1250 ),
inference(superposition,[],[f9810,f5913]) ).
fof(f32117,plain,
( spl0_2448
| ~ spl0_1050
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9490,f9225,f8590,f32115]) ).
fof(f32115,plain,
( spl0_2448
<=> ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oparts(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f8590,plain,
( spl0_1050
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f9225,plain,
( spl0_1157
<=> ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f9490,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oparts(X0) )
| ~ spl0_1050
| ~ spl0_1157 ),
inference(superposition,[],[f8591,f9226]) ).
fof(f9226,plain,
( ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9225]) ).
fof(f8591,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X12 )
| ~ spl0_1050 ),
inference(avatar_component_clause,[],[f8590]) ).
fof(f32113,plain,
( spl0_2447
| ~ spl0_1051
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9489,f9225,f8594,f32111]) ).
fof(f32111,plain,
( spl0_2447
<=> ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).
fof(f8594,plain,
( spl0_1051
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f9489,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) )
| ~ spl0_1051
| ~ spl0_1157 ),
inference(superposition,[],[f8595,f9226]) ).
fof(f8595,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X13 )
| ~ spl0_1051 ),
inference(avatar_component_clause,[],[f8594]) ).
fof(f32109,plain,
( spl0_2446
| ~ spl0_857
| ~ spl0_1141 ),
inference(avatar_split_clause,[],[f9467,f9161,f7610,f32107]) ).
fof(f32107,plain,
( spl0_2446
<=> ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).
fof(f9161,plain,
( spl0_1141
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f9467,plain,
( ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) )
| ~ spl0_857
| ~ spl0_1141 ),
inference(resolution,[],[f9162,f7611]) ).
fof(f9162,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat)
| c_0 = X21 )
| ~ spl0_1141 ),
inference(avatar_component_clause,[],[f9161]) ).
fof(f32105,plain,
( spl0_2445
| ~ spl0_852
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f9438,f9117,f7590,f32103]) ).
fof(f32103,plain,
( spl0_2445
<=> ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f9117,plain,
( spl0_1130
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f9438,plain,
( ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_852
| ~ spl0_1130 ),
inference(resolution,[],[f9118,f7591]) ).
fof(f9118,plain,
( ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) )
| ~ spl0_1130 ),
inference(avatar_component_clause,[],[f9117]) ).
fof(f32101,plain,
( spl0_2444
| ~ spl0_832
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f9437,f9117,f7510,f32099]) ).
fof(f32099,plain,
( spl0_2444
<=> ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).
fof(f7510,plain,
( spl0_832
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f9437,plain,
( ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_832
| ~ spl0_1130 ),
inference(resolution,[],[f9118,f7511]) ).
fof(f7511,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_832 ),
inference(avatar_component_clause,[],[f7510]) ).
fof(f32096,plain,
( spl0_2443
| ~ spl0_825
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9394,f9057,f7482,f32094]) ).
fof(f9057,plain,
( spl0_1115
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f9394,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_825
| ~ spl0_1115 ),
inference(resolution,[],[f9058,f7483]) ).
fof(f9058,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f9057]) ).
fof(f32092,plain,
( spl0_2442
| ~ spl0_1172
| ~ spl0_2401 ),
inference(avatar_split_clause,[],[f31655,f30900,f9420,f32090]) ).
fof(f32090,plain,
( spl0_2442
<=> ! [X0] : c_Main_Omod__eq__0D__dest__1(c_1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2442])]) ).
fof(f9420,plain,
( spl0_1172
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f30900,plain,
( spl0_2401
<=> ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).
fof(f31655,plain,
( ! [X0] : c_Main_Omod__eq__0D__dest__1(c_1,X0) = X0
| ~ spl0_1172
| ~ spl0_2401 ),
inference(superposition,[],[f30901,f9421]) ).
fof(f9421,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_1172 ),
inference(avatar_component_clause,[],[f9420]) ).
fof(f30901,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_2401 ),
inference(avatar_component_clause,[],[f30900]) ).
fof(f32087,plain,
( spl0_2441
| ~ spl0_824
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9393,f9057,f7478,f32085]) ).
fof(f9393,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_824
| ~ spl0_1115 ),
inference(resolution,[],[f9058,f7479]) ).
fof(f32083,plain,
( spl0_2440
| ~ spl0_843
| ~ spl0_1113 ),
inference(avatar_split_clause,[],[f9384,f9048,f7554,f32081]) ).
fof(f32081,plain,
( spl0_2440
<=> ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2440])]) ).
fof(f7554,plain,
( spl0_843
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f9048,plain,
( spl0_1113
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f9384,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_843
| ~ spl0_1113 ),
inference(resolution,[],[f9049,f7555]) ).
fof(f7555,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7554]) ).
fof(f9049,plain,
( ! [X48,X11] :
( c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1113 ),
inference(avatar_component_clause,[],[f9048]) ).
fof(f32079,plain,
( spl0_2439
| ~ spl0_655
| ~ spl0_1111 ),
inference(avatar_split_clause,[],[f9379,f9040,f5979,f32077]) ).
fof(f32077,plain,
( spl0_2439
<=> ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2439])]) ).
fof(f5979,plain,
( spl0_655
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f9379,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) )
| ~ spl0_655
| ~ spl0_1111 ),
inference(superposition,[],[f9041,f5981]) ).
fof(f5981,plain,
( c_1 = c_IntDef_Onat(c_1)
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f5979]) ).
fof(f32075,plain,
( spl0_2438
| ~ spl0_679
| ~ spl0_1110 ),
inference(avatar_split_clause,[],[f9362,f9036,f6846,f32073]) ).
fof(f32073,plain,
( spl0_2438
<=> ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2438])]) ).
fof(f9036,plain,
( spl0_1110
<=> ! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f9362,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) )
| ~ spl0_679
| ~ spl0_1110 ),
inference(superposition,[],[f9037,f6847]) ).
fof(f9037,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1110 ),
inference(avatar_component_clause,[],[f9036]) ).
fof(f32071,plain,
( spl0_2437
| ~ spl0_640
| ~ spl0_1109 ),
inference(avatar_split_clause,[],[f9359,f9032,f5911,f32069]) ).
fof(f32069,plain,
( spl0_2437
<=> ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2437])]) ).
fof(f9032,plain,
( spl0_1109
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f9359,plain,
( ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) )
| ~ spl0_640
| ~ spl0_1109 ),
inference(superposition,[],[f9033,f5913]) ).
fof(f9033,plain,
( ! [X21,X15] :
( c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_less(X15,X21,tc_nat) )
| ~ spl0_1109 ),
inference(avatar_component_clause,[],[f9032]) ).
fof(f32067,plain,
( spl0_2436
| ~ spl0_640
| ~ spl0_1108 ),
inference(avatar_split_clause,[],[f9353,f9028,f5911,f32065]) ).
fof(f32065,plain,
( spl0_2436
<=> ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f9028,plain,
( spl0_1108
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f9353,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) )
| ~ spl0_640
| ~ spl0_1108 ),
inference(superposition,[],[f9029,f5913]) ).
fof(f9029,plain,
( ! [X21,X15] :
( ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| c_less(X15,X21,tc_nat) )
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f9028]) ).
fof(f32063,plain,
( spl0_2435
| ~ spl0_641
| ~ spl0_1106 ),
inference(avatar_split_clause,[],[f9350,f9019,f5916,f32061]) ).
fof(f32061,plain,
( spl0_2435
<=> ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2435])]) ).
fof(f9019,plain,
( spl0_1106
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f9350,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_641
| ~ spl0_1106 ),
inference(superposition,[],[f9020,f5918]) ).
fof(f9020,plain,
( ! [X21,X15] :
( c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1106 ),
inference(avatar_component_clause,[],[f9019]) ).
fof(f32059,plain,
( spl0_2434
| ~ spl0_640
| ~ spl0_1106 ),
inference(avatar_split_clause,[],[f9349,f9019,f5911,f32057]) ).
fof(f32057,plain,
( spl0_2434
<=> ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2434])]) ).
fof(f9349,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_640
| ~ spl0_1106 ),
inference(superposition,[],[f9020,f5913]) ).
fof(f32055,plain,
( spl0_2433
| ~ spl0_640
| ~ spl0_1106 ),
inference(avatar_split_clause,[],[f9347,f9019,f5911,f32053]) ).
fof(f32053,plain,
( spl0_2433
<=> ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2433])]) ).
fof(f9347,plain,
( ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_640
| ~ spl0_1106 ),
inference(superposition,[],[f9020,f5913]) ).
fof(f32051,plain,
( spl0_2432
| ~ spl0_641
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f9345,f9015,f5916,f32049]) ).
fof(f32049,plain,
( spl0_2432
<=> ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2432])]) ).
fof(f9015,plain,
( spl0_1105
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f9345,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_641
| ~ spl0_1105 ),
inference(superposition,[],[f9016,f5918]) ).
fof(f9016,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f9015]) ).
fof(f32047,plain,
( spl0_2431
| ~ spl0_640
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f9344,f9015,f5911,f32045]) ).
fof(f32045,plain,
( spl0_2431
<=> ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f9344,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_640
| ~ spl0_1105 ),
inference(superposition,[],[f9016,f5913]) ).
fof(f32043,plain,
( spl0_2430
| ~ spl0_640
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f9342,f9015,f5911,f32041]) ).
fof(f32041,plain,
( spl0_2430
<=> ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2430])]) ).
fof(f9342,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_640
| ~ spl0_1105 ),
inference(superposition,[],[f9016,f5913]) ).
fof(f32038,plain,
( spl0_100
| spl0_2429
| ~ spl0_640
| ~ spl0_1101 ),
inference(avatar_split_clause,[],[f9328,f8999,f5911,f32036,f3744]) ).
fof(f32036,plain,
( spl0_2429
<=> ! [X0] : c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).
fof(f8999,plain,
( spl0_1101
<=> ! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f9328,plain,
( ! [X0] :
( c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0)
| c_0 = c_1 )
| ~ spl0_640
| ~ spl0_1101 ),
inference(superposition,[],[f9000,f5913]) ).
fof(f9000,plain,
( ! [X21,X15] :
( c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15)
| c_0 = X21 )
| ~ spl0_1101 ),
inference(avatar_component_clause,[],[f8999]) ).
fof(f32034,plain,
( spl0_2428
| ~ spl0_857
| ~ spl0_1095 ),
inference(avatar_split_clause,[],[f9310,f8975,f7610,f32032]) ).
fof(f32032,plain,
( spl0_2428
<=> ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).
fof(f8975,plain,
( spl0_1095
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f9310,plain,
( ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 )
| ~ spl0_857
| ~ spl0_1095 ),
inference(resolution,[],[f8976,f7611]) ).
fof(f8976,plain,
( ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) )
| ~ spl0_1095 ),
inference(avatar_component_clause,[],[f8975]) ).
fof(f32030,plain,
( spl0_2427
| ~ spl0_906
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f9289,f8934,f7880,f32028]) ).
fof(f32028,plain,
( spl0_2427
<=> ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2427])]) ).
fof(f7880,plain,
( spl0_906
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f9289,plain,
( ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_906
| ~ spl0_1085 ),
inference(superposition,[],[f7881,f8935]) ).
fof(f7881,plain,
( ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1))
| ~ spl0_906 ),
inference(avatar_component_clause,[],[f7880]) ).
fof(f32026,plain,
( spl0_2426
| ~ spl0_967
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f9286,f8930,f8127,f32024]) ).
fof(f32024,plain,
( spl0_2426
<=> ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2426])]) ).
fof(f9286,plain,
( ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_967
| ~ spl0_1084 ),
inference(superposition,[],[f8931,f8129]) ).
fof(f32022,plain,
( spl0_2425
| ~ spl0_679
| ~ spl0_1075 ),
inference(avatar_split_clause,[],[f8917,f8690,f6846,f32020]) ).
fof(f32020,plain,
( spl0_2425
<=> ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2425])]) ).
fof(f8690,plain,
( spl0_1075
<=> ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f8917,plain,
( ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_679
| ~ spl0_1075 ),
inference(superposition,[],[f8691,f6847]) ).
fof(f8691,plain,
( ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f8690]) ).
fof(f32018,plain,
( spl0_2424
| ~ spl0_679
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f8911,f8686,f6846,f32016]) ).
fof(f32016,plain,
( spl0_2424
<=> ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f8686,plain,
( spl0_1074
<=> ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f8911,plain,
( ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_679
| ~ spl0_1074 ),
inference(superposition,[],[f8687,f6847]) ).
fof(f8687,plain,
( ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f8686]) ).
fof(f32014,plain,
( spl0_2423
| ~ spl0_883
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f8903,f8674,f7716,f32012]) ).
fof(f32012,plain,
( spl0_2423
<=> ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X0,c_Numeral_Obit_OB1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).
fof(f32010,plain,
( spl0_2422
| ~ spl0_1020
| ~ spl0_1021 ),
inference(avatar_split_clause,[],[f8811,f8473,f8469,f32008]) ).
fof(f32008,plain,
( spl0_2422
<=> ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).
fof(f8469,plain,
( spl0_1020
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f8811,plain,
( ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_1020
| ~ spl0_1021 ),
inference(superposition,[],[f8470,f8474]) ).
fof(f8470,plain,
( ! [X1,X23] :
( c_0 != c_Nat_Osize(X23,tc_List_Olist(X1))
| c_List_Olist_ONil = X23 )
| ~ spl0_1020 ),
inference(avatar_component_clause,[],[f8469]) ).
fof(f32006,plain,
( spl0_2421
| ~ spl0_838
| ~ spl0_996 ),
inference(avatar_split_clause,[],[f8728,f8372,f7534,f32004]) ).
fof(f32004,plain,
( spl0_2421
<=> ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).
fof(f7534,plain,
( spl0_838
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f8372,plain,
( spl0_996
<=> ! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f8728,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(X0) )
| ~ spl0_838
| ~ spl0_996 ),
inference(superposition,[],[f8373,f7535]) ).
fof(f7535,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f7534]) ).
fof(f8373,plain,
( ! [X48] :
( ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| c_0 = X48 )
| ~ spl0_996 ),
inference(avatar_component_clause,[],[f8372]) ).
fof(f31911,plain,
( ~ spl0_2420
| ~ spl0_1695
| ~ spl0_2249
| ~ spl0_2391 ),
inference(avatar_split_clause,[],[f31527,f30858,f28501,f16461,f31908]) ).
fof(f31908,plain,
( spl0_2420
<=> c_emptyset = c_Message_Oparts(c_IntDef_ONats) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).
fof(f16461,plain,
( spl0_1695
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f30858,plain,
( spl0_2391
<=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).
fof(f31527,plain,
( c_emptyset != c_Message_Oparts(c_IntDef_ONats)
| ~ spl0_1695
| ~ spl0_2249
| ~ spl0_2391 ),
inference(forward_demodulation,[],[f31522,f28503]) ).
fof(f31522,plain,
( c_emptyset != c_Message_Oparts(c_UNIV)
| ~ spl0_1695
| ~ spl0_2391 ),
inference(superposition,[],[f30859,f16462]) ).
fof(f16462,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_1695 ),
inference(avatar_component_clause,[],[f16461]) ).
fof(f30859,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_2391 ),
inference(avatar_component_clause,[],[f30858]) ).
fof(f31571,plain,
( spl0_2419
| ~ spl0_2249
| ~ spl0_2399 ),
inference(avatar_split_clause,[],[f30894,f30891,f28501,f31569]) ).
fof(f30891,plain,
( spl0_2399
<=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).
fof(f30894,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0)
| ~ spl0_2249
| ~ spl0_2399 ),
inference(forward_demodulation,[],[f30892,f28503]) ).
fof(f30892,plain,
( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_2399 ),
inference(avatar_component_clause,[],[f30891]) ).
fof(f31567,plain,
( spl0_2418
| ~ spl0_2249
| ~ spl0_2398 ),
inference(avatar_split_clause,[],[f30889,f30886,f28501,f31565]) ).
fof(f30886,plain,
( spl0_2398
<=> ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).
fof(f30889,plain,
( ! [X0] : c_IntDef_ONats = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_IntDef_ONats,X0),X0,X0)
| ~ spl0_2249
| ~ spl0_2398 ),
inference(forward_demodulation,[],[f30887,f28503]) ).
fof(f30887,plain,
( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_2398 ),
inference(avatar_component_clause,[],[f30886]) ).
fof(f31540,plain,
( ~ spl0_2417
| ~ spl0_1695
| ~ spl0_2249
| ~ spl0_2387 ),
inference(avatar_split_clause,[],[f31495,f30842,f28501,f16461,f31537]) ).
fof(f31537,plain,
( spl0_2417
<=> c_emptyset = c_Message_Oanalz(c_IntDef_ONats) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).
fof(f30842,plain,
( spl0_2387
<=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).
fof(f31495,plain,
( c_emptyset != c_Message_Oanalz(c_IntDef_ONats)
| ~ spl0_1695
| ~ spl0_2249
| ~ spl0_2387 ),
inference(forward_demodulation,[],[f31490,f28503]) ).
fof(f31490,plain,
( c_emptyset != c_Message_Oanalz(c_UNIV)
| ~ spl0_1695
| ~ spl0_2387 ),
inference(superposition,[],[f30843,f16462]) ).
fof(f30843,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_2387 ),
inference(avatar_component_clause,[],[f30842]) ).
fof(f31362,plain,
( spl0_2416
| ~ spl0_71
| ~ spl0_2367 ),
inference(avatar_split_clause,[],[f31273,f30695,f3602,f31360]) ).
fof(f31360,plain,
( spl0_2416
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f30695,plain,
( spl0_2367
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2367])]) ).
fof(f31273,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_nat)
| ~ spl0_71
| ~ spl0_2367 ),
inference(resolution,[],[f30696,f3604]) ).
fof(f30696,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_2367 ),
inference(avatar_component_clause,[],[f30695]) ).
fof(f31278,plain,
( spl0_2415
| ~ spl0_23
| ~ spl0_2367 ),
inference(avatar_split_clause,[],[f31272,f30695,f3362,f31276]) ).
fof(f31276,plain,
( spl0_2415
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).
fof(f31272,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_2367 ),
inference(resolution,[],[f30696,f3364]) ).
fof(f31102,plain,
( spl0_2414
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2352 ),
inference(avatar_split_clause,[],[f30572,f30568,f18552,f9544,f3292,f31099]) ).
fof(f31099,plain,
( spl0_2414
<=> c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f30568,plain,
( spl0_2352
<=> c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2352])]) ).
fof(f30572,plain,
( c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1184
| ~ spl0_1825
| ~ spl0_2352 ),
inference(forward_demodulation,[],[f30570,f19334]) ).
fof(f30570,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2352 ),
inference(avatar_component_clause,[],[f30568]) ).
fof(f31097,plain,
( spl0_2413
| ~ spl0_797
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28618,f28501,f7358,f31095]) ).
fof(f31095,plain,
( spl0_2413
<=> ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).
fof(f28618,plain,
( ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0))
| ~ spl0_797
| ~ spl0_2249 ),
inference(superposition,[],[f7359,f28503]) ).
fof(f31008,plain,
( spl0_2412
| ~ spl0_649
| ~ spl0_2114 ),
inference(avatar_split_clause,[],[f25278,f25008,f5952,f31006]) ).
fof(f31006,plain,
( spl0_2412
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).
fof(f25008,plain,
( spl0_2114
<=> ! [X12,X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f25278,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
| ~ spl0_649
| ~ spl0_2114 ),
inference(resolution,[],[f25009,f5953]) ).
fof(f25009,plain,
( ! [X2,X1,X27,X5,X12] :
( c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1) )
| ~ spl0_2114 ),
inference(avatar_component_clause,[],[f25008]) ).
fof(f30983,plain,
( ~ spl0_23
| ~ spl0_50
| ~ spl0_2406 ),
inference(avatar_split_clause,[],[f30966,f30920,f3497,f3362]) ).
fof(f30920,plain,
( spl0_2406
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).
fof(f30966,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_2406 ),
inference(resolution,[],[f30921,f3499]) ).
fof(f3499,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f3497]) ).
fof(f30921,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_2406 ),
inference(avatar_component_clause,[],[f30920]) ).
fof(f30982,plain,
( spl0_2411
| ~ spl0_916
| ~ spl0_1786
| ~ spl0_1901 ),
inference(avatar_split_clause,[],[f20506,f20008,f17345,f7921,f30980]) ).
fof(f30980,plain,
( spl0_2411
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2411])]) ).
fof(f7921,plain,
( spl0_916
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f17345,plain,
( spl0_1786
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f20008,plain,
( spl0_1901
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f20506,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_916
| ~ spl0_1786
| ~ spl0_1901 ),
inference(forward_demodulation,[],[f20503,f17347]) ).
fof(f17347,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_1786 ),
inference(avatar_component_clause,[],[f17345]) ).
fof(f20503,plain,
( ! [X0] : c_Divides_Oop_Advd(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_916
| ~ spl0_1901 ),
inference(trivial_inequality_removal,[],[f20500]) ).
fof(f20500,plain,
( ! [X0] :
( c_0 != c_0
| c_Divides_Oop_Advd(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_916
| ~ spl0_1901 ),
inference(superposition,[],[f20009,f7922]) ).
fof(f7922,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_916 ),
inference(avatar_component_clause,[],[f7921]) ).
fof(f20009,plain,
( ! [X3,X0] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1901 ),
inference(avatar_component_clause,[],[f20008]) ).
fof(f30978,plain,
( spl0_2410
| ~ spl0_856
| ~ spl0_1871 ),
inference(avatar_split_clause,[],[f19843,f18890,f7606,f30976]) ).
fof(f30976,plain,
( spl0_2410
<=> ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2410])]) ).
fof(f19843,plain,
( ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_856
| ~ spl0_1871 ),
inference(superposition,[],[f7607,f18891]) ).
fof(f30974,plain,
( spl0_2409
| ~ spl0_775
| ~ spl0_1670 ),
inference(avatar_split_clause,[],[f15314,f15310,f7269,f30972]) ).
fof(f30972,plain,
( spl0_2409
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2409])]) ).
fof(f15314,plain,
( ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat)
| ~ spl0_775
| ~ spl0_1670 ),
inference(superposition,[],[f15311,f7270]) ).
fof(f30970,plain,
( spl0_2408
| ~ spl0_113
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f14183,f13695,f3803,f30968]) ).
fof(f30968,plain,
( spl0_2408
<=> ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).
fof(f3803,plain,
( spl0_113
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f13695,plain,
( spl0_1537
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f14183,plain,
( ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) )
| ~ spl0_113
| ~ spl0_1537 ),
inference(resolution,[],[f13696,f3804]) ).
fof(f3804,plain,
( ! [X21] : ~ c_less(X21,X21,tc_nat)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3803]) ).
fof(f13696,plain,
( ! [X48,X11] :
( c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(X11,X48,tc_IntDef_Oint) )
| ~ spl0_1537 ),
inference(avatar_component_clause,[],[f13695]) ).
fof(f30965,plain,
( spl0_2406
| spl0_2407
| ~ spl0_786
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f14152,f13691,f7314,f30963,f30920]) ).
fof(f30963,plain,
( spl0_2407
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).
fof(f7314,plain,
( spl0_786
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f13691,plain,
( spl0_1536
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f14152,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_786
| ~ spl0_1536 ),
inference(resolution,[],[f13692,f7315]) ).
fof(f7315,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f7314]) ).
fof(f13692,plain,
( ! [X48,X11,X1] :
( c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1536 ),
inference(avatar_component_clause,[],[f13691]) ).
fof(f30922,plain,
( spl0_2406
| spl0_1892
| ~ spl0_738
| ~ spl0_1533 ),
inference(avatar_split_clause,[],[f14122,f13679,f7120,f19032,f30920]) ).
fof(f19032,plain,
( spl0_1892
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f7120,plain,
( spl0_738
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f13679,plain,
( spl0_1533
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f14122,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_738
| ~ spl0_1533 ),
inference(resolution,[],[f13680,f7121]) ).
fof(f7121,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_738 ),
inference(avatar_component_clause,[],[f7120]) ).
fof(f13680,plain,
( ! [X48,X11,X1] :
( ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1533 ),
inference(avatar_component_clause,[],[f13679]) ).
fof(f30918,plain,
( spl0_2405
| ~ spl0_758
| ~ spl0_1525 ),
inference(avatar_split_clause,[],[f14028,f13647,f7201,f30916]) ).
fof(f7201,plain,
( spl0_758
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f13647,plain,
( spl0_1525
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f14028,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_758
| ~ spl0_1525 ),
inference(trivial_inequality_removal,[],[f14013]) ).
fof(f14013,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 )
| ~ spl0_758
| ~ spl0_1525 ),
inference(superposition,[],[f13648,f7202]) ).
fof(f7202,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint)
| ~ spl0_758 ),
inference(avatar_component_clause,[],[f7201]) ).
fof(f13648,plain,
( ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 )
| ~ spl0_1525 ),
inference(avatar_component_clause,[],[f13647]) ).
fof(f30914,plain,
( spl0_2404
| ~ spl0_757
| ~ spl0_1525 ),
inference(avatar_split_clause,[],[f14027,f13647,f7197,f30912]) ).
fof(f7197,plain,
( spl0_757
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f14027,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_757
| ~ spl0_1525 ),
inference(trivial_inequality_removal,[],[f14015]) ).
fof(f14015,plain,
( ! [X0] :
( c_0 != c_0
| c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0 )
| ~ spl0_757
| ~ spl0_1525 ),
inference(superposition,[],[f13648,f7198]) ).
fof(f7198,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint)
| ~ spl0_757 ),
inference(avatar_component_clause,[],[f7197]) ).
fof(f30910,plain,
( spl0_2403
| ~ spl0_759
| ~ spl0_1525 ),
inference(avatar_split_clause,[],[f14025,f13647,f7205,f30908]) ).
fof(f30908,plain,
( spl0_2403
<=> ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2403])]) ).
fof(f7205,plain,
( spl0_759
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f14025,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint)
| ~ spl0_759
| ~ spl0_1525 ),
inference(trivial_inequality_removal,[],[f14017]) ).
fof(f14017,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint) )
| ~ spl0_759
| ~ spl0_1525 ),
inference(superposition,[],[f13648,f7206]) ).
fof(f7206,plain,
( ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint)
| ~ spl0_759 ),
inference(avatar_component_clause,[],[f7205]) ).
fof(f30906,plain,
( spl0_2402
| ~ spl0_746
| ~ spl0_1524 ),
inference(avatar_split_clause,[],[f14011,f13643,f7152,f30904]) ).
fof(f13643,plain,
( spl0_1524
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f14011,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_746
| ~ spl0_1524 ),
inference(trivial_inequality_removal,[],[f13999]) ).
fof(f13999,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 )
| ~ spl0_746
| ~ spl0_1524 ),
inference(superposition,[],[f13644,f7153]) ).
fof(f13644,plain,
( ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 )
| ~ spl0_1524 ),
inference(avatar_component_clause,[],[f13643]) ).
fof(f30902,plain,
( spl0_2401
| ~ spl0_819
| ~ spl0_1524 ),
inference(avatar_split_clause,[],[f14010,f13643,f7448,f30900]) ).
fof(f7448,plain,
( spl0_819
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f14010,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_819
| ~ spl0_1524 ),
inference(trivial_inequality_removal,[],[f14000]) ).
fof(f14000,plain,
( ! [X0] :
( c_0 != c_0
| c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 )
| ~ spl0_819
| ~ spl0_1524 ),
inference(superposition,[],[f13644,f7449]) ).
fof(f7449,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7448]) ).
fof(f30898,plain,
( spl0_2400
| ~ spl0_745
| ~ spl0_1524 ),
inference(avatar_split_clause,[],[f14009,f13643,f7148,f30896]) ).
fof(f30896,plain,
( spl0_2400
<=> ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).
fof(f7148,plain,
( spl0_745
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f14009,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat)
| ~ spl0_745
| ~ spl0_1524 ),
inference(trivial_inequality_removal,[],[f14001]) ).
fof(f14001,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) )
| ~ spl0_745
| ~ spl0_1524 ),
inference(superposition,[],[f13644,f7149]) ).
fof(f7149,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_745 ),
inference(avatar_component_clause,[],[f7148]) ).
fof(f30893,plain,
( spl0_2399
| ~ spl0_799
| ~ spl0_1505 ),
inference(avatar_split_clause,[],[f13557,f12270,f7366,f30891]) ).
fof(f12270,plain,
( spl0_1505
<=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f13557,plain,
( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_799
| ~ spl0_1505 ),
inference(superposition,[],[f12271,f7367]) ).
fof(f12271,plain,
( ! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1)
| ~ spl0_1505 ),
inference(avatar_component_clause,[],[f12270]) ).
fof(f30888,plain,
( spl0_2398
| ~ spl0_799
| ~ spl0_1504 ),
inference(avatar_split_clause,[],[f13549,f12266,f7366,f30886]) ).
fof(f12266,plain,
( spl0_1504
<=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f13549,plain,
( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_799
| ~ spl0_1504 ),
inference(superposition,[],[f12267,f7367]) ).
fof(f12267,plain,
( ! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1)
| ~ spl0_1504 ),
inference(avatar_component_clause,[],[f12266]) ).
fof(f30884,plain,
( spl0_2397
| ~ spl0_804
| ~ spl0_1495 ),
inference(avatar_split_clause,[],[f13503,f12226,f7386,f30882]) ).
fof(f30882,plain,
( spl0_2397
<=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).
fof(f12226,plain,
( spl0_1495
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f13503,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1495 ),
inference(superposition,[],[f7387,f12227]) ).
fof(f12227,plain,
( ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1495 ),
inference(avatar_component_clause,[],[f12226]) ).
fof(f30880,plain,
( spl0_2396
| ~ spl0_804
| ~ spl0_1494 ),
inference(avatar_split_clause,[],[f13486,f12222,f7386,f30878]) ).
fof(f30878,plain,
( spl0_2396
<=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2396])]) ).
fof(f12222,plain,
( spl0_1494
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f13486,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1494 ),
inference(superposition,[],[f7387,f12223]) ).
fof(f12223,plain,
( ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1494 ),
inference(avatar_component_clause,[],[f12222]) ).
fof(f30876,plain,
( spl0_2395
| ~ spl0_804
| ~ spl0_1493 ),
inference(avatar_split_clause,[],[f13470,f12218,f7386,f30874]) ).
fof(f30874,plain,
( spl0_2395
<=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2395])]) ).
fof(f12218,plain,
( spl0_1493
<=> ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f13470,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1493 ),
inference(superposition,[],[f7387,f12219]) ).
fof(f12219,plain,
( ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1493 ),
inference(avatar_component_clause,[],[f12218]) ).
fof(f30872,plain,
( spl0_2394
| ~ spl0_804
| ~ spl0_1492 ),
inference(avatar_split_clause,[],[f13453,f12214,f7386,f30870]) ).
fof(f30870,plain,
( spl0_2394
<=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f12214,plain,
( spl0_1492
<=> ! [X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f13453,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1492 ),
inference(superposition,[],[f7387,f12215]) ).
fof(f12215,plain,
( ! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1492 ),
inference(avatar_component_clause,[],[f12214]) ).
fof(f30868,plain,
( spl0_2392
| ~ spl0_2393
| ~ spl0_1050
| ~ spl0_2235 ),
inference(avatar_split_clause,[],[f28447,f27636,f8590,f30865,f30862]) ).
fof(f30862,plain,
( spl0_2392
<=> ! [X0] : c_IntDef_ONats = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).
fof(f30865,plain,
( spl0_2393
<=> c_emptyset = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).
fof(f27636,plain,
( spl0_2235
<=> ! [X0] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
fof(f28447,plain,
( ! [X0] :
( c_emptyset != c_IntDef_ONats
| c_IntDef_ONats = X0 )
| ~ spl0_1050
| ~ spl0_2235 ),
inference(inner_rewriting,[],[f28431]) ).
fof(f28431,plain,
( ! [X0] :
( c_emptyset != c_IntDef_ONats
| c_emptyset = X0 )
| ~ spl0_1050
| ~ spl0_2235 ),
inference(superposition,[],[f8591,f27637]) ).
fof(f27637,plain,
( ! [X0] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_2235 ),
inference(avatar_component_clause,[],[f27636]) ).
fof(f30860,plain,
( spl0_2391
| ~ spl0_804
| ~ spl0_1491 ),
inference(avatar_split_clause,[],[f13432,f12205,f7386,f30858]) ).
fof(f12205,plain,
( spl0_1491
<=> ! [X102,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f13432,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1491 ),
inference(superposition,[],[f7387,f12206]) ).
fof(f12206,plain,
( ! [X88,X102] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1491 ),
inference(avatar_component_clause,[],[f12205]) ).
fof(f30856,plain,
( spl0_2390
| ~ spl0_804
| ~ spl0_1487 ),
inference(avatar_split_clause,[],[f13381,f12189,f7386,f30854]) ).
fof(f30854,plain,
( spl0_2390
<=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2390])]) ).
fof(f12189,plain,
( spl0_1487
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f13381,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1487 ),
inference(superposition,[],[f7387,f12190]) ).
fof(f12190,plain,
( ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ spl0_1487 ),
inference(avatar_component_clause,[],[f12189]) ).
fof(f30852,plain,
( spl0_2389
| ~ spl0_804
| ~ spl0_1486 ),
inference(avatar_split_clause,[],[f13362,f12185,f7386,f30850]) ).
fof(f30850,plain,
( spl0_2389
<=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).
fof(f12185,plain,
( spl0_1486
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f13362,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1486 ),
inference(superposition,[],[f7387,f12186]) ).
fof(f12186,plain,
( ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ spl0_1486 ),
inference(avatar_component_clause,[],[f12185]) ).
fof(f30848,plain,
( spl0_2388
| ~ spl0_804
| ~ spl0_1485 ),
inference(avatar_split_clause,[],[f13343,f12181,f7386,f30846]) ).
fof(f30846,plain,
( spl0_2388
<=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).
fof(f12181,plain,
( spl0_1485
<=> ! [X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f13343,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1485 ),
inference(superposition,[],[f7387,f12182]) ).
fof(f12182,plain,
( ! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ spl0_1485 ),
inference(avatar_component_clause,[],[f12181]) ).
fof(f30844,plain,
( spl0_2387
| ~ spl0_804
| ~ spl0_1484 ),
inference(avatar_split_clause,[],[f13324,f12177,f7386,f30842]) ).
fof(f12177,plain,
( spl0_1484
<=> ! [X102,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f13324,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_804
| ~ spl0_1484 ),
inference(superposition,[],[f7387,f12178]) ).
fof(f12178,plain,
( ! [X88,X102] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ spl0_1484 ),
inference(avatar_component_clause,[],[f12177]) ).
fof(f30840,plain,
( spl0_2386
| ~ spl0_663
| ~ spl0_1482 ),
inference(avatar_split_clause,[],[f13297,f12169,f6777,f30838]) ).
fof(f30838,plain,
( spl0_2386
<=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).
fof(f6777,plain,
( spl0_663
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f12169,plain,
( spl0_1482
<=> ! [X13,X12,X0,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f13297,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| ~ spl0_663
| ~ spl0_1482 ),
inference(resolution,[],[f12170,f6778]) ).
fof(f6778,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f6777]) ).
fof(f12170,plain,
( ! [X0,X1,X12,X13] :
( ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1482 ),
inference(avatar_component_clause,[],[f12169]) ).
fof(f30836,plain,
( spl0_2385
| ~ spl0_663
| ~ spl0_1479 ),
inference(avatar_split_clause,[],[f13277,f12151,f6777,f30834]) ).
fof(f30834,plain,
( spl0_2385
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f12151,plain,
( spl0_1479
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f13277,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| ~ spl0_663
| ~ spl0_1479 ),
inference(resolution,[],[f12152,f6778]) ).
fof(f12152,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X13,X32,tc_set(X1)) )
| ~ spl0_1479 ),
inference(avatar_component_clause,[],[f12151]) ).
fof(f30832,plain,
( spl0_2384
| ~ spl0_663
| ~ spl0_1478 ),
inference(avatar_split_clause,[],[f13262,f12147,f6777,f30830]) ).
fof(f30830,plain,
( spl0_2384
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).
fof(f13262,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_663
| ~ spl0_1478 ),
inference(resolution,[],[f12148,f6778]) ).
fof(f30828,plain,
( spl0_2383
| ~ spl0_985
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f13154,f12080,f8327,f30826]) ).
fof(f30826,plain,
( spl0_2383
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).
fof(f8327,plain,
( spl0_985
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f13154,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_985
| ~ spl0_1464 ),
inference(superposition,[],[f8328,f12081]) ).
fof(f8328,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
| ~ spl0_985 ),
inference(avatar_component_clause,[],[f8327]) ).
fof(f30824,plain,
( spl0_2382
| ~ spl0_986
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f13153,f12080,f8331,f30822]) ).
fof(f30822,plain,
( spl0_2382
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f8331,plain,
( spl0_986
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f13153,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_986
| ~ spl0_1464 ),
inference(superposition,[],[f8332,f12081]) ).
fof(f8332,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
| ~ spl0_986 ),
inference(avatar_component_clause,[],[f8331]) ).
fof(f30767,plain,
( spl0_2381
| ~ spl0_985
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f13148,f12076,f8327,f30765]) ).
fof(f30765,plain,
( spl0_2381
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).
fof(f12076,plain,
( spl0_1463
<=> ! [X2,X1,X3] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f13148,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_985
| ~ spl0_1463 ),
inference(superposition,[],[f8328,f12077]) ).
fof(f12077,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1463 ),
inference(avatar_component_clause,[],[f12076]) ).
fof(f30762,plain,
( spl0_2380
| ~ spl0_986
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f13147,f12076,f8331,f30760]) ).
fof(f30760,plain,
( spl0_2380
<=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).
fof(f13147,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_986
| ~ spl0_1463 ),
inference(superposition,[],[f8332,f12077]) ).
fof(f30758,plain,
( spl0_2379
| ~ spl0_804
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f12632,f11920,f7386,f30756]) ).
fof(f30756,plain,
( spl0_2379
<=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).
fof(f12632,plain,
( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
| ~ spl0_804
| ~ spl0_1427 ),
inference(superposition,[],[f7387,f11921]) ).
fof(f30754,plain,
( spl0_2378
| ~ spl0_766
| ~ spl0_1420 ),
inference(avatar_split_clause,[],[f12561,f11888,f7233,f30752]) ).
fof(f30752,plain,
( spl0_2378
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).
fof(f7233,plain,
( spl0_766
<=> ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f12561,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 )
| ~ spl0_766
| ~ spl0_1420 ),
inference(superposition,[],[f7234,f11889]) ).
fof(f7234,plain,
( ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23
| ~ spl0_766 ),
inference(avatar_component_clause,[],[f7233]) ).
fof(f30750,plain,
( spl0_2377
| ~ spl0_980
| ~ spl0_1413 ),
inference(avatar_split_clause,[],[f12507,f11860,f8181,f30748]) ).
fof(f30748,plain,
( spl0_2377
<=> ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2377])]) ).
fof(f8181,plain,
( spl0_980
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f11860,plain,
( spl0_1413
<=> ! [X16,X21,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f12507,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) )
| ~ spl0_980
| ~ spl0_1413 ),
inference(superposition,[],[f11861,f8182]) ).
fof(f8182,plain,
( ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat))
| ~ spl0_980 ),
inference(avatar_component_clause,[],[f8181]) ).
fof(f11861,plain,
( ! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(X16,X15,tc_nat) )
| ~ spl0_1413 ),
inference(avatar_component_clause,[],[f11860]) ).
fof(f30744,plain,
( spl0_2376
| ~ spl0_727
| ~ spl0_1404 ),
inference(avatar_split_clause,[],[f12399,f11822,f7061,f30742]) ).
fof(f30742,plain,
( spl0_2376
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f11822,plain,
( spl0_1404
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f12399,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_727
| ~ spl0_1404 ),
inference(resolution,[],[f11823,f7062]) ).
fof(f11823,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1404 ),
inference(avatar_component_clause,[],[f11822]) ).
fof(f30740,plain,
( spl0_2375
| ~ spl0_662
| ~ spl0_1402 ),
inference(avatar_split_clause,[],[f12376,f11814,f6773,f30738]) ).
fof(f30738,plain,
( spl0_2375
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f11814,plain,
( spl0_1402
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f12376,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_662
| ~ spl0_1402 ),
inference(resolution,[],[f11815,f6774]) ).
fof(f11815,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13
| c_less(X12,X13,tc_set(X1)) )
| ~ spl0_1402 ),
inference(avatar_component_clause,[],[f11814]) ).
fof(f30734,plain,
( spl0_2374
| ~ spl0_727
| ~ spl0_1402 ),
inference(avatar_split_clause,[],[f12367,f11814,f7061,f30732]) ).
fof(f30732,plain,
( spl0_2374
<=> ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).
fof(f12367,plain,
( ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) )
| ~ spl0_727
| ~ spl0_1402 ),
inference(resolution,[],[f11815,f7062]) ).
fof(f30730,plain,
( spl0_2373
| ~ spl0_774
| ~ spl0_853
| ~ spl0_1511 ),
inference(avatar_split_clause,[],[f12323,f12300,f7594,f7265,f30728]) ).
fof(f30728,plain,
( spl0_2373
<=> ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).
fof(f7594,plain,
( spl0_853
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f12300,plain,
( spl0_1511
<=> ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f12323,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 )
| ~ spl0_774
| ~ spl0_853
| ~ spl0_1511 ),
inference(forward_demodulation,[],[f12310,f7266]) ).
fof(f12310,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
| c_0 = X0 )
| ~ spl0_853
| ~ spl0_1511 ),
inference(resolution,[],[f12301,f7595]) ).
fof(f7595,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_853 ),
inference(avatar_component_clause,[],[f7594]) ).
fof(f12301,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) )
| ~ spl0_1511 ),
inference(avatar_component_clause,[],[f12300]) ).
fof(f30726,plain,
( spl0_2372
| ~ spl0_774
| ~ spl0_967
| ~ spl0_1508 ),
inference(avatar_split_clause,[],[f12289,f12283,f8127,f7265,f30723]) ).
fof(f30723,plain,
( spl0_2372
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2372])]) ).
fof(f12283,plain,
( spl0_1508
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f12289,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_774
| ~ spl0_967
| ~ spl0_1508 ),
inference(forward_demodulation,[],[f12286,f8129]) ).
fof(f12286,plain,
( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_774
| ~ spl0_1508 ),
inference(superposition,[],[f12284,f7266]) ).
fof(f12284,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_1508 ),
inference(avatar_component_clause,[],[f12283]) ).
fof(f30719,plain,
( spl0_2371
| ~ spl0_894
| ~ spl0_1508 ),
inference(avatar_split_clause,[],[f12288,f12283,f7830,f30717]) ).
fof(f30717,plain,
( spl0_2371
<=> ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2371])]) ).
fof(f7830,plain,
( spl0_894
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f12288,plain,
( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_894
| ~ spl0_1508 ),
inference(superposition,[],[f7831,f12284]) ).
fof(f7831,plain,
( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_894 ),
inference(avatar_component_clause,[],[f7830]) ).
fof(f30715,plain,
( spl0_2370
| ~ spl0_875
| ~ spl0_1362 ),
inference(avatar_split_clause,[],[f11456,f10663,f7682,f30713]) ).
fof(f30713,plain,
( spl0_2370
<=> ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2370])]) ).
fof(f10663,plain,
( spl0_1362
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f11456,plain,
( ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) )
| ~ spl0_875
| ~ spl0_1362 ),
inference(superposition,[],[f10664,f7683]) ).
fof(f10664,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_minus(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1362 ),
inference(avatar_component_clause,[],[f10663]) ).
fof(f30711,plain,
( spl0_2369
| ~ spl0_738
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11425,f10627,f7120,f30709]) ).
fof(f11425,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_738
| ~ spl0_1354 ),
inference(duplicate_literal_removal,[],[f11392]) ).
fof(f11392,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_738
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f7121]) ).
fof(f30701,plain,
( spl0_2368
| ~ spl0_71
| ~ spl0_112
| ~ spl0_1354 ),
inference(avatar_split_clause,[],[f11398,f10627,f3799,f3602,f30699]) ).
fof(f30699,plain,
( spl0_2368
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).
fof(f3799,plain,
( spl0_112
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f11398,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
| ~ spl0_112
| ~ spl0_1354 ),
inference(resolution,[],[f10628,f3800]) ).
fof(f3800,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3799]) ).
fof(f30697,plain,
( spl0_2367
| ~ spl0_738
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11360,f10591,f7120,f30695]) ).
fof(f11360,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_738
| ~ spl0_1345 ),
inference(duplicate_literal_removal,[],[f11327]) ).
fof(f11327,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_738
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f7121]) ).
fof(f30679,plain,
( spl0_2366
| ~ spl0_71
| ~ spl0_112
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11333,f10591,f3799,f3602,f30677]) ).
fof(f30677,plain,
( spl0_2366
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).
fof(f11333,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
| ~ spl0_112
| ~ spl0_1345 ),
inference(resolution,[],[f10592,f3800]) ).
fof(f30671,plain,
( spl0_2365
| ~ spl0_23
| ~ spl0_658
| ~ spl0_1344 ),
inference(avatar_split_clause,[],[f11308,f10587,f5993,f3362,f30668]) ).
fof(f30668,plain,
( spl0_2365
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2365])]) ).
fof(f5993,plain,
( spl0_658
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f11308,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_658
| ~ spl0_1344 ),
inference(resolution,[],[f10588,f5995]) ).
fof(f5995,plain,
( c_less(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_658 ),
inference(avatar_component_clause,[],[f5993]) ).
fof(f30639,plain,
( spl0_2364
| ~ spl0_71
| ~ spl0_646
| ~ spl0_1344 ),
inference(avatar_split_clause,[],[f11307,f10587,f5938,f3602,f30636]) ).
fof(f30636,plain,
( spl0_2364
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f11307,plain,
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
| ~ spl0_646
| ~ spl0_1344 ),
inference(resolution,[],[f10588,f5940]) ).
fof(f30632,plain,
( spl0_2362
| ~ spl0_2363
| ~ spl0_782
| ~ spl0_1256 ),
inference(avatar_split_clause,[],[f10251,f9837,f7297,f30629,f30626]) ).
fof(f30626,plain,
( spl0_2362
<=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).
fof(f30629,plain,
( spl0_2363
<=> c_lessequals(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f7297,plain,
( spl0_782
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f9837,plain,
( spl0_1256
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f10251,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_0,tc_nat)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_782
| ~ spl0_1256 ),
inference(superposition,[],[f9838,f7298]) ).
fof(f7298,plain,
( ! [X21] : c_0 = c_times(c_0,X21,tc_nat)
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f7297]) ).
fof(f9838,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) )
| ~ spl0_1256 ),
inference(avatar_component_clause,[],[f9837]) ).
fof(f30616,plain,
( spl0_2361
| ~ spl0_40
| ~ spl0_680
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f10083,f9712,f6850,f3447,f30614]) ).
fof(f30614,plain,
( spl0_2361
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f10083,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_680
| ~ spl0_1226 ),
inference(resolution,[],[f9713,f6851]) ).
fof(f30612,plain,
( spl0_2360
| ~ spl0_9
| ~ spl0_1137 ),
inference(avatar_split_clause,[],[f9460,f9145,f3292,f30610]) ).
fof(f30610,plain,
( spl0_2360
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2360])]) ).
fof(f9145,plain,
( spl0_1137
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f9460,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1137 ),
inference(resolution,[],[f9146,f3294]) ).
fof(f9146,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) )
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f9145]) ).
fof(f30608,plain,
( spl0_2359
| ~ spl0_9
| ~ spl0_1133 ),
inference(avatar_split_clause,[],[f9449,f9129,f3292,f30606]) ).
fof(f30606,plain,
( spl0_2359
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).
fof(f9129,plain,
( spl0_1133
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f9449,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1133 ),
inference(resolution,[],[f9130,f3294]) ).
fof(f9130,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) )
| ~ spl0_1133 ),
inference(avatar_component_clause,[],[f9129]) ).
fof(f30604,plain,
( spl0_2358
| ~ spl0_9
| ~ spl0_1131 ),
inference(avatar_split_clause,[],[f9445,f9121,f3292,f30602]) ).
fof(f30602,plain,
( spl0_2358
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).
fof(f9121,plain,
( spl0_1131
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f9445,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_1131 ),
inference(resolution,[],[f9122,f3294]) ).
fof(f9122,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) )
| ~ spl0_1131 ),
inference(avatar_component_clause,[],[f9121]) ).
fof(f30600,plain,
( spl0_2357
| ~ spl0_22
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f9335,f9011,f3357,f30598]) ).
fof(f30598,plain,
( spl0_2357
<=> ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2357])]) ).
fof(f9011,plain,
( spl0_1104
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f9335,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_1104 ),
inference(resolution,[],[f9012,f3359]) ).
fof(f9012,plain,
( ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f9011]) ).
fof(f30588,plain,
( spl0_2356
| ~ spl0_91
| ~ spl0_1099 ),
inference(avatar_split_clause,[],[f9326,f8991,f3702,f30586]) ).
fof(f30586,plain,
( spl0_2356
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).
fof(f8991,plain,
( spl0_1099
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f9326,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_91
| ~ spl0_1099 ),
inference(resolution,[],[f8992,f3704]) ).
fof(f8992,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1099 ),
inference(avatar_component_clause,[],[f8991]) ).
fof(f30584,plain,
( spl0_2355
| ~ spl0_27
| ~ spl0_1099 ),
inference(avatar_split_clause,[],[f9325,f8991,f3382,f30582]) ).
fof(f30582,plain,
( spl0_2355
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).
fof(f9325,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_1099 ),
inference(resolution,[],[f8992,f3384]) ).
fof(f30580,plain,
( spl0_2354
| ~ spl0_91
| ~ spl0_1098 ),
inference(avatar_split_clause,[],[f9324,f8987,f3702,f30578]) ).
fof(f30578,plain,
( spl0_2354
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).
fof(f8987,plain,
( spl0_1098
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f9324,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_91
| ~ spl0_1098 ),
inference(resolution,[],[f8988,f3704]) ).
fof(f8988,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1098 ),
inference(avatar_component_clause,[],[f8987]) ).
fof(f30576,plain,
( spl0_2353
| ~ spl0_27
| ~ spl0_1098 ),
inference(avatar_split_clause,[],[f9323,f8987,f3382,f30574]) ).
fof(f30574,plain,
( spl0_2353
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2353])]) ).
fof(f9323,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_1098 ),
inference(resolution,[],[f8988,f3384]) ).
fof(f30571,plain,
( spl0_2352
| ~ spl0_640
| ~ spl0_1162 ),
inference(avatar_split_clause,[],[f9250,f9247,f5911,f30568]) ).
fof(f9247,plain,
( spl0_1162
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f9250,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1162 ),
inference(superposition,[],[f9248,f5913]) ).
fof(f9248,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1162 ),
inference(avatar_component_clause,[],[f9247]) ).
fof(f30566,plain,
( spl0_2351
| ~ spl0_968
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f8867,f8586,f8132,f30564]) ).
fof(f30564,plain,
( spl0_2351
<=> ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f8132,plain,
( spl0_968
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f8867,plain,
( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_968
| ~ spl0_1049 ),
inference(superposition,[],[f8133,f8587]) ).
fof(f8133,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8132]) ).
fof(f30562,plain,
( spl0_2350
| ~ spl0_852
| ~ spl0_1030 ),
inference(avatar_split_clause,[],[f8838,f8509,f7590,f30560]) ).
fof(f30560,plain,
( spl0_2350
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f8509,plain,
( spl0_1030
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f8838,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
| ~ spl0_852
| ~ spl0_1030 ),
inference(resolution,[],[f8510,f7591]) ).
fof(f8510,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1030 ),
inference(avatar_component_clause,[],[f8509]) ).
fof(f30558,plain,
( spl0_2349
| ~ spl0_832
| ~ spl0_1030 ),
inference(avatar_split_clause,[],[f8837,f8509,f7510,f30556]) ).
fof(f30556,plain,
( spl0_2349
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f8837,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
| ~ spl0_832
| ~ spl0_1030 ),
inference(resolution,[],[f8510,f7511]) ).
fof(f30554,plain,
( spl0_2348
| ~ spl0_968
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f8812,f8477,f8132,f30552]) ).
fof(f30552,plain,
( spl0_2348
<=> ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).
fof(f8812,plain,
( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_968
| ~ spl0_1022 ),
inference(superposition,[],[f8133,f8478]) ).
fof(f30550,plain,
( spl0_2347
| ~ spl0_838
| ~ spl0_1005 ),
inference(avatar_split_clause,[],[f8776,f8408,f7534,f30548]) ).
fof(f30548,plain,
( spl0_2347
<=> ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2347])]) ).
fof(f8408,plain,
( spl0_1005
<=> ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f8776,plain,
( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_838
| ~ spl0_1005 ),
inference(superposition,[],[f8409,f7535]) ).
fof(f8409,plain,
( ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1005 ),
inference(avatar_component_clause,[],[f8408]) ).
fof(f30537,plain,
( spl0_2346
| ~ spl0_857
| ~ spl0_1001 ),
inference(avatar_split_clause,[],[f8750,f8392,f7610,f30535]) ).
fof(f30535,plain,
( spl0_2346
<=> ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).
fof(f8392,plain,
( spl0_1001
<=> ! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f8750,plain,
( ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) )
| ~ spl0_857
| ~ spl0_1001 ),
inference(resolution,[],[f8393,f7611]) ).
fof(f8393,plain,
( ! [X48] :
( ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1001 ),
inference(avatar_component_clause,[],[f8392]) ).
fof(f30533,plain,
( spl0_2345
| ~ spl0_731
| ~ spl0_971 ),
inference(avatar_split_clause,[],[f8314,f8144,f7079,f30531]) ).
fof(f30531,plain,
( spl0_2345
<=> ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).
fof(f7079,plain,
( spl0_731
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f8144,plain,
( spl0_971
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f8314,plain,
( ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 )
| ~ spl0_731
| ~ spl0_971 ),
inference(superposition,[],[f8145,f7080]) ).
fof(f7080,plain,
( ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3
| ~ spl0_731 ),
inference(avatar_component_clause,[],[f7079]) ).
fof(f8145,plain,
( ! [X91,X92] :
( c_Message_OinvKey(X91) != c_Message_OinvKey(X92)
| X91 = X92 )
| ~ spl0_971 ),
inference(avatar_component_clause,[],[f8144]) ).
fof(f30520,plain,
( spl0_2344
| ~ spl0_40
| ~ spl0_913
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8277,f8046,f7909,f3447,f30518]) ).
fof(f30518,plain,
( spl0_2344
<=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).
fof(f7909,plain,
( spl0_913
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f8277,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
| ~ spl0_913
| ~ spl0_947 ),
inference(resolution,[],[f8047,f7910]) ).
fof(f7910,plain,
( ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) )
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f7909]) ).
fof(f30516,plain,
( spl0_2343
| ~ spl0_847
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f8228,f7933,f7570,f30514]) ).
fof(f30514,plain,
( spl0_2343
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2343])]) ).
fof(f7933,plain,
( spl0_919
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f8228,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_847
| ~ spl0_919 ),
inference(superposition,[],[f7934,f7571]) ).
fof(f7934,plain,
( ! [X1,X23] :
( c_List_Olist_ONil != c_List_Orev(X23,X1)
| c_List_Olist_ONil = X23 )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f7933]) ).
fof(f30503,plain,
spl0_2342,
inference(avatar_split_clause,[],[f6,f30501]) ).
fof(f30501,plain,
( spl0_2342
<=> ! [X5,X10,X9,X7,X8,X6,X2,X1] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).
fof(f6,axiom,
! [X2,X10,X1,X8,X6,X9,X7,X5] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f30480,plain,
spl0_2341,
inference(avatar_split_clause,[],[f10,f30478]) ).
fof(f30478,plain,
( spl0_2341
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2341])]) ).
fof(f10,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f30433,plain,
spl0_2340,
inference(avatar_split_clause,[],[f9,f30431]) ).
fof(f30431,plain,
( spl0_2340
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).
fof(f9,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f30429,plain,
spl0_2339,
inference(avatar_split_clause,[],[f8,f30427]) ).
fof(f30427,plain,
( spl0_2339
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).
fof(f8,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f30406,plain,
spl0_2338,
inference(avatar_split_clause,[],[f7,f30404]) ).
fof(f30404,plain,
( spl0_2338
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f7,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f30385,plain,
spl0_2337,
inference(avatar_split_clause,[],[f3,f30383]) ).
fof(f30383,plain,
( spl0_2337
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).
fof(f3,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f30369,plain,
spl0_2336,
inference(avatar_split_clause,[],[f12,f30367]) ).
fof(f30367,plain,
( spl0_2336
<=> ! [X5,X7,X8,X6,X2,X1] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).
fof(f12,axiom,
! [X2,X1,X8,X6,X7,X5] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f30352,plain,
spl0_2335,
inference(avatar_split_clause,[],[f11,f30350]) ).
fof(f30350,plain,
( spl0_2335
<=> ! [X6,X9,X10,X5,X2,X1] :
( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2335])]) ).
fof(f11,axiom,
! [X2,X10,X1,X6,X9,X5] :
( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f30308,plain,
( spl0_2334
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1724
| ~ spl0_1725
| ~ spl0_2333 ),
inference(avatar_split_clause,[],[f30304,f30299,f16597,f16593,f13904,f9680,f8538,f7309,f3507,f30306]) ).
fof(f30306,plain,
( spl0_2334
<=> ! [X11,X47] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2334])]) ).
fof(f13904,plain,
( spl0_1589
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f16593,plain,
( spl0_1724
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f16597,plain,
( spl0_1725
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f30299,plain,
( spl0_2333
<=> ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).
fof(f30304,plain,
( ! [X11,X47] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1724
| ~ spl0_1725
| ~ spl0_2333 ),
inference(forward_demodulation,[],[f30303,f17695]) ).
fof(f17695,plain,
( ! [X0,X1] : c_plus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,X1),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1724 ),
inference(resolution,[],[f16594,f3509]) ).
fof(f16594,plain,
( ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) )
| ~ spl0_1724 ),
inference(avatar_component_clause,[],[f16593]) ).
fof(f30303,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2333 ),
inference(forward_demodulation,[],[f30302,f14495]) ).
fof(f14495,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14494,f7311]) ).
fof(f14494,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0)
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f14493,f8539]) ).
fof(f14493,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X0)
| ~ spl0_1218
| ~ spl0_1589 ),
inference(superposition,[],[f9681,f13905]) ).
fof(f13905,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f13904]) ).
fof(f30302,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1725
| ~ spl0_2333 ),
inference(forward_demodulation,[],[f30300,f17696]) ).
fof(f17696,plain,
( ! [X0,X1] : c_times(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X0,X1),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1725 ),
inference(resolution,[],[f16598,f3509]) ).
fof(f16598,plain,
( ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) )
| ~ spl0_1725 ),
inference(avatar_component_clause,[],[f16597]) ).
fof(f30300,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2333 ),
inference(avatar_component_clause,[],[f30299]) ).
fof(f30301,plain,
spl0_2333,
inference(avatar_split_clause,[],[f3228,f30299]) ).
fof(f3228,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3227,f2156]) ).
fof(f2156,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3227,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3226,f2154]) ).
fof(f2154,axiom,
! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3226,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1452,f2156]) ).
fof(f1452,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
fof(f30170,plain,
spl0_2332,
inference(avatar_split_clause,[],[f1620,f30168]) ).
fof(f30168,plain,
( spl0_2332
<=> ! [X5,X18,X3,X0,X27,X1] :
( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f1620,axiom,
! [X3,X0,X18,X1,X27,X5] :
( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
fof(f30166,plain,
spl0_2331,
inference(avatar_split_clause,[],[f1501,f30164]) ).
fof(f30164,plain,
( spl0_2331
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).
fof(f1501,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
fof(f30160,plain,
spl0_2330,
inference(avatar_split_clause,[],[f5,f30158]) ).
fof(f30158,plain,
( spl0_2330
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2330])]) ).
fof(f5,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f30156,plain,
spl0_2329,
inference(avatar_split_clause,[],[f4,f30154]) ).
fof(f30154,plain,
( spl0_2329
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2329])]) ).
fof(f4,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f30116,plain,
spl0_2328,
inference(avatar_split_clause,[],[f1503,f30114]) ).
fof(f30114,plain,
( spl0_2328
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2328])]) ).
fof(f1503,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
fof(f30112,plain,
spl0_2327,
inference(avatar_split_clause,[],[f1369,f30110]) ).
fof(f30110,plain,
( spl0_2327
<=> ! [X0,X3] :
( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).
fof(f1369,axiom,
! [X3,X0] :
( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
fof(f30108,plain,
spl0_2326,
inference(avatar_split_clause,[],[f1368,f30106]) ).
fof(f30106,plain,
( spl0_2326
<=> ! [X0,X3] :
( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2326])]) ).
fof(f1368,axiom,
! [X3,X0] :
( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
fof(f30090,plain,
( spl0_2325
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2323 ),
inference(avatar_split_clause,[],[f30081,f30077,f16597,f13904,f9680,f8538,f7309,f3507,f30088]) ).
fof(f30088,plain,
( spl0_2325
<=> ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).
fof(f30077,plain,
( spl0_2323
<=> ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).
fof(f30081,plain,
( ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2323 ),
inference(forward_demodulation,[],[f30080,f14495]) ).
fof(f30080,plain,
( ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1725
| ~ spl0_2323 ),
inference(forward_demodulation,[],[f30078,f17696]) ).
fof(f30078,plain,
( ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2323 ),
inference(avatar_component_clause,[],[f30077]) ).
fof(f30086,plain,
( spl0_2324
| ~ spl0_1170
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28625,f28501,f9337,f30083]) ).
fof(f30083,plain,
( spl0_2324
<=> c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).
fof(f9337,plain,
( spl0_1170
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f28625,plain,
( c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat)
| ~ spl0_1170
| ~ spl0_2249 ),
inference(superposition,[],[f9339,f28503]) ).
fof(f9339,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| ~ spl0_1170 ),
inference(avatar_component_clause,[],[f9337]) ).
fof(f30079,plain,
spl0_2323,
inference(avatar_split_clause,[],[f3222,f30077]) ).
fof(f3222,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3221,f2156]) ).
fof(f3221,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3220,f2154]) ).
fof(f3220,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1461,f2156]) ).
fof(f1461,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
fof(f30040,plain,
spl0_2322,
inference(avatar_split_clause,[],[f1791,f30038]) ).
fof(f30038,plain,
( spl0_2322
<=> ! [X52,X53,X23,X25,X2,X1] :
( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
| c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2322])]) ).
fof(f1791,axiom,
! [X2,X1,X52,X53,X25,X23] :
( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
| c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
fof(f30021,plain,
( spl0_2321
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2320 ),
inference(avatar_split_clause,[],[f30017,f30013,f16597,f13904,f9680,f8538,f7309,f3507,f30019]) ).
fof(f30019,plain,
( spl0_2321
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).
fof(f30013,plain,
( spl0_2320
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).
fof(f30017,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2320 ),
inference(forward_demodulation,[],[f30016,f14495]) ).
fof(f30016,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1725
| ~ spl0_2320 ),
inference(forward_demodulation,[],[f30014,f17696]) ).
fof(f30014,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2320 ),
inference(avatar_component_clause,[],[f30013]) ).
fof(f30015,plain,
spl0_2320,
inference(avatar_split_clause,[],[f3225,f30013]) ).
fof(f3225,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3224,f2156]) ).
fof(f3224,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3223,f2154]) ).
fof(f3223,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1450,f2156]) ).
fof(f1450,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
fof(f29976,plain,
( spl0_2319
| ~ spl0_52
| ~ spl0_1724
| ~ spl0_1786
| ~ spl0_2318 ),
inference(avatar_split_clause,[],[f29972,f29967,f17345,f16593,f3507,f29974]) ).
fof(f29974,plain,
( spl0_2319
<=> ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2319])]) ).
fof(f29967,plain,
( spl0_2318
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).
fof(f29972,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1724
| ~ spl0_1786
| ~ spl0_2318 ),
inference(forward_demodulation,[],[f29971,f17347]) ).
fof(f29971,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1724
| ~ spl0_2318 ),
inference(forward_demodulation,[],[f29970,f17695]) ).
fof(f29970,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1724
| ~ spl0_2318 ),
inference(forward_demodulation,[],[f29968,f17695]) ).
fof(f29968,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2318 ),
inference(avatar_component_clause,[],[f29967]) ).
fof(f29969,plain,
spl0_2318,
inference(avatar_split_clause,[],[f1451,f29967]) ).
fof(f1451,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
fof(f29934,plain,
( spl0_2317
| ~ spl0_727
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28617,f28501,f7061,f29932]) ).
fof(f29932,plain,
( spl0_2317
<=> ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).
fof(f28617,plain,
( ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1))
| ~ spl0_727
| ~ spl0_2249 ),
inference(superposition,[],[f7062,f28503]) ).
fof(f29930,plain,
spl0_2316,
inference(avatar_split_clause,[],[f1504,f29928]) ).
fof(f29928,plain,
( spl0_2316
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f1504,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
fof(f29902,plain,
( spl0_2315
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2314 ),
inference(avatar_split_clause,[],[f29898,f29894,f16597,f13904,f9680,f8538,f7309,f3507,f29900]) ).
fof(f29900,plain,
( spl0_2315
<=> ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2315])]) ).
fof(f29894,plain,
( spl0_2314
<=> ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).
fof(f29898,plain,
( ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_785
| ~ spl0_1037
| ~ spl0_1218
| ~ spl0_1589
| ~ spl0_1725
| ~ spl0_2314 ),
inference(forward_demodulation,[],[f29897,f14495]) ).
fof(f29897,plain,
( ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1725
| ~ spl0_2314 ),
inference(forward_demodulation,[],[f29895,f17696]) ).
fof(f29895,plain,
( ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2314 ),
inference(avatar_component_clause,[],[f29894]) ).
fof(f29896,plain,
spl0_2314,
inference(avatar_split_clause,[],[f3219,f29894]) ).
fof(f3219,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3218,f2156]) ).
fof(f3218,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3217,f2154]) ).
fof(f3217,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1459,f2156]) ).
fof(f1459,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
fof(f29892,plain,
spl0_2313,
inference(avatar_split_clause,[],[f54,f29890]) ).
fof(f29890,plain,
( spl0_2313
<=> ! [X3,X23,X5,X25,X1] :
( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2313])]) ).
fof(f54,axiom,
! [X3,X1,X5,X25,X23] :
( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
fof(f29888,plain,
spl0_2312,
inference(avatar_split_clause,[],[f51,f29886]) ).
fof(f29886,plain,
( spl0_2312
<=> ! [X3,X23,X5,X25,X1] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2312])]) ).
fof(f51,axiom,
! [X3,X1,X5,X25,X23] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
fof(f29868,plain,
( spl0_2311
| ~ spl0_724
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28616,f28501,f7049,f29866]) ).
fof(f29866,plain,
( spl0_2311
<=> ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).
fof(f7049,plain,
( spl0_724
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f28616,plain,
( ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0)
| ~ spl0_724
| ~ spl0_2249 ),
inference(superposition,[],[f7050,f28503]) ).
fof(f7050,plain,
( ! [X1] : c_UNIV = c_Union(c_UNIV,X1)
| ~ spl0_724 ),
inference(avatar_component_clause,[],[f7049]) ).
fof(f29851,plain,
( spl0_2310
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2305 ),
inference(avatar_split_clause,[],[f29748,f29745,f12080,f9173,f29849]) ).
fof(f29849,plain,
( spl0_2310
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f29745,plain,
( spl0_2305
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2305])]) ).
fof(f29748,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2305 ),
inference(forward_demodulation,[],[f29746,f13149]) ).
fof(f29746,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2305 ),
inference(avatar_component_clause,[],[f29745]) ).
fof(f29847,plain,
( spl0_2309
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2304 ),
inference(avatar_split_clause,[],[f29743,f29740,f12080,f9169,f29845]) ).
fof(f29845,plain,
( spl0_2309
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f29740,plain,
( spl0_2304
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f29743,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2304 ),
inference(forward_demodulation,[],[f29741,f13150]) ).
fof(f29741,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2304 ),
inference(avatar_component_clause,[],[f29740]) ).
fof(f29843,plain,
( spl0_2308
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2303 ),
inference(avatar_split_clause,[],[f29738,f29735,f12080,f9173,f29841]) ).
fof(f29841,plain,
( spl0_2308
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).
fof(f29735,plain,
( spl0_2303
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f29738,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2303 ),
inference(forward_demodulation,[],[f29736,f13149]) ).
fof(f29736,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2303 ),
inference(avatar_component_clause,[],[f29735]) ).
fof(f29839,plain,
( spl0_2307
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2302 ),
inference(avatar_split_clause,[],[f29733,f29730,f12080,f9169,f29837]) ).
fof(f29837,plain,
( spl0_2307
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).
fof(f29730,plain,
( spl0_2302
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f29733,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2302 ),
inference(forward_demodulation,[],[f29731,f13150]) ).
fof(f29731,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2302 ),
inference(avatar_component_clause,[],[f29730]) ).
fof(f29752,plain,
( spl0_2306
| ~ spl0_723
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28615,f28501,f7045,f29750]) ).
fof(f29750,plain,
( spl0_2306
<=> ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).
fof(f7045,plain,
( spl0_723
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f28615,plain,
( ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0)
| ~ spl0_723
| ~ spl0_2249 ),
inference(superposition,[],[f7046,f28503]) ).
fof(f7046,plain,
( ! [X1] : c_UNIV = c_Pow(c_UNIV,X1)
| ~ spl0_723 ),
inference(avatar_component_clause,[],[f7045]) ).
fof(f29747,plain,
spl0_2305,
inference(avatar_split_clause,[],[f3216,f29745]) ).
fof(f3216,plain,
! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1446,f1456]) ).
fof(f1456,axiom,
! [X49,X5] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f1446,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f29742,plain,
spl0_2304,
inference(avatar_split_clause,[],[f3215,f29740]) ).
fof(f3215,plain,
! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1436,f1456]) ).
fof(f1436,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f29737,plain,
spl0_2303,
inference(avatar_split_clause,[],[f3214,f29735]) ).
fof(f3214,plain,
! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1443,f1456]) ).
fof(f1443,axiom,
! [X11,X47] :
( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f29732,plain,
spl0_2302,
inference(avatar_split_clause,[],[f3213,f29730]) ).
fof(f3213,plain,
! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1433,f1456]) ).
fof(f1433,axiom,
! [X11,X47] :
( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f29728,plain,
spl0_2301,
inference(avatar_split_clause,[],[f1622,f29726]) ).
fof(f29726,plain,
( spl0_2301
<=> ! [X62,X3,X0,X5,X1] :
( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f1622,axiom,
! [X3,X0,X1,X62,X5] :
( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
fof(f29724,plain,
spl0_2300,
inference(avatar_split_clause,[],[f1505,f29722]) ).
fof(f29722,plain,
( spl0_2300
<=> ! [X23,X0,X5,X25,X1] :
( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f1505,axiom,
! [X0,X1,X5,X25,X23] :
( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
fof(f29720,plain,
spl0_2299,
inference(avatar_split_clause,[],[f1188,f29718]) ).
fof(f29718,plain,
( spl0_2299
<=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f1188,axiom,
! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f29716,plain,
spl0_2298,
inference(avatar_split_clause,[],[f1187,f29714]) ).
fof(f29714,plain,
( spl0_2298
<=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).
fof(f1187,axiom,
! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f29687,plain,
( spl0_2297
| ~ spl0_721
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28614,f28501,f7037,f29685]) ).
fof(f29685,plain,
( spl0_2297
<=> ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2297])]) ).
fof(f7037,plain,
( spl0_721
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f28614,plain,
( ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0)
| ~ spl0_721
| ~ spl0_2249 ),
inference(superposition,[],[f7038,f28503]) ).
fof(f7038,plain,
( ! [X1] : c_emptyset = c_Inter(c_UNIV,X1)
| ~ spl0_721 ),
inference(avatar_component_clause,[],[f7037]) ).
fof(f29683,plain,
( spl0_2296
| ~ spl0_1786
| ~ spl0_2294 ),
inference(avatar_split_clause,[],[f29675,f29672,f17345,f29681]) ).
fof(f29681,plain,
( spl0_2296
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).
fof(f29672,plain,
( spl0_2294
<=> ! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f29675,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1786
| ~ spl0_2294 ),
inference(forward_demodulation,[],[f29673,f17347]) ).
fof(f29673,plain,
( ! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2294 ),
inference(avatar_component_clause,[],[f29672]) ).
fof(f29679,plain,
spl0_2295,
inference(avatar_split_clause,[],[f1705,f29677]) ).
fof(f29677,plain,
( spl0_2295
<=> ! [X43,X23,X25,X2,X1] :
( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
| ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).
fof(f1705,axiom,
! [X2,X1,X25,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
| ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f29674,plain,
spl0_2294,
inference(avatar_split_clause,[],[f1449,f29672]) ).
fof(f1449,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f29521,plain,
( spl0_2293
| ~ spl0_684
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28613,f28501,f6866,f29519]) ).
fof(f29519,plain,
( spl0_2293
<=> ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).
fof(f6866,plain,
( spl0_684
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f28613,plain,
( ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0)
| ~ spl0_684
| ~ spl0_2249 ),
inference(superposition,[],[f6867,f28503]) ).
fof(f6867,plain,
( ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1)
| ~ spl0_684 ),
inference(avatar_component_clause,[],[f6866]) ).
fof(f29517,plain,
spl0_2292,
inference(avatar_split_clause,[],[f1619,f29515]) ).
fof(f29515,plain,
( spl0_2292
<=> ! [X18,X3,X0,X5,X27,X1] :
( X18 = X27
| c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2292])]) ).
fof(f1619,axiom,
! [X3,X0,X18,X1,X27,X5] :
( X18 = X27
| c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
fof(f29513,plain,
spl0_2291,
inference(avatar_split_clause,[],[f1500,f29511]) ).
fof(f29511,plain,
( spl0_2291
<=> ! [X3,X23,X0,X5,X25,X1] :
( X0 = X3
| c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).
fof(f1500,axiom,
! [X3,X0,X1,X5,X25,X23] :
( X0 = X3
| c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
fof(f29509,plain,
spl0_2290,
inference(avatar_split_clause,[],[f1383,f29507]) ).
fof(f29507,plain,
( spl0_2290
<=> ! [X47,X0,X14,X3] :
( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
| c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2290])]) ).
fof(f1383,axiom,
! [X3,X0,X47,X14] :
( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
| c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
fof(f29505,plain,
spl0_2289,
inference(avatar_split_clause,[],[f1382,f29503]) ).
fof(f29503,plain,
( spl0_2289
<=> ! [X47,X0,X14,X3] :
( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
| ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).
fof(f1382,axiom,
! [X3,X0,X47,X14] :
( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
| ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
fof(f29501,plain,
spl0_2288,
inference(avatar_split_clause,[],[f85,f29499]) ).
fof(f29499,plain,
( spl0_2288
<=> ! [X31,X4,X18,X6,X5,X27,X2,X1] :
( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
| ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
| c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f85,axiom,
! [X2,X31,X18,X1,X6,X27,X4,X5] :
( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
| ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
| c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f29497,plain,
spl0_2287,
inference(avatar_split_clause,[],[f53,f29495]) ).
fof(f29495,plain,
( spl0_2287
<=> ! [X5,X3,X23,X25,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f53,axiom,
! [X3,X1,X5,X25,X23] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f29493,plain,
spl0_2286,
inference(avatar_split_clause,[],[f50,f29491]) ).
fof(f29491,plain,
( spl0_2286
<=> ! [X5,X3,X23,X25,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f50,axiom,
! [X3,X1,X5,X25,X23] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f29478,plain,
( ~ spl0_2285
| spl0_677
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28612,f28501,f6837,f29475]) ).
fof(f29475,plain,
( spl0_2285
<=> c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f6837,plain,
( spl0_677
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f28612,plain,
( ~ c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_677
| ~ spl0_2249 ),
inference(superposition,[],[f6839,f28503]) ).
fof(f6839,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_677 ),
inference(avatar_component_clause,[],[f6837]) ).
fof(f29444,plain,
( spl0_2284
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2279 ),
inference(avatar_split_clause,[],[f29405,f29402,f12080,f9173,f29442]) ).
fof(f29442,plain,
( spl0_2284
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f29402,plain,
( spl0_2279
<=> ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f29405,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2279 ),
inference(forward_demodulation,[],[f29403,f13149]) ).
fof(f29403,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2279 ),
inference(avatar_component_clause,[],[f29402]) ).
fof(f29440,plain,
( spl0_2283
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2278 ),
inference(avatar_split_clause,[],[f29387,f29384,f12080,f9173,f29438]) ).
fof(f29438,plain,
( spl0_2283
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).
fof(f29384,plain,
( spl0_2278
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).
fof(f29387,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2278 ),
inference(forward_demodulation,[],[f29385,f13149]) ).
fof(f29385,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2278 ),
inference(avatar_component_clause,[],[f29384]) ).
fof(f29436,plain,
( spl0_2282
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2277 ),
inference(avatar_split_clause,[],[f29382,f29379,f12080,f9169,f29434]) ).
fof(f29434,plain,
( spl0_2282
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f29379,plain,
( spl0_2277
<=> ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f29382,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2277 ),
inference(forward_demodulation,[],[f29380,f13150]) ).
fof(f29380,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2277 ),
inference(avatar_component_clause,[],[f29379]) ).
fof(f29432,plain,
( spl0_2281
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f29377,f29374,f12080,f9169,f29430]) ).
fof(f29430,plain,
( spl0_2281
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f29374,plain,
( spl0_2276
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f29377,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2276 ),
inference(forward_demodulation,[],[f29375,f13150]) ).
fof(f29375,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2276 ),
inference(avatar_component_clause,[],[f29374]) ).
fof(f29409,plain,
spl0_2280,
inference(avatar_split_clause,[],[f1502,f29407]) ).
fof(f29407,plain,
( spl0_2280
<=> ! [X5,X23,X0,X3,X25,X1] :
( X0 = X3
| c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).
fof(f1502,axiom,
! [X3,X0,X1,X5,X25,X23] :
( X0 = X3
| c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
fof(f29404,plain,
spl0_2279,
inference(avatar_split_clause,[],[f1448,f29402]) ).
fof(f1448,axiom,
! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f29386,plain,
spl0_2278,
inference(avatar_split_clause,[],[f1444,f29384]) ).
fof(f1444,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f29381,plain,
spl0_2277,
inference(avatar_split_clause,[],[f1438,f29379]) ).
fof(f1438,axiom,
! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f29376,plain,
spl0_2276,
inference(avatar_split_clause,[],[f1434,f29374]) ).
fof(f1434,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f29372,plain,
spl0_2275,
inference(avatar_split_clause,[],[f55,f29370]) ).
fof(f29370,plain,
( spl0_2275
<=> ! [X3,X23,X5,X25,X1] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(f55,axiom,
! [X3,X1,X5,X25,X23] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f29368,plain,
spl0_2274,
inference(avatar_split_clause,[],[f52,f29366]) ).
fof(f29366,plain,
( spl0_2274
<=> ! [X3,X23,X5,X25,X1] :
( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f52,axiom,
! [X3,X1,X5,X25,X23] :
( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f29224,plain,
spl0_2273,
inference(avatar_split_clause,[],[f1470,f29222]) ).
fof(f29222,plain,
( spl0_2273
<=> ! [X11,X27,X47] :
( c_Numeral_Obit_OB0 = X27
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f1470,axiom,
! [X11,X47,X27] :
( c_Numeral_Obit_OB0 = X27
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f29220,plain,
( spl0_2272
| ~ spl0_114
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28611,f28501,f3807,f29218]) ).
fof(f29218,plain,
( spl0_2272
<=> ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f3807,plain,
( spl0_114
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f28611,plain,
( ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1)
| ~ spl0_114
| ~ spl0_2249 ),
inference(superposition,[],[f3808,f28503]) ).
fof(f3808,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f3807]) ).
fof(f29216,plain,
spl0_2271,
inference(avatar_split_clause,[],[f83,f29214]) ).
fof(f29214,plain,
( spl0_2271
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f83,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f29212,plain,
spl0_2270,
inference(avatar_split_clause,[],[f82,f29210]) ).
fof(f29210,plain,
( spl0_2270
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f82,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f29208,plain,
spl0_2269,
inference(avatar_split_clause,[],[f20,f29206]) ).
fof(f29206,plain,
( spl0_2269
<=> ! [X13,X14,X12,X2,X1] :
( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f20,axiom,
! [X2,X1,X14,X12,X13] :
( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f29068,plain,
spl0_2268,
inference(avatar_split_clause,[],[f3120,f29066]) ).
fof(f29066,plain,
( spl0_2268
<=> ! [X15,X47] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f3120,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3119,f2156]) ).
fof(f3119,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3118,f2878]) ).
fof(f2878,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2101,f2544,f2544]) ).
fof(f2544,axiom,
! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f2101,axiom,
! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3118,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2931,f3084]) ).
fof(f3084,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3083,f2156]) ).
fof(f3083,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3082,f2154]) ).
fof(f3082,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2899,f2156]) ).
fof(f2899,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1882,f2544,f2544]) ).
fof(f1882,axiom,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f2931,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1880,f2544,f2544,f2544]) ).
fof(f1880,axiom,
! [X47,X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f29046,plain,
( spl0_2267
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2266 ),
inference(avatar_split_clause,[],[f29042,f29038,f20187,f10767,f10447,f6846,f5911,f29044]) ).
fof(f29044,plain,
( spl0_2267
<=> ! [X15,X47] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f29038,plain,
( spl0_2266
<=> ! [X15,X47] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f29042,plain,
( ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2266 ),
inference(forward_demodulation,[],[f29041,f20188]) ).
fof(f29041,plain,
( ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2266 ),
inference(forward_demodulation,[],[f29039,f11726]) ).
fof(f29039,plain,
( ! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ spl0_2266 ),
inference(avatar_component_clause,[],[f29038]) ).
fof(f29040,plain,
spl0_2266,
inference(avatar_split_clause,[],[f3117,f29038]) ).
fof(f3117,plain,
! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3116,f2156]) ).
fof(f3116,plain,
! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3115,f2878]) ).
fof(f3115,plain,
! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2930,f3084]) ).
fof(f2930,plain,
! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1879,f2544,f2544,f2544]) ).
fof(f1879,axiom,
! [X47,X15] : c_div(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f29036,plain,
spl0_2265,
inference(avatar_split_clause,[],[f3008,f29034]) ).
fof(f29034,plain,
( spl0_2265
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f3008,plain,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2724,f2716]) ).
fof(f2716,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f2724,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f29032,plain,
spl0_2264,
inference(avatar_split_clause,[],[f3007,f29030]) ).
fof(f29030,plain,
( spl0_2264
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f3007,plain,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2721,f2716]) ).
fof(f2721,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f29028,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1621,f29026]) ).
fof(f29026,plain,
( spl0_2263
<=> ! [X5,X18,X3,X0,X27,X1] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f1621,axiom,
! [X3,X0,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f29024,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1460,f29022]) ).
fof(f29022,plain,
( spl0_2262
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f1460,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f29020,plain,
spl0_2261,
inference(avatar_split_clause,[],[f19,f29018]) ).
fof(f29018,plain,
( spl0_2261
<=> ! [X13,X14,X12,X2,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f19,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f29016,plain,
spl0_2260,
inference(avatar_split_clause,[],[f18,f29014]) ).
fof(f29014,plain,
( spl0_2260
<=> ! [X14,X13,X12,X2,X1] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f18,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f28965,plain,
( spl0_2259
| ~ spl0_1523
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f28626,f28501,f13566,f28963]) ).
fof(f28963,plain,
( spl0_2259
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f13566,plain,
( spl0_1523
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f28626,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0)
| ~ spl0_1523
| ~ spl0_2249 ),
inference(superposition,[],[f13567,f28503]) ).
fof(f13567,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_1523 ),
inference(avatar_component_clause,[],[f13566]) ).
fof(f28937,plain,
spl0_2258,
inference(avatar_split_clause,[],[f2979,f28935]) ).
fof(f28935,plain,
( spl0_2258
<=> ! [X47,X0,X23,X1] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f2979,plain,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ),
inference(definition_unfolding,[],[f1768,f1766,f1766]) ).
fof(f1766,axiom,
! [X21,X1,X26] : c_List_Osublist(X26,c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Otake(X21,X26,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f1768,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f28933,plain,
spl0_2257,
inference(avatar_split_clause,[],[f17,f28931]) ).
fof(f28931,plain,
( spl0_2257
<=> ! [X13,X14,X12,X2,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f17,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f28610,plain,
spl0_2256,
inference(avatar_split_clause,[],[f2927,f28608]) ).
fof(f28608,plain,
( spl0_2256
<=> ! [X21,X23,X25,X1] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f2927,plain,
! [X21,X1,X25,X23] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1),
inference(definition_unfolding,[],[f1771,f1766,f1766,f1766]) ).
fof(f1771,axiom,
! [X21,X1,X25,X23] : c_List_Otake(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Otake(X21,X23,X1),c_List_Otake(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f28606,plain,
spl0_2255,
inference(avatar_split_clause,[],[f1998,f28604]) ).
fof(f28604,plain,
( spl0_2255
<=> ! [X2,X27,X18,X47] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).
fof(f1998,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f28602,plain,
spl0_2254,
inference(avatar_split_clause,[],[f1992,f28600]) ).
fof(f28600,plain,
( spl0_2254
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).
fof(f1992,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f28598,plain,
spl0_2253,
inference(avatar_split_clause,[],[f1986,f28596]) ).
fof(f28596,plain,
( spl0_2253
<=> ! [X2,X27,X18,X47] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f1986,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f28594,plain,
spl0_2252,
inference(avatar_split_clause,[],[f1980,f28592]) ).
fof(f28592,plain,
( spl0_2252
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f1980,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f28590,plain,
spl0_2251,
inference(avatar_split_clause,[],[f115,f28588]) ).
fof(f28588,plain,
( spl0_2251
<=> ! [X13,X14,X12,X2,X1] :
( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f115,axiom,
! [X2,X1,X14,X12,X13] :
( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f28586,plain,
spl0_2250,
inference(avatar_split_clause,[],[f84,f28584]) ).
fof(f28584,plain,
( spl0_2250
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f84,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f28504,plain,
( spl0_2249
| ~ spl0_799
| ~ spl0_2235 ),
inference(avatar_split_clause,[],[f28428,f27636,f7366,f28501]) ).
fof(f28428,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_799
| ~ spl0_2235 ),
inference(superposition,[],[f27637,f7367]) ).
fof(f28493,plain,
( spl0_2248
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2247 ),
inference(avatar_split_clause,[],[f28489,f28486,f20187,f7301,f7265,f28491]) ).
fof(f28491,plain,
( spl0_2248
<=> ! [X18,X21,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f28486,plain,
( spl0_2247
<=> ! [X18,X21,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f28489,plain,
( ! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2247 ),
inference(forward_demodulation,[],[f28487,f20270]) ).
fof(f28487,plain,
( ! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_2247 ),
inference(avatar_component_clause,[],[f28486]) ).
fof(f28488,plain,
spl0_2247,
inference(avatar_split_clause,[],[f3210,f28486]) ).
fof(f3210,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f3209,f2156]) ).
fof(f3209,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f3208,f2154]) ).
fof(f3208,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f1875,f2156]) ).
fof(f1875,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f28484,plain,
spl0_2246,
inference(avatar_split_clause,[],[f2995,f28482]) ).
fof(f28482,plain,
( spl0_2246
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f2995,plain,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2723,f2716]) ).
fof(f2723,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f28480,plain,
spl0_2245,
inference(avatar_split_clause,[],[f2994,f28478]) ).
fof(f28478,plain,
( spl0_2245
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f2994,plain,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f2720,f2716]) ).
fof(f2720,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f28476,plain,
spl0_2244,
inference(avatar_split_clause,[],[f2900,f28474]) ).
fof(f28474,plain,
( spl0_2244
<=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f2900,plain,
! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1),
inference(definition_unfolding,[],[f2711,f2716,f2716,f2716]) ).
fof(f2711,axiom,
! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X85,X1),c_Transitive__Closure_Ortrancl(X85,X1),X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f28472,plain,
spl0_2243,
inference(avatar_split_clause,[],[f16,f28470]) ).
fof(f28470,plain,
( spl0_2243
<=> ! [X9,X13,X7,X12,X2,X1] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f16,axiom,
! [X2,X1,X9,X7,X12,X13] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f28427,plain,
( spl0_2242
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2238 ),
inference(avatar_split_clause,[],[f27661,f27658,f12080,f9173,f28425]) ).
fof(f28425,plain,
( spl0_2242
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f27658,plain,
( spl0_2238
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).
fof(f27661,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2238 ),
inference(forward_demodulation,[],[f27659,f13149]) ).
fof(f27659,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2238 ),
inference(avatar_component_clause,[],[f27658]) ).
fof(f28423,plain,
( spl0_2241
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2237 ),
inference(avatar_split_clause,[],[f27656,f27653,f12080,f9169,f28421]) ).
fof(f28421,plain,
( spl0_2241
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f27653,plain,
( spl0_2237
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f27656,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2237 ),
inference(forward_demodulation,[],[f27654,f13150]) ).
fof(f27654,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2237 ),
inference(avatar_component_clause,[],[f27653]) ).
fof(f28195,plain,
( spl0_2240
| ~ spl0_802
| ~ spl0_1476
| ~ spl0_1742
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f27537,f27471,f16665,f12139,f7378,f28192]) ).
fof(f28192,plain,
( spl0_2240
<=> c_IntDef_ONats = c_uminus(c_emptyset,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f7378,plain,
( spl0_802
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f12139,plain,
( spl0_1476
<=> ! [X13,X12,X1] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f27471,plain,
( spl0_2218
<=> ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f27537,plain,
( c_IntDef_ONats = c_uminus(c_emptyset,tc_set(tc_nat))
| ~ spl0_802
| ~ spl0_1476
| ~ spl0_1742
| ~ spl0_2218 ),
inference(forward_demodulation,[],[f27525,f27535]) ).
fof(f27535,plain,
( ! [X0] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_802
| ~ spl0_1476
| ~ spl0_2218 ),
inference(forward_demodulation,[],[f27520,f7379]) ).
fof(f7379,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7378]) ).
fof(f27520,plain,
( ! [X0] : c_union(X0,c_IntDef_ONats,tc_nat) = c_union(c_emptyset,c_IntDef_ONats,tc_nat)
| ~ spl0_1476
| ~ spl0_2218 ),
inference(superposition,[],[f12140,f27472]) ).
fof(f27472,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_2218 ),
inference(avatar_component_clause,[],[f27471]) ).
fof(f12140,plain,
( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
| ~ spl0_1476 ),
inference(avatar_component_clause,[],[f12139]) ).
fof(f27525,plain,
( ! [X0] : c_uminus(c_emptyset,tc_set(tc_nat)) = c_union(c_uminus(X0,tc_set(tc_nat)),c_IntDef_ONats,tc_nat)
| ~ spl0_1742
| ~ spl0_2218 ),
inference(superposition,[],[f16666,f27472]) ).
fof(f27810,plain,
( spl0_2239
| ~ spl0_803
| ~ spl0_1477
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f27536,f27471,f12143,f7382,f27808]) ).
fof(f27808,plain,
( spl0_2239
<=> ! [X0] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f12143,plain,
( spl0_1477
<=> ! [X13,X12,X1] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f27536,plain,
( ! [X0] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,tc_nat)
| ~ spl0_803
| ~ spl0_1477
| ~ spl0_2218 ),
inference(forward_demodulation,[],[f27521,f7383]) ).
fof(f27521,plain,
( ! [X0] : c_union(c_IntDef_ONats,X0,tc_nat) = c_union(c_IntDef_ONats,c_emptyset,tc_nat)
| ~ spl0_1477
| ~ spl0_2218 ),
inference(superposition,[],[f12144,f27472]) ).
fof(f12144,plain,
( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
| ~ spl0_1477 ),
inference(avatar_component_clause,[],[f12143]) ).
fof(f27660,plain,
spl0_2238,
inference(avatar_split_clause,[],[f3167,f27658]) ).
fof(f3167,plain,
! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1445,f1456]) ).
fof(f1445,axiom,
! [X11] :
( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f27655,plain,
spl0_2237,
inference(avatar_split_clause,[],[f3166,f27653]) ).
fof(f3166,plain,
! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1435,f1456]) ).
fof(f1435,axiom,
! [X11] :
( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f27642,plain,
( spl0_2236
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2234 ),
inference(avatar_split_clause,[],[f27634,f27630,f20187,f10767,f10447,f7301,f7265,f6846,f5911,f27640]) ).
fof(f27640,plain,
( spl0_2236
<=> ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
fof(f27630,plain,
( spl0_2234
<=> ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f27634,plain,
( ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2234 ),
inference(forward_demodulation,[],[f27633,f11726]) ).
fof(f27633,plain,
( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2234 ),
inference(forward_demodulation,[],[f27631,f20270]) ).
fof(f27631,plain,
( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2234 ),
inference(avatar_component_clause,[],[f27630]) ).
fof(f27638,plain,
( spl0_2235
| ~ spl0_802
| ~ spl0_1476
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f27535,f27471,f12139,f7378,f27636]) ).
fof(f27632,plain,
spl0_2234,
inference(avatar_split_clause,[],[f3114,f27630]) ).
fof(f3114,plain,
! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3113,f3084]) ).
fof(f3113,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3112,f2156]) ).
fof(f3112,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3111,f2154]) ).
fof(f3111,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2929,f2156]) ).
fof(f2929,plain,
! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1884,f2544,f2544,f2544]) ).
fof(f1884,axiom,
! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f27583,plain,
( spl0_2233
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2232 ),
inference(avatar_split_clause,[],[f27579,f27575,f20187,f10767,f10447,f6846,f5911,f27581]) ).
fof(f27581,plain,
( spl0_2233
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f27575,plain,
( spl0_2232
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f27579,plain,
( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2232 ),
inference(forward_demodulation,[],[f27578,f20188]) ).
fof(f27578,plain,
( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2232 ),
inference(forward_demodulation,[],[f27576,f11726]) ).
fof(f27576,plain,
( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat)
| ~ spl0_2232 ),
inference(avatar_component_clause,[],[f27575]) ).
fof(f27577,plain,
spl0_2232,
inference(avatar_split_clause,[],[f3106,f27575]) ).
fof(f3106,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3105,f2156]) ).
fof(f3105,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3104,f2878]) ).
fof(f3104,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2924,f3084]) ).
fof(f2924,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1977,f2544,f2544,f2544]) ).
fof(f1977,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f27561,plain,
( spl0_2231
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2230 ),
inference(avatar_split_clause,[],[f27557,f27553,f20187,f10767,f10447,f6846,f5911,f27559]) ).
fof(f27559,plain,
( spl0_2231
<=> ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f27553,plain,
( spl0_2230
<=> ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f27557,plain,
( ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2230 ),
inference(forward_demodulation,[],[f27556,f20188]) ).
fof(f27556,plain,
( ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2230 ),
inference(forward_demodulation,[],[f27554,f11726]) ).
fof(f27554,plain,
( ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat)
| ~ spl0_2230 ),
inference(avatar_component_clause,[],[f27553]) ).
fof(f27555,plain,
spl0_2230,
inference(avatar_split_clause,[],[f3103,f27553]) ).
fof(f3103,plain,
! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3102,f2156]) ).
fof(f3102,plain,
! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3101,f2878]) ).
fof(f3101,plain,
! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2923,f3084]) ).
fof(f2923,plain,
! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1885,f2544,f2544,f2544]) ).
fof(f1885,axiom,
! [X21,X15] : c_div(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f27547,plain,
( spl0_2229
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2228 ),
inference(avatar_split_clause,[],[f27543,f27539,f20187,f10767,f10447,f6846,f5911,f27545]) ).
fof(f27545,plain,
( spl0_2229
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f27539,plain,
( spl0_2228
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).
fof(f27543,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2228 ),
inference(forward_demodulation,[],[f27542,f11726]) ).
fof(f27542,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
| ~ spl0_1935
| ~ spl0_2228 ),
inference(forward_demodulation,[],[f27540,f20188]) ).
fof(f27540,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
| ~ spl0_2228 ),
inference(avatar_component_clause,[],[f27539]) ).
fof(f27541,plain,
spl0_2228,
inference(avatar_split_clause,[],[f3100,f27539]) ).
fof(f3100,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2922,f3084]) ).
fof(f2922,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1204,f2544,f2544,f2544]) ).
fof(f1204,axiom,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f27511,plain,
( spl0_2227
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2226 ),
inference(avatar_split_clause,[],[f27507,f27503,f20187,f10767,f10447,f6846,f5911,f27509]) ).
fof(f27509,plain,
( spl0_2227
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).
fof(f27503,plain,
( spl0_2226
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f27507,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1935
| ~ spl0_2226 ),
inference(forward_demodulation,[],[f27506,f11726]) ).
fof(f27506,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
| ~ spl0_1935
| ~ spl0_2226 ),
inference(forward_demodulation,[],[f27504,f20188]) ).
fof(f27504,plain,
( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
| ~ spl0_2226 ),
inference(avatar_component_clause,[],[f27503]) ).
fof(f27505,plain,
spl0_2226,
inference(avatar_split_clause,[],[f3099,f27503]) ).
fof(f3099,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2921,f3084]) ).
fof(f2921,plain,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1205,f2544,f2544,f2544]) ).
fof(f1205,axiom,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f27501,plain,
spl0_2225,
inference(avatar_split_clause,[],[f2003,f27499]) ).
fof(f27499,plain,
( spl0_2225
<=> ! [X4,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f2003,axiom,
! [X2,X47,X27,X4] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f27497,plain,
spl0_2224,
inference(avatar_split_clause,[],[f2002,f27495]) ).
fof(f27495,plain,
( spl0_2224
<=> ! [X4,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f2002,axiom,
! [X2,X47,X27,X4] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f27493,plain,
spl0_2223,
inference(avatar_split_clause,[],[f2000,f27491]) ).
fof(f27491,plain,
( spl0_2223
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f2000,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f27489,plain,
spl0_2222,
inference(avatar_split_clause,[],[f1999,f27487]) ).
fof(f27487,plain,
( spl0_2222
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f1999,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f27485,plain,
spl0_2221,
inference(avatar_split_clause,[],[f1997,f27483]) ).
fof(f27483,plain,
( spl0_2221
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f1997,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f27481,plain,
spl0_2220,
inference(avatar_split_clause,[],[f1996,f27479]) ).
fof(f27479,plain,
( spl0_2220
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f1996,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f27477,plain,
spl0_2219,
inference(avatar_split_clause,[],[f1994,f27475]) ).
fof(f27475,plain,
( spl0_2219
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f1994,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f27473,plain,
( spl0_2218
| ~ spl0_1363
| ~ spl0_1394 ),
inference(avatar_split_clause,[],[f11463,f10832,f10667,f27471]) ).
fof(f10832,plain,
( spl0_1394
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f11463,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1363
| ~ spl0_1394 ),
inference(resolution,[],[f10668,f10833]) ).
fof(f10833,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1394 ),
inference(avatar_component_clause,[],[f10832]) ).
fof(f27469,plain,
spl0_2217,
inference(avatar_split_clause,[],[f1993,f27467]) ).
fof(f27467,plain,
( spl0_2217
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f1993,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f27465,plain,
spl0_2216,
inference(avatar_split_clause,[],[f1991,f27463]) ).
fof(f27463,plain,
( spl0_2216
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f1991,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f27461,plain,
spl0_2215,
inference(avatar_split_clause,[],[f1990,f27459]) ).
fof(f27459,plain,
( spl0_2215
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f1990,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f27457,plain,
spl0_2214,
inference(avatar_split_clause,[],[f1988,f27455]) ).
fof(f27455,plain,
( spl0_2214
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f1988,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f27453,plain,
spl0_2213,
inference(avatar_split_clause,[],[f1987,f27451]) ).
fof(f27451,plain,
( spl0_2213
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f1987,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f27449,plain,
spl0_2212,
inference(avatar_split_clause,[],[f1985,f27447]) ).
fof(f27447,plain,
( spl0_2212
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f1985,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f27445,plain,
spl0_2211,
inference(avatar_split_clause,[],[f1984,f27443]) ).
fof(f27443,plain,
( spl0_2211
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f1984,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f27441,plain,
spl0_2210,
inference(avatar_split_clause,[],[f1982,f27439]) ).
fof(f27439,plain,
( spl0_2210
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f1982,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f27437,plain,
spl0_2209,
inference(avatar_split_clause,[],[f1981,f27435]) ).
fof(f27435,plain,
( spl0_2209
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f1981,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f27433,plain,
spl0_2208,
inference(avatar_split_clause,[],[f1979,f27431]) ).
fof(f27431,plain,
( spl0_2208
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f1979,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f27428,plain,
spl0_2207,
inference(avatar_split_clause,[],[f1978,f27426]) ).
fof(f27426,plain,
( spl0_2207
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f1978,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f27424,plain,
spl0_2206,
inference(avatar_split_clause,[],[f1948,f27422]) ).
fof(f27422,plain,
( spl0_2206
<=> ! [X18,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f1948,axiom,
! [X2,X18,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f27420,plain,
spl0_2205,
inference(avatar_split_clause,[],[f1947,f27418]) ).
fof(f27418,plain,
( spl0_2205
<=> ! [X18,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f1947,axiom,
! [X2,X18,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f27416,plain,
spl0_2204,
inference(avatar_split_clause,[],[f1862,f27414]) ).
fof(f27414,plain,
( spl0_2204
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f1862,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f27412,plain,
spl0_2203,
inference(avatar_split_clause,[],[f117,f27410]) ).
fof(f27410,plain,
( spl0_2203
<=> ! [X2,X14,X13,X12,X1] :
( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f117,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f27408,plain,
spl0_2202,
inference(avatar_split_clause,[],[f116,f27406]) ).
fof(f27406,plain,
( spl0_2202
<=> ! [X13,X14,X12,X2,X1] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f116,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f27404,plain,
spl0_2201,
inference(avatar_split_clause,[],[f13,f27402]) ).
fof(f27402,plain,
( spl0_2201
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f13,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f27244,plain,
( spl0_2200
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2199 ),
inference(avatar_split_clause,[],[f27240,f27237,f10767,f10447,f6846,f5911,f27242]) ).
fof(f27242,plain,
( spl0_2200
<=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f27237,plain,
( spl0_2199
<=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f27240,plain,
( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2199 ),
inference(forward_demodulation,[],[f27238,f11726]) ).
fof(f27238,plain,
( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
| ~ spl0_2199 ),
inference(avatar_component_clause,[],[f27237]) ).
fof(f27239,plain,
spl0_2199,
inference(avatar_split_clause,[],[f2928,f27237]) ).
fof(f2928,plain,
! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1208,f2544]) ).
fof(f1208,axiom,
! [X2,X1,X9,X16,X7] : c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f27235,plain,
spl0_2198,
inference(avatar_split_clause,[],[f2331,f27233]) ).
fof(f27233,plain,
( spl0_2198
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f2331,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f27231,plain,
spl0_2197,
inference(avatar_split_clause,[],[f2321,f27229]) ).
fof(f27229,plain,
( spl0_2197
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f2321,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f27227,plain,
spl0_2196,
inference(avatar_split_clause,[],[f1469,f27225]) ).
fof(f27225,plain,
( spl0_2196
<=> ! [X27,X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f1469,axiom,
! [X11,X47,X27] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
fof(f27223,plain,
spl0_2195,
inference(avatar_split_clause,[],[f77,f27221]) ).
fof(f77,axiom,
! [X2,X29,X1,X5] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f26823,plain,
spl0_2194,
inference(avatar_split_clause,[],[f3049,f26821]) ).
fof(f26821,plain,
( spl0_2194
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f3049,plain,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1840,f2129]) ).
fof(f2129,axiom,
! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f1840,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f26819,plain,
spl0_2193,
inference(avatar_split_clause,[],[f3048,f26817]) ).
fof(f26817,plain,
( spl0_2193
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f3048,plain,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1839,f2129]) ).
fof(f1839,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f26815,plain,
spl0_2192,
inference(avatar_split_clause,[],[f3047,f26813]) ).
fof(f26813,plain,
( spl0_2192
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f3047,plain,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1842,f2129]) ).
fof(f1842,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f26811,plain,
spl0_2191,
inference(avatar_split_clause,[],[f3046,f26809]) ).
fof(f26809,plain,
( spl0_2191
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f3046,plain,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1844,f2129]) ).
fof(f1844,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f26807,plain,
spl0_2190,
inference(avatar_split_clause,[],[f3044,f26805]) ).
fof(f26805,plain,
( spl0_2190
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f3044,plain,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1846,f2129]) ).
fof(f1846,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f26803,plain,
spl0_2189,
inference(avatar_split_clause,[],[f2001,f26801]) ).
fof(f26801,plain,
( spl0_2189
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f2001,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f26799,plain,
spl0_2188,
inference(avatar_split_clause,[],[f1995,f26797]) ).
fof(f26797,plain,
( spl0_2188
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f1995,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f26785,plain,
spl0_2187,
inference(avatar_split_clause,[],[f1989,f26783]) ).
fof(f26783,plain,
( spl0_2187
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f1989,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f26781,plain,
spl0_2186,
inference(avatar_split_clause,[],[f1983,f26779]) ).
fof(f26779,plain,
( spl0_2186
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f1983,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f26777,plain,
spl0_2185,
inference(avatar_split_clause,[],[f1794,f26775]) ).
fof(f26775,plain,
( spl0_2185
<=> ! [X0,X23,X25,X2,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f1794,axiom,
! [X2,X0,X1,X25,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f26773,plain,
spl0_2184,
inference(avatar_split_clause,[],[f1793,f26771]) ).
fof(f26771,plain,
( spl0_2184
<=> ! [X0,X23,X25,X2,X1] :
( ~ c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f1793,axiom,
! [X2,X0,X1,X25,X23] :
( ~ c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f26769,plain,
spl0_2183,
inference(avatar_split_clause,[],[f1789,f26767]) ).
fof(f26767,plain,
( spl0_2183
<=> ! [X3,X0,X23,X25,X2,X1] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f1789,axiom,
! [X2,X3,X0,X1,X25,X23] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f26765,plain,
spl0_2182,
inference(avatar_split_clause,[],[f1616,f26763]) ).
fof(f26763,plain,
( spl0_2182
<=> ! [X5,X1,X3] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
| ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f1616,axiom,
! [X3,X1,X5] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
| ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f26761,plain,
spl0_2181,
inference(avatar_split_clause,[],[f1458,f26759]) ).
fof(f26759,plain,
( spl0_2181
<=> ! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f1458,axiom,
! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f26757,plain,
spl0_2180,
inference(avatar_split_clause,[],[f118,f26755]) ).
fof(f26755,plain,
( spl0_2180
<=> ! [X13,X14,X12,X2,X1] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f118,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f26612,plain,
spl0_2179,
inference(avatar_split_clause,[],[f3043,f26610]) ).
fof(f26610,plain,
( spl0_2179
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(X25,X1)
| c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f3043,plain,
! [X1,X25,X23] :
( ~ c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(X25,X1)
| c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
inference(definition_unfolding,[],[f1558,f2373]) ).
fof(f2373,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f1558,axiom,
! [X1,X25,X23] :
( ~ c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(X25,X1)
| c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset != c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f26608,plain,
spl0_2178,
inference(avatar_split_clause,[],[f3015,f26606]) ).
fof(f26606,plain,
( spl0_2178
<=> ! [X18,X13,X12,X1] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f3015,plain,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2679,f2373,f2373]) ).
fof(f2679,axiom,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_inter(X12,X13,X1)
| c_emptyset = c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
fof(f26604,plain,
spl0_2177,
inference(avatar_split_clause,[],[f3013,f26602]) ).
fof(f26602,plain,
( spl0_2177
<=> ! [X13,X12,X27,X1] :
( c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f3013,plain,
! [X1,X27,X12,X13] :
( c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
inference(definition_unfolding,[],[f2666,f2373,f2373]) ).
fof(f2666,axiom,
! [X1,X27,X12,X13] :
( c_in(X27,X12,X1)
| c_emptyset != c_inter(X12,X13,X1)
| c_emptyset = c_inter(X12,c_insert(X27,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
fof(f26600,plain,
spl0_2176,
inference(avatar_split_clause,[],[f2788,f26598]) ).
fof(f26598,plain,
( spl0_2176
<=> ! [X86,X91,X88] :
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f2788,axiom,
! [X91,X88,X86] :
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
fof(f26596,plain,
spl0_2175,
inference(avatar_split_clause,[],[f1792,f26594]) ).
fof(f26594,plain,
( spl0_2175
<=> ! [X59,X43,X0,X3,X2,X1] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f1792,axiom,
! [X2,X3,X0,X59,X1,X43] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f26592,plain,
spl0_2174,
inference(avatar_split_clause,[],[f1698,f26590]) ).
fof(f26590,plain,
( spl0_2174
<=> ! [X43,X23,X21,X1] :
( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f1698,axiom,
! [X21,X1,X23,X43] :
( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f26588,plain,
( ~ spl0_52
| ~ spl0_2173
| ~ spl0_859
| ~ spl0_1786 ),
inference(avatar_split_clause,[],[f21939,f17345,f7618,f26585,f3507]) ).
fof(f26585,plain,
( spl0_2173
<=> c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f7618,plain,
( spl0_859
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f21939,plain,
( ~ c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_859
| ~ spl0_1786 ),
inference(superposition,[],[f7619,f17347]) ).
fof(f7619,plain,
( ! [X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7618]) ).
fof(f26539,plain,
( spl0_2172
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_2167 ),
inference(avatar_split_clause,[],[f26107,f26104,f12291,f3507,f26537]) ).
fof(f26537,plain,
( spl0_2172
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f12291,plain,
( spl0_1509
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f26104,plain,
( spl0_2167
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f26107,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_2167 ),
inference(forward_demodulation,[],[f26105,f13579]) ).
fof(f13579,plain,
( ! [X0] : c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1509 ),
inference(resolution,[],[f12292,f3509]) ).
fof(f12292,plain,
( ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) )
| ~ spl0_1509 ),
inference(avatar_component_clause,[],[f12291]) ).
fof(f26105,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_2167 ),
inference(avatar_component_clause,[],[f26104]) ).
fof(f26338,plain,
( spl0_2171
| ~ spl0_1068
| ~ spl0_1695
| ~ spl0_1772 ),
inference(avatar_split_clause,[],[f18341,f17109,f16461,f8662,f26336]) ).
fof(f26336,plain,
( spl0_2171
<=> ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f18341,plain,
( ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) )
| ~ spl0_1068
| ~ spl0_1695
| ~ spl0_1772 ),
inference(forward_demodulation,[],[f18324,f8663]) ).
fof(f18324,plain,
( ! [X2,X0,X1] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X2,X1),c_UNIV,X1,X1)
| ~ c_in(X0,X2,X1) )
| ~ spl0_1695
| ~ spl0_1772 ),
inference(superposition,[],[f17110,f16462]) ).
fof(f26191,plain,
( spl0_2170
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2149 ),
inference(avatar_split_clause,[],[f25945,f25942,f12080,f9173,f26189]) ).
fof(f26189,plain,
( spl0_2170
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f25942,plain,
( spl0_2149
<=> ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f25945,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1144
| ~ spl0_1464
| ~ spl0_2149 ),
inference(forward_demodulation,[],[f25943,f13149]) ).
fof(f25943,plain,
( ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2149 ),
inference(avatar_component_clause,[],[f25942]) ).
fof(f26187,plain,
( spl0_2169
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2148 ),
inference(avatar_split_clause,[],[f25940,f25937,f12080,f9169,f26185]) ).
fof(f26185,plain,
( spl0_2169
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f25937,plain,
( spl0_2148
<=> ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f25940,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1143
| ~ spl0_1464
| ~ spl0_2148 ),
inference(forward_demodulation,[],[f25938,f13150]) ).
fof(f25938,plain,
( ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2148 ),
inference(avatar_component_clause,[],[f25937]) ).
fof(f26146,plain,
( spl0_2168
| ~ spl0_1498
| ~ spl0_1567 ),
inference(avatar_split_clause,[],[f14166,f13815,f12238,f26144]) ).
fof(f26144,plain,
( spl0_2168
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f12238,plain,
( spl0_1498
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f13815,plain,
( spl0_1567
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f14166,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg))
| ~ spl0_1498
| ~ spl0_1567 ),
inference(resolution,[],[f13816,f12239]) ).
fof(f12239,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1498 ),
inference(avatar_component_clause,[],[f12238]) ).
fof(f13816,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
| ~ spl0_1567 ),
inference(avatar_component_clause,[],[f13815]) ).
fof(f26106,plain,
spl0_2167,
inference(avatar_split_clause,[],[f3022,f26104]) ).
fof(f3022,plain,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1859,f2129,f2129]) ).
fof(f1859,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f26102,plain,
spl0_2166,
inference(avatar_split_clause,[],[f2937,f26100]) ).
fof(f26100,plain,
( spl0_2166
<=> ! [X4,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f2937,plain,
! [X11,X1,X47,X4] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1),X4,X1) ),
inference(definition_unfolding,[],[f2107,f2129]) ).
fof(f2107,axiom,
! [X11,X1,X47,X4] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f26092,plain,
( spl0_2165
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2164 ),
inference(avatar_split_clause,[],[f26088,f26085,f10767,f10447,f6846,f5911,f26090]) ).
fof(f26090,plain,
( spl0_2165
<=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f26085,plain,
( spl0_2164
<=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f26088,plain,
( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41)))
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2164 ),
inference(forward_demodulation,[],[f26086,f11726]) ).
fof(f26086,plain,
( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41)))
| ~ spl0_2164 ),
inference(avatar_component_clause,[],[f26085]) ).
fof(f26087,plain,
spl0_2164,
inference(avatar_split_clause,[],[f2925,f26085]) ).
fof(f2925,plain,
! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))),
inference(definition_unfolding,[],[f2391,f2544]) ).
fof(f2391,axiom,
! [X21,X41,X85] : c_Nat_Opower(X85,c_Suc(X21),tc_set(tc_prod(X41,X41))) = c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f26083,plain,
spl0_2163,
inference(avatar_split_clause,[],[f2920,f26081]) ).
fof(f26081,plain,
( spl0_2163
<=> ! [X18,X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f2920,plain,
! [X18,X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1),
inference(definition_unfolding,[],[f2686,f2373,f2373]) ).
fof(f2686,axiom,
! [X18,X1,X12,X13] : c_inter(c_insert(X18,X12,X1),c_insert(X18,X13,X1),X1) = c_insert(X18,c_inter(X12,X13,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f26079,plain,
spl0_2162,
inference(avatar_split_clause,[],[f2913,f26077]) ).
fof(f26077,plain,
( spl0_2162
<=> ! [X13,X12,X1] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f2913,plain,
! [X1,X12,X13] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
inference(definition_unfolding,[],[f1637,f2373,f2373]) ).
fof(f1637,axiom,
! [X1,X12,X13] : c_List_Olists(c_inter(X12,X13,X1),X1) = c_inter(c_List_Olists(X12,X1),c_List_Olists(X13,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f26075,plain,
spl0_2161,
inference(avatar_split_clause,[],[f2912,f26073]) ).
fof(f26073,plain,
( spl0_2161
<=> ! [X13,X12,X1] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f2912,plain,
! [X1,X12,X13] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)),
inference(definition_unfolding,[],[f2624,f2373,f2373]) ).
fof(f2624,axiom,
! [X1,X12,X13] : c_Pow(c_inter(X12,X13,X1),X1) = c_inter(c_Pow(X12,X1),c_Pow(X13,X1),tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f26071,plain,
( spl0_2160
| ~ spl0_814
| ~ spl0_1556 ),
inference(avatar_split_clause,[],[f14066,f13771,f7426,f26069]) ).
fof(f26069,plain,
( spl0_2160
<=> ! [X0] : c_lessequals(c_Message_Oanalz(X0),c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f13771,plain,
( spl0_1556
<=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f14066,plain,
( ! [X0] : c_lessequals(c_Message_Oanalz(X0),c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_814
| ~ spl0_1556 ),
inference(superposition,[],[f13772,f7427]) ).
fof(f13772,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f13771]) ).
fof(f25989,plain,
( spl0_2159
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2158 ),
inference(avatar_split_clause,[],[f25985,f25981,f10767,f10447,f6846,f5911,f25987]) ).
fof(f25987,plain,
( spl0_2159
<=> ! [X16,X21] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f25981,plain,
( spl0_2158
<=> ! [X16,X21] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f25985,plain,
( ! [X21,X16] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat))
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2158 ),
inference(forward_demodulation,[],[f25984,f11726]) ).
fof(f25984,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2158 ),
inference(forward_demodulation,[],[f25982,f11726]) ).
fof(f25982,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2158 ),
inference(avatar_component_clause,[],[f25981]) ).
fof(f25983,plain,
spl0_2158,
inference(avatar_split_clause,[],[f2906,f25981]) ).
fof(f2906,plain,
! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f1162,f2544,f2544,f2544]) ).
fof(f1162,axiom,
! [X21,X16] : c_Binomial_Obinomial(c_Suc(X21),c_Suc(X16)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Suc(X16)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f25977,plain,
spl0_2157,
inference(avatar_split_clause,[],[f2868,f25975]) ).
fof(f25975,plain,
( spl0_2157
<=> ! [X5,X1] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f2868,plain,
! [X1,X5] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2710,f2716,f2716,f2716]) ).
fof(f2710,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f25973,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2316,f25971]) ).
fof(f25971,plain,
( spl0_2156
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f2316,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f25969,plain,
spl0_2155,
inference(avatar_split_clause,[],[f1826,f25967]) ).
fof(f25967,plain,
( spl0_2155
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f1826,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f25965,plain,
spl0_2154,
inference(avatar_split_clause,[],[f1695,f25963]) ).
fof(f25963,plain,
( spl0_2154
<=> ! [X0,X1,X23,X47] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f1695,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f25961,plain,
spl0_2153,
inference(avatar_split_clause,[],[f1573,f25959]) ).
fof(f25959,plain,
( spl0_2153
<=> ! [X21,X23,X25,X1] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f1573,axiom,
! [X21,X1,X25,X23] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f25957,plain,
spl0_2152,
inference(avatar_split_clause,[],[f1571,f25955]) ).
fof(f25955,plain,
( spl0_2152
<=> ! [X47,X0,X23,X1] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f1571,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f25953,plain,
spl0_2151,
inference(avatar_split_clause,[],[f1526,f25951]) ).
fof(f25951,plain,
( spl0_2151
<=> ! [X23,X12,X25,X1] :
( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f1526,axiom,
! [X1,X25,X12,X23] :
( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f25949,plain,
( spl0_2150
| ~ spl0_1064
| ~ spl0_1526 ),
inference(avatar_split_clause,[],[f14040,f13651,f8646,f25947]) ).
fof(f25947,plain,
( spl0_2150
<=> ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f8646,plain,
( spl0_1064
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f14040,plain,
( ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat))
| ~ spl0_1064
| ~ spl0_1526 ),
inference(resolution,[],[f13652,f8647]) ).
fof(f8647,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1064 ),
inference(avatar_component_clause,[],[f8646]) ).
fof(f25944,plain,
spl0_2149,
inference(avatar_split_clause,[],[f1447,f25942]) ).
fof(f1447,axiom,
! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f25939,plain,
spl0_2148,
inference(avatar_split_clause,[],[f1437,f25937]) ).
fof(f1437,axiom,
! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f25935,plain,
spl0_2147,
inference(avatar_split_clause,[],[f1381,f25933]) ).
fof(f25933,plain,
( spl0_2147
<=> ! [X0,X3] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f1381,axiom,
! [X3,X0] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
fof(f25931,plain,
spl0_2146,
inference(avatar_split_clause,[],[f1269,f25929]) ).
fof(f25929,plain,
( spl0_2146
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f1269,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f25927,plain,
spl0_2145,
inference(avatar_split_clause,[],[f1266,f25925]) ).
fof(f25925,plain,
( spl0_2145
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f1266,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f25923,plain,
spl0_2144,
inference(avatar_split_clause,[],[f1262,f25921]) ).
fof(f25921,plain,
( spl0_2144
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f1262,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f25919,plain,
spl0_2143,
inference(avatar_split_clause,[],[f1259,f25917]) ).
fof(f25917,plain,
( spl0_2143
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f1259,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f25915,plain,
spl0_2142,
inference(avatar_split_clause,[],[f78,f25913]) ).
fof(f25913,plain,
( spl0_2142
<=> ! [X5,X29,X2,X1] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f78,axiom,
! [X2,X29,X1,X5] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f25505,plain,
( spl0_2141
| ~ spl0_40
| ~ spl0_737
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f10135,f9724,f7115,f3447,f25502]) ).
fof(f25502,plain,
( spl0_2141
<=> c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f7115,plain,
( spl0_737
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f10135,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint)
| ~ spl0_737
| ~ spl0_1229 ),
inference(resolution,[],[f9725,f7117]) ).
fof(f7117,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_737 ),
inference(avatar_component_clause,[],[f7115]) ).
fof(f25185,plain,
( spl0_2140
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2139 ),
inference(avatar_split_clause,[],[f25181,f25178,f20187,f7301,f7265,f25183]) ).
fof(f25183,plain,
( spl0_2140
<=> ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_plus(c_1,c_1,tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f25178,plain,
( spl0_2139
<=> ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f25181,plain,
( ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_plus(c_1,c_1,tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) )
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2139 ),
inference(forward_demodulation,[],[f25179,f20270]) ).
fof(f25179,plain,
( ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) )
| ~ spl0_2139 ),
inference(avatar_component_clause,[],[f25178]) ).
fof(f25180,plain,
spl0_2139,
inference(avatar_split_clause,[],[f3207,f25178]) ).
fof(f3207,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f3206,f2156]) ).
fof(f3206,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f3205,f2154]) ).
fof(f3205,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f1874,f2156]) ).
fof(f1874,axiom,
! [X2,X11] :
( ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2)
| c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f25176,plain,
spl0_2138,
inference(avatar_split_clause,[],[f3140,f25174]) ).
fof(f25174,plain,
( spl0_2138
<=> ! [X16,X59,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f3140,plain,
! [X59,X16,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3139,f2885]) ).
fof(f2885,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat),
inference(definition_unfolding,[],[f2540,f2544]) ).
fof(f2540,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Suc(X14),X26,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3139,plain,
! [X59,X16,X15] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f2954,f2885]) ).
fof(f2954,plain,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),c_plus(X16,X15,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1798,f2544,f2544]) ).
fof(f1798,axiom,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(c_Suc(c_minus(X59,X16,tc_nat)),X15,tc_nat) = c_minus(c_Suc(X59),c_plus(X16,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f25172,plain,
spl0_2137,
inference(avatar_split_clause,[],[f3138,f25170]) ).
fof(f25170,plain,
( spl0_2137
<=> ! [X16,X59,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f3138,plain,
! [X59,X16,X15] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f3137,f2884]) ).
fof(f2884,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2547,f2544]) ).
fof(f2547,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3137,plain,
! [X59,X16,X15] :
( c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X16,X59,tc_nat) ),
inference(forward_demodulation,[],[f2953,f2884]) ).
fof(f2953,plain,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1797,f2544,f2544]) ).
fof(f1797,axiom,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X15,c_Suc(c_minus(X59,X16,tc_nat)),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Suc(X59),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f25122,plain,
( spl0_2136
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2135 ),
inference(avatar_split_clause,[],[f25118,f25115,f10767,f10447,f6846,f5911,f25120]) ).
fof(f25120,plain,
( spl0_2136
<=> ! [X12,X0,X1] :
( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
| c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f25115,plain,
( spl0_2135
<=> ! [X12,X0,X1] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f25118,plain,
( ! [X0,X1,X12] :
( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
| c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2135 ),
inference(forward_demodulation,[],[f25116,f11726]) ).
fof(f25116,plain,
( ! [X0,X1,X12] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) )
| ~ spl0_2135 ),
inference(avatar_component_clause,[],[f25115]) ).
fof(f25117,plain,
spl0_2135,
inference(avatar_split_clause,[],[f3012,f25115]) ).
fof(f3012,plain,
! [X0,X1,X12] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1280,f2544]) ).
fof(f1280,axiom,
! [X0,X1,X12] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Suc(c_Finite__Set_Ocard(X12,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f25092,plain,
( spl0_2134
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2133 ),
inference(avatar_split_clause,[],[f25088,f25085,f10767,f10447,f6846,f5911,f25090]) ).
fof(f25090,plain,
( spl0_2134
<=> ! [X0,X23,X21,X1] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f25085,plain,
( spl0_2133
<=> ! [X0,X23,X21,X1] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f25088,plain,
( ! [X21,X0,X1,X23] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2133 ),
inference(forward_demodulation,[],[f25086,f11726]) ).
fof(f25086,plain,
( ! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1)
| ~ spl0_2133 ),
inference(avatar_component_clause,[],[f25085]) ).
fof(f25087,plain,
spl0_2133,
inference(avatar_split_clause,[],[f2915,f25085]) ).
fof(f2915,plain,
! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1),
inference(definition_unfolding,[],[f1769,f1766,f2544,f1766]) ).
fof(f1769,axiom,
! [X21,X0,X1,X23] : c_List_Otake(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(X21,X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f25083,plain,
( spl0_2132
| ~ spl0_40
| ~ spl0_737
| ~ spl0_1226 ),
inference(avatar_split_clause,[],[f10084,f9712,f7115,f3447,f25080]) ).
fof(f25080,plain,
( spl0_2132
<=> c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f10084,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint)
| ~ spl0_737
| ~ spl0_1226 ),
inference(resolution,[],[f9713,f7117]) ).
fof(f25078,plain,
spl0_2131,
inference(avatar_split_clause,[],[f2385,f25076]) ).
fof(f25076,plain,
( spl0_2131
<=> ! [X18,X5,X27,X2,X1] :
( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f2385,axiom,
! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f25074,plain,
spl0_2130,
inference(avatar_split_clause,[],[f2384,f25072]) ).
fof(f25072,plain,
( spl0_2130
<=> ! [X18,X5,X27,X2,X1] :
( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f2384,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f25070,plain,
spl0_2129,
inference(avatar_split_clause,[],[f2332,f25068]) ).
fof(f25068,plain,
( spl0_2129
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f2332,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f25066,plain,
spl0_2128,
inference(avatar_split_clause,[],[f2322,f25064]) ).
fof(f25064,plain,
( spl0_2128
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f2322,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f25062,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1877,f25060]) ).
fof(f25060,plain,
( spl0_2127
<=> ! [X11,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f1877,axiom,
! [X11,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f25058,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1828,f25056]) ).
fof(f25056,plain,
( spl0_2126
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f1828,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f25054,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1273,f25052]) ).
fof(f25052,plain,
( spl0_2125
<=> ! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f1273,axiom,
! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f25050,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1271,f25048]) ).
fof(f25048,plain,
( spl0_2124
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f1271,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f25046,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1270,f25044]) ).
fof(f25044,plain,
( spl0_2123
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f1270,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f25042,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1268,f25040]) ).
fof(f25040,plain,
( spl0_2122
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f1268,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f25038,plain,
( spl0_2121
| ~ spl0_888
| ~ spl0_1005 ),
inference(avatar_split_clause,[],[f8778,f8408,f7790,f25036]) ).
fof(f25036,plain,
( spl0_2121
<=> ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f7790,plain,
( spl0_888
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f8778,plain,
( ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_888
| ~ spl0_1005 ),
inference(superposition,[],[f8409,f7792]) ).
fof(f7792,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f7790]) ).
fof(f25034,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1267,f25032]) ).
fof(f25032,plain,
( spl0_2120
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f1267,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f25030,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1264,f25028]) ).
fof(f25028,plain,
( spl0_2119
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f1264,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f25026,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1263,f25024]) ).
fof(f25024,plain,
( spl0_2118
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f1263,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f25022,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1261,f25020]) ).
fof(f25020,plain,
( spl0_2117
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f1261,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f25018,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1260,f25016]) ).
fof(f25016,plain,
( spl0_2116
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f1260,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f25014,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1258,f25012]) ).
fof(f25012,plain,
( spl0_2115
<=> ! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f1258,axiom,
! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f25010,plain,
spl0_2114,
inference(avatar_split_clause,[],[f73,f25008]) ).
fof(f73,axiom,
! [X2,X1,X27,X5,X12] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f25006,plain,
spl0_2113,
inference(avatar_split_clause,[],[f15,f25004]) ).
fof(f25004,plain,
( spl0_2113
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f15,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f25002,plain,
spl0_2112,
inference(avatar_split_clause,[],[f14,f25000]) ).
fof(f25000,plain,
( spl0_2112
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f14,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f24658,plain,
( spl0_100
| ~ spl0_2111
| ~ spl0_887
| ~ spl0_996 ),
inference(avatar_split_clause,[],[f8729,f8372,f7769,f24655,f3744]) ).
fof(f24655,plain,
( spl0_2111
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f7769,plain,
( spl0_887
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f8729,plain,
( ~ c_less(c_1,c_1,tc_IntDef_Oint)
| c_0 = c_1
| ~ spl0_887
| ~ spl0_996 ),
inference(superposition,[],[f8373,f7771]) ).
fof(f7771,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_887 ),
inference(avatar_component_clause,[],[f7769]) ).
fof(f24268,plain,
spl0_2110,
inference(avatar_split_clause,[],[f3021,f24266]) ).
fof(f24266,plain,
( spl0_2110
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f3021,plain,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1856,f2129]) ).
fof(f1856,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f24255,plain,
spl0_2109,
inference(avatar_split_clause,[],[f3020,f24253]) ).
fof(f24253,plain,
( spl0_2109
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f3020,plain,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1857,f2129]) ).
fof(f1857,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f24251,plain,
spl0_2108,
inference(avatar_split_clause,[],[f2993,f24249]) ).
fof(f24249,plain,
( spl0_2108
<=> ! [X21,X43,X15] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f2993,plain,
! [X21,X15,X43] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1777,f1766]) ).
fof(f1777,axiom,
! [X21,X15,X43] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Otake(X15,c_List_Oupt(X43,X21),tc_nat) = c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f24247,plain,
spl0_2107,
inference(avatar_split_clause,[],[f2880,f24245]) ).
fof(f24245,plain,
( spl0_2107
<=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f2880,plain,
! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2712,f2716,f2716]) ).
fof(f2712,axiom,
! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Transitive__Closure_Ortrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f24243,plain,
spl0_2106,
inference(avatar_split_clause,[],[f2789,f24241]) ).
fof(f24241,plain,
( spl0_2106
<=> ! [X86,X91,X88] :
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f2789,axiom,
! [X91,X88,X86] :
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
fof(f24239,plain,
spl0_2105,
inference(avatar_split_clause,[],[f2562,f24237]) ).
fof(f24237,plain,
( spl0_2105
<=> ! [X15,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X43,X21,X1)
| c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f2562,axiom,
! [X21,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X43,X21,X1)
| c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f24235,plain,
spl0_2104,
inference(avatar_split_clause,[],[f2356,f24233]) ).
fof(f24233,plain,
( spl0_2104
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f2356,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f24231,plain,
spl0_2103,
inference(avatar_split_clause,[],[f2355,f24229]) ).
fof(f24229,plain,
( spl0_2103
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_less(X0,X3,tc_nat)
| ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f2355,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_less(X0,X3,tc_nat)
| ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f24227,plain,
spl0_2102,
inference(avatar_split_clause,[],[f2351,f24225]) ).
fof(f24225,plain,
( spl0_2102
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f2351,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f24223,plain,
spl0_2101,
inference(avatar_split_clause,[],[f2350,f24221]) ).
fof(f24221,plain,
( spl0_2101
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f2350,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f24219,plain,
spl0_2100,
inference(avatar_split_clause,[],[f2336,f24217]) ).
fof(f24217,plain,
( spl0_2100
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f2336,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f24212,plain,
spl0_2099,
inference(avatar_split_clause,[],[f2333,f24210]) ).
fof(f24210,plain,
( spl0_2099
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f2333,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f24208,plain,
spl0_2098,
inference(avatar_split_clause,[],[f2330,f24206]) ).
fof(f24206,plain,
( spl0_2098
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f2330,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f24204,plain,
spl0_2097,
inference(avatar_split_clause,[],[f2328,f24202]) ).
fof(f24202,plain,
( spl0_2097
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f2328,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f24200,plain,
spl0_2096,
inference(avatar_split_clause,[],[f2325,f24198]) ).
fof(f24198,plain,
( spl0_2096
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f2325,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f24196,plain,
spl0_2095,
inference(avatar_split_clause,[],[f2319,f24194]) ).
fof(f24194,plain,
( spl0_2095
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f2319,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f24192,plain,
spl0_2094,
inference(avatar_split_clause,[],[f2168,f24190]) ).
fof(f24190,plain,
( spl0_2094
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f2168,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f24188,plain,
spl0_2093,
inference(avatar_split_clause,[],[f2108,f24186]) ).
fof(f24186,plain,
( spl0_2093
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f2108,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f24184,plain,
spl0_2092,
inference(avatar_split_clause,[],[f1861,f24182]) ).
fof(f24182,plain,
( spl0_2092
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f1861,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f24180,plain,
spl0_2091,
inference(avatar_split_clause,[],[f1835,f24178]) ).
fof(f24178,plain,
( spl0_2091
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f1835,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f24176,plain,
spl0_2090,
inference(avatar_split_clause,[],[f1825,f24174]) ).
fof(f24174,plain,
( spl0_2090
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f1825,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f24172,plain,
( spl0_2089
| ~ spl0_114
| ~ spl0_1799 ),
inference(avatar_split_clause,[],[f19074,f18448,f3807,f24170]) ).
fof(f24170,plain,
( spl0_2089
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f18448,plain,
( spl0_1799
<=> ! [X5,X18,X27,X2,X1] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f19074,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_114
| ~ spl0_1799 ),
inference(resolution,[],[f18449,f3808]) ).
fof(f18449,plain,
( ! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
| c_in(X27,c_Relation_ORange(X5,X1,X2),X2) )
| ~ spl0_1799 ),
inference(avatar_component_clause,[],[f18448]) ).
fof(f24168,plain,
spl0_2088,
inference(avatar_split_clause,[],[f1635,f24166]) ).
fof(f24166,plain,
( spl0_2088
<=> ! [X43,X23,X0,X3,X1] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f1635,axiom,
! [X3,X0,X1,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f24164,plain,
spl0_2087,
inference(avatar_split_clause,[],[f1634,f24162]) ).
fof(f24162,plain,
( spl0_2087
<=> ! [X3,X0,X23,X25,X1] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f1634,axiom,
! [X3,X0,X1,X25,X23] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f24160,plain,
spl0_2086,
inference(avatar_split_clause,[],[f1355,f24158]) ).
fof(f24158,plain,
( spl0_2086
<=> ! [X0,X3] :
( X0 = X3
| c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
| ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f1355,axiom,
! [X3,X0] :
( X0 = X3
| c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
| ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f24156,plain,
spl0_2085,
inference(avatar_split_clause,[],[f1294,f24154]) ).
fof(f24154,plain,
( spl0_2085
<=> ! [X2,X12,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f1294,axiom,
! [X2,X3,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f24152,plain,
spl0_2084,
inference(avatar_split_clause,[],[f1293,f24150]) ).
fof(f24150,plain,
( spl0_2084
<=> ! [X2,X12,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f1293,axiom,
! [X2,X3,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f24148,plain,
spl0_2083,
inference(avatar_split_clause,[],[f1222,f24146]) ).
fof(f24146,plain,
( spl0_2083
<=> ! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f1222,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f24144,plain,
spl0_2082,
inference(avatar_split_clause,[],[f1220,f24142]) ).
fof(f24142,plain,
( spl0_2082
<=> ! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f1220,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f24140,plain,
spl0_2081,
inference(avatar_split_clause,[],[f121,f24138]) ).
fof(f24138,plain,
( spl0_2081
<=> ! [X5,X18,X27,X1] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f121,axiom,
! [X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f24136,plain,
spl0_2080,
inference(avatar_split_clause,[],[f74,f24134]) ).
fof(f24134,plain,
( spl0_2080
<=> ! [X5,X18,X12,X27,X2,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f74,axiom,
! [X2,X18,X1,X27,X5,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f24079,plain,
( spl0_2079
| ~ spl0_114
| ~ spl0_1794 ),
inference(avatar_split_clause,[],[f19014,f18428,f3807,f24077]) ).
fof(f24077,plain,
( spl0_2079
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f18428,plain,
( spl0_1794
<=> ! [X18,X5,X27,X2,X1] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f19014,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_114
| ~ spl0_1794 ),
inference(resolution,[],[f18429,f3808]) ).
fof(f18429,plain,
( ! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
| c_in(X18,c_Relation_ODomain(X5,X1,X2),X1) )
| ~ spl0_1794 ),
inference(avatar_component_clause,[],[f18428]) ).
fof(f23112,plain,
( spl0_2078
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2077 ),
inference(avatar_split_clause,[],[f23108,f23104,f20187,f7301,f7265,f23110]) ).
fof(f23110,plain,
( spl0_2078
<=> ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f23104,plain,
( spl0_2077
<=> ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f23108,plain,
( ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2077 ),
inference(forward_demodulation,[],[f23107,f20270]) ).
fof(f23107,plain,
( ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_774
| ~ spl0_783
| ~ spl0_1935
| ~ spl0_2077 ),
inference(forward_demodulation,[],[f23105,f20270]) ).
fof(f23105,plain,
( ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_2077 ),
inference(avatar_component_clause,[],[f23104]) ).
fof(f23106,plain,
spl0_2077,
inference(avatar_split_clause,[],[f3193,f23104]) ).
fof(f3193,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3192,f2156]) ).
fof(f3192,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3191,f2154]) ).
fof(f3191,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3190,f2156]) ).
fof(f3190,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3189,f2156]) ).
fof(f3189,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3188,f2154]) ).
fof(f3188,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f1975,f2156]) ).
fof(f1975,axiom,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).
fof(f23079,plain,
( spl0_2076
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2075 ),
inference(avatar_split_clause,[],[f23075,f23072,f10767,f10447,f6846,f5911,f23077]) ).
fof(f23077,plain,
( spl0_2076
<=> ! [X16,X21,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f23072,plain,
( spl0_2075
<=> ! [X16,X21,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f23075,plain,
( ! [X21,X16,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2075 ),
inference(forward_demodulation,[],[f23073,f11726]) ).
fof(f23073,plain,
( ! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat)
| ~ spl0_2075 ),
inference(avatar_component_clause,[],[f23072]) ).
fof(f23074,plain,
spl0_2075,
inference(avatar_split_clause,[],[f3096,f23072]) ).
fof(f3096,plain,
! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3095,f2037]) ).
fof(f2037,axiom,
! [X59,X16,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3095,plain,
! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2916,f2885]) ).
fof(f2916,plain,
! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2018,f2544,f2544]) ).
fof(f2018,axiom,
! [X21,X16,X15] : c_minus(c_minus(c_Suc(X15),X21,tc_nat),c_Suc(X16),tc_nat) = c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f23070,plain,
spl0_2074,
inference(avatar_split_clause,[],[f3042,f23068]) ).
fof(f23068,plain,
( spl0_2074
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f3042,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2140,f2129]) ).
fof(f2140,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f23066,plain,
spl0_2073,
inference(avatar_split_clause,[],[f3041,f23064]) ).
fof(f23064,plain,
( spl0_2073
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f3041,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2148,f2129]) ).
fof(f2148,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f23062,plain,
spl0_2072,
inference(avatar_split_clause,[],[f3040,f23060]) ).
fof(f23060,plain,
( spl0_2072
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f3040,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2149,f2129]) ).
fof(f2149,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f23058,plain,
spl0_2071,
inference(avatar_split_clause,[],[f3039,f23056]) ).
fof(f23056,plain,
( spl0_2071
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f3039,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
inference(definition_unfolding,[],[f2139,f2129]) ).
fof(f2139,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f23054,plain,
spl0_2070,
inference(avatar_split_clause,[],[f3019,f23052]) ).
fof(f23052,plain,
( spl0_2070
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f3019,plain,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2611,f2373]) ).
fof(f2611,axiom,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f23050,plain,
spl0_2069,
inference(avatar_split_clause,[],[f2990,f23048]) ).
fof(f23048,plain,
( spl0_2069
<=> ! [X13,X12,X1,X18] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f2990,plain,
! [X1,X18,X12,X13] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2678,f2373,f2373]) ).
fof(f2678,axiom,
! [X1,X18,X12,X13] :
( c_emptyset = c_inter(X12,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
fof(f23042,plain,
spl0_2068,
inference(avatar_split_clause,[],[f2988,f23040]) ).
fof(f23040,plain,
( spl0_2068
<=> ! [X18,X13,X12,X1] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f2988,plain,
! [X1,X18,X12,X13] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X13,X1),X12,X1,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X13,X1),c_insert(X18,X12,X1),X1,X1) ),
inference(definition_unfolding,[],[f2662,f2373,f2373]) ).
fof(f2662,axiom,
! [X1,X18,X12,X13] :
( c_emptyset = c_inter(X13,X12,X1)
| c_emptyset != c_inter(X13,c_insert(X18,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
fof(f22981,plain,
( spl0_2067
| ~ spl0_640
| ~ spl0_679
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1762
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f22977,f22973,f17014,f10767,f10447,f7265,f7245,f6846,f5911,f22979]) ).
fof(f22973,plain,
( spl0_2066
<=> ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f22977,plain,
( ! [X59,X43] :
( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
| ~ c_lessequals(X43,X59,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1762
| ~ spl0_2066 ),
inference(forward_demodulation,[],[f22976,f17040]) ).
fof(f22976,plain,
( ! [X59,X43] :
( c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| ~ c_lessequals(X43,X59,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2066 ),
inference(forward_demodulation,[],[f22974,f11726]) ).
fof(f22974,plain,
( ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_2066 ),
inference(avatar_component_clause,[],[f22973]) ).
fof(f22975,plain,
spl0_2066,
inference(avatar_split_clause,[],[f2952,f22973]) ).
fof(f2952,plain,
! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1782,f2544]) ).
fof(f1782,axiom,
! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f22971,plain,
spl0_2065,
inference(avatar_split_clause,[],[f2919,f22969]) ).
fof(f22969,plain,
( spl0_2065
<=> ! [X13,X12,X1] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f2919,plain,
! [X1,X12,X13] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)),
inference(definition_unfolding,[],[f2575,f2373]) ).
fof(f2575,axiom,
! [X1,X12,X13] : c_uminus(c_inter(X12,X13,X1),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f22967,plain,
spl0_2064,
inference(avatar_split_clause,[],[f2918,f22965]) ).
fof(f22965,plain,
( spl0_2064
<=> ! [X13,X12,X1] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f2918,plain,
! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2577,f2373]) ).
fof(f2577,axiom,
! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_inter(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f22963,plain,
spl0_2063,
inference(avatar_split_clause,[],[f2911,f22961]) ).
fof(f22961,plain,
( spl0_2063
<=> ! [X15,X23,X21,X1] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f2911,plain,
! [X21,X1,X15,X23] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1),
inference(definition_unfolding,[],[f1776,f1766,f1766,f1766]) ).
fof(f1776,axiom,
! [X21,X1,X15,X23] : c_List_Otake(X21,c_List_Otake(X15,X23,X1),X1) = c_List_Otake(c_Orderings_Omin(X21,X15,tc_nat),X23,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f22940,plain,
( spl0_2062
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2061 ),
inference(avatar_split_clause,[],[f22936,f22931,f10767,f10447,f6846,f5911,f22938]) ).
fof(f22931,plain,
( spl0_2061
<=> ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f22936,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f22935,f11726]) ).
fof(f22935,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f22934,f11726]) ).
fof(f22934,plain,
( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f22932,f11726]) ).
fof(f22932,plain,
( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_2061 ),
inference(avatar_component_clause,[],[f22931]) ).
fof(f22933,plain,
spl0_2061,
inference(avatar_split_clause,[],[f2887,f22931]) ).
fof(f2887,plain,
! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2055,f2544,f2544,f2544]) ).
fof(f2055,axiom,
! [X21,X15] : c_Orderings_Omin(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omin(X15,X21,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f22910,plain,
( spl0_2060
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2059 ),
inference(avatar_split_clause,[],[f22906,f22901,f10767,f10447,f6846,f5911,f22908]) ).
fof(f22908,plain,
( spl0_2060
<=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f22901,plain,
( spl0_2059
<=> ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f22906,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2059 ),
inference(forward_demodulation,[],[f22905,f11726]) ).
fof(f22905,plain,
( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2059 ),
inference(forward_demodulation,[],[f22904,f11726]) ).
fof(f22904,plain,
( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_2059 ),
inference(forward_demodulation,[],[f22902,f11726]) ).
fof(f22902,plain,
( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_2059 ),
inference(avatar_component_clause,[],[f22901]) ).
fof(f22903,plain,
spl0_2059,
inference(avatar_split_clause,[],[f2886,f22901]) ).
fof(f2886,plain,
! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2052,f2544,f2544,f2544]) ).
fof(f2052,axiom,
! [X21,X15] : c_Orderings_Omax(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omax(X15,X21,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f22899,plain,
spl0_2058,
inference(avatar_split_clause,[],[f2810,f22897]) ).
fof(f2810,axiom,
! [X88,X86,X87] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
fof(f22895,plain,
spl0_2057,
inference(avatar_split_clause,[],[f2796,f22893]) ).
fof(f2796,axiom,
! [X88,X86,X87] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
fof(f22891,plain,
spl0_2056,
inference(avatar_split_clause,[],[f2566,f22889]) ).
fof(f22889,plain,
( spl0_2056
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X15,X43,X1)
| ~ c_lessequals(X59,X21,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f2566,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X15,X43,X1)
| ~ c_lessequals(X59,X21,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f22887,plain,
spl0_2055,
inference(avatar_split_clause,[],[f2564,f22885]) ).
fof(f22885,plain,
( spl0_2055
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X59,X21,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f2564,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X59,X21,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f22883,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2563,f22881]) ).
fof(f22881,plain,
( spl0_2054
<=> ! [X59,X43,X21,X15,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X15,X43,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f2563,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X15,X43,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f22879,plain,
spl0_2053,
inference(avatar_split_clause,[],[f2376,f22877]) ).
fof(f22877,plain,
( spl0_2053
<=> ! [X5,X18,X27,X2,X1] :
( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f2376,axiom,
! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f22875,plain,
spl0_2052,
inference(avatar_split_clause,[],[f2375,f22873]) ).
fof(f22873,plain,
( spl0_2052
<=> ! [X5,X18,X27,X2,X1] :
( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f2375,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f22871,plain,
( spl0_2051
| ~ spl0_641
| ~ spl0_1818 ),
inference(avatar_split_clause,[],[f22779,f18524,f5916,f22868]) ).
fof(f22868,plain,
( spl0_2051
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f18524,plain,
( spl0_1818
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f22779,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1818 ),
inference(superposition,[],[f18525,f5918]) ).
fof(f18525,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1818 ),
inference(avatar_component_clause,[],[f18524]) ).
fof(f22866,plain,
spl0_2050,
inference(avatar_split_clause,[],[f2335,f22864]) ).
fof(f22864,plain,
( spl0_2050
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f2335,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f22862,plain,
spl0_2049,
inference(avatar_split_clause,[],[f2318,f22860]) ).
fof(f22860,plain,
( spl0_2049
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f2318,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f22858,plain,
spl0_2048,
inference(avatar_split_clause,[],[f2174,f22856]) ).
fof(f22856,plain,
( spl0_2048
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f2174,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f22854,plain,
spl0_2047,
inference(avatar_split_clause,[],[f2121,f22852]) ).
fof(f22852,plain,
( spl0_2047
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f2121,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f22850,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1810,f22848]) ).
fof(f22848,plain,
( spl0_2046
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_lessequals(X21,X15,tc_nat)
| c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f1810,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_lessequals(X21,X15,tc_nat)
| c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f22846,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1672,f22844]) ).
fof(f22844,plain,
( spl0_2045
<=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f1672,axiom,
! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f22842,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1671,f22840]) ).
fof(f22840,plain,
( spl0_2044
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f1671,axiom,
! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f22838,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1670,f22836]) ).
fof(f22836,plain,
( spl0_2043
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f1670,axiom,
! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f22834,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1669,f22832]) ).
fof(f22832,plain,
( spl0_2042
<=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f1669,axiom,
! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f22830,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1668,f22828]) ).
fof(f22828,plain,
( spl0_2041
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f1668,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f22826,plain,
( spl0_2040
| ~ spl0_640
| ~ spl0_1818 ),
inference(avatar_split_clause,[],[f22778,f18524,f5911,f22823]) ).
fof(f22823,plain,
( spl0_2040
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f22778,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1818 ),
inference(superposition,[],[f18525,f5913]) ).
fof(f22821,plain,
spl0_2039,
inference(avatar_split_clause,[],[f1667,f22819]) ).
fof(f22819,plain,
( spl0_2039
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f1667,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f22817,plain,
spl0_2038,
inference(avatar_split_clause,[],[f1666,f22815]) ).
fof(f22815,plain,
( spl0_2038
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f1666,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f22813,plain,
spl0_2037,
inference(avatar_split_clause,[],[f1665,f22811]) ).
fof(f22811,plain,
( spl0_2037
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f1665,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f22809,plain,
spl0_2036,
inference(avatar_split_clause,[],[f1664,f22807]) ).
fof(f22807,plain,
( spl0_2036
<=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f1664,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f22805,plain,
spl0_2035,
inference(avatar_split_clause,[],[f1663,f22803]) ).
fof(f22803,plain,
( spl0_2035
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f1663,axiom,
! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f22801,plain,
spl0_2034,
inference(avatar_split_clause,[],[f1662,f22799]) ).
fof(f22799,plain,
( spl0_2034
<=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f1662,axiom,
! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f22797,plain,
spl0_2033,
inference(avatar_split_clause,[],[f1661,f22795]) ).
fof(f22795,plain,
( spl0_2033
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f1661,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f22793,plain,
spl0_2032,
inference(avatar_split_clause,[],[f1660,f22791]) ).
fof(f22791,plain,
( spl0_2032
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f1660,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f22789,plain,
spl0_2031,
inference(avatar_split_clause,[],[f1659,f22787]) ).
fof(f22787,plain,
( spl0_2031
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f1659,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f22785,plain,
spl0_2030,
inference(avatar_split_clause,[],[f1658,f22783]) ).
fof(f22783,plain,
( spl0_2030
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f1658,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f22775,plain,
spl0_2029,
inference(avatar_split_clause,[],[f1657,f22773]) ).
fof(f22773,plain,
( spl0_2029
<=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f1657,axiom,
! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f22771,plain,
spl0_2028,
inference(avatar_split_clause,[],[f1656,f22769]) ).
fof(f22769,plain,
( spl0_2028
<=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f1656,axiom,
! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f22767,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1655,f22765]) ).
fof(f22765,plain,
( spl0_2027
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1655,axiom,
! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f22763,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1654,f22761]) ).
fof(f22761,plain,
( spl0_2026
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1654,axiom,
! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f22759,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1653,f22757]) ).
fof(f22757,plain,
( spl0_2025
<=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f1653,axiom,
! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f22755,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1652,f22753]) ).
fof(f22753,plain,
( spl0_2024
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1652,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f22751,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1651,f22749]) ).
fof(f22749,plain,
( spl0_2023
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1651,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f22747,plain,
spl0_2022,
inference(avatar_split_clause,[],[f1650,f22745]) ).
fof(f22745,plain,
( spl0_2022
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f1650,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f22743,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1649,f22741]) ).
fof(f22741,plain,
( spl0_2021
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f1649,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f22739,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1648,f22737]) ).
fof(f22737,plain,
( spl0_2020
<=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1648,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f22733,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1647,f22731]) ).
fof(f22731,plain,
( spl0_2019
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1647,axiom,
! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f22729,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1646,f22727]) ).
fof(f22727,plain,
( spl0_2018
<=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1646,axiom,
! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f22725,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1645,f22723]) ).
fof(f22723,plain,
( spl0_2017
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1645,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f22721,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1644,f22719]) ).
fof(f22719,plain,
( spl0_2016
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f1644,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f22717,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1643,f22715]) ).
fof(f22715,plain,
( spl0_2015
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f1643,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f22713,plain,
spl0_2014,
inference(avatar_split_clause,[],[f1642,f22711]) ).
fof(f22711,plain,
( spl0_2014
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f1642,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f22709,plain,
spl0_2013,
inference(avatar_split_clause,[],[f1641,f22707]) ).
fof(f22707,plain,
( spl0_2013
<=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f1641,axiom,
! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f22705,plain,
spl0_2012,
inference(avatar_split_clause,[],[f1629,f22703]) ).
fof(f22703,plain,
( spl0_2012
<=> ! [X41,X60,X18,X65] :
( ~ c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f1629,axiom,
! [X65,X41,X18,X60] :
( ~ c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f22701,plain,
spl0_2011,
inference(avatar_split_clause,[],[f1614,f22699]) ).
fof(f22699,plain,
( spl0_2011
<=> ! [X23,X25,X2,X1] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f1614,axiom,
! [X2,X1,X25,X23] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f22697,plain,
spl0_2010,
inference(avatar_split_clause,[],[f1523,f22695]) ).
fof(f22695,plain,
( spl0_2010
<=> ! [X53,X23,X25,X52,X1] :
( X52 = X53
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f1523,axiom,
! [X1,X52,X53,X25,X23] :
( X52 = X53
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f22691,plain,
spl0_2009,
inference(avatar_split_clause,[],[f1522,f22689]) ).
fof(f22689,plain,
( spl0_2009
<=> ! [X52,X53,X23,X25,X1] :
( X23 = X25
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f1522,axiom,
! [X1,X52,X53,X25,X23] :
( X23 = X25
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f22687,plain,
spl0_2008,
inference(avatar_split_clause,[],[f1521,f22685]) ).
fof(f22685,plain,
( spl0_2008
<=> ! [X53,X23,X25,X52,X1] :
( X52 = X53
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f1521,axiom,
! [X1,X52,X53,X25,X23] :
( X52 = X53
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f22683,plain,
spl0_2007,
inference(avatar_split_clause,[],[f1520,f22681]) ).
fof(f22681,plain,
( spl0_2007
<=> ! [X52,X53,X23,X25,X1] :
( X23 = X25
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f1520,axiom,
! [X1,X52,X53,X25,X23] :
( X23 = X25
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f22679,plain,
spl0_2006,
inference(avatar_split_clause,[],[f1468,f22677]) ).
fof(f22677,plain,
( spl0_2006
<=> ! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f1468,axiom,
! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
fof(f22675,plain,
spl0_2005,
inference(avatar_split_clause,[],[f1283,f22673]) ).
fof(f22673,plain,
( spl0_2005
<=> ! [X18,X13,X12,X1] :
( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f1283,axiom,
! [X1,X18,X12,X13] :
( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f22671,plain,
spl0_2004,
inference(avatar_split_clause,[],[f1282,f22669]) ).
fof(f22669,plain,
( spl0_2004
<=> ! [X18,X13,X12,X1] :
( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f1282,axiom,
! [X1,X18,X12,X13] :
( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f22667,plain,
spl0_2003,
inference(avatar_split_clause,[],[f79,f22665]) ).
fof(f22665,plain,
( spl0_2003
<=> ! [X12,X1,X4] :
( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f79,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f22663,plain,
spl0_2002,
inference(avatar_split_clause,[],[f75,f22661]) ).
fof(f22661,plain,
( spl0_2002
<=> ! [X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f75,axiom,
! [X2,X1,X27,X5] :
( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f22659,plain,
spl0_2001,
inference(avatar_split_clause,[],[f69,f22657]) ).
fof(f22657,plain,
( spl0_2001
<=> ! [X18,X5,X2,X1] :
( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f69,axiom,
! [X2,X18,X1,X5] :
( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f22655,plain,
spl0_2000,
inference(avatar_split_clause,[],[f60,f22653]) ).
fof(f22653,plain,
( spl0_2000
<=> ! [X18,X12,X1,X26] :
( ~ c_in(X18,X12,X1)
| ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f60,axiom,
! [X18,X1,X26,X12] :
( ~ c_in(X18,X12,X1)
| ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f22650,plain,
spl0_1999,
inference(avatar_split_clause,[],[f22,f22648]) ).
fof(f22648,plain,
( spl0_1999
<=> ! [X13,X7,X12,X2,X1] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f22,axiom,
! [X2,X1,X7,X12,X13] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f22646,plain,
spl0_1998,
inference(avatar_split_clause,[],[f21,f22644]) ).
fof(f22644,plain,
( spl0_1998
<=> ! [X13,X12,X9,X2,X1] :
( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f21,axiom,
! [X2,X1,X9,X12,X13] :
( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f22537,plain,
( spl0_1997
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_1980 ),
inference(avatar_split_clause,[],[f21999,f21996,f12291,f3507,f22535]) ).
fof(f22535,plain,
( spl0_1997
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f21996,plain,
( spl0_1980
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f21999,plain,
( ! [X83,X47] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_1980 ),
inference(forward_demodulation,[],[f21997,f13579]) ).
fof(f21997,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_1980 ),
inference(avatar_component_clause,[],[f21996]) ).
fof(f22533,plain,
( spl0_1996
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_1979 ),
inference(avatar_split_clause,[],[f21994,f21991,f12291,f3507,f22531]) ).
fof(f22531,plain,
( spl0_1996
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f21991,plain,
( spl0_1979
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f21994,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_52
| ~ spl0_1509
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21992,f13579]) ).
fof(f21992,plain,
( ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
| ~ spl0_1979 ),
inference(avatar_component_clause,[],[f21991]) ).
fof(f22163,plain,
( spl0_1995
| ~ spl0_1578
| ~ spl0_1994 ),
inference(avatar_split_clause,[],[f22159,f22156,f13859,f22161]) ).
fof(f22161,plain,
( spl0_1995
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f13859,plain,
( spl0_1578
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f22156,plain,
( spl0_1994
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f22159,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1578
| ~ spl0_1994 ),
inference(forward_demodulation,[],[f22157,f13861]) ).
fof(f13861,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1578 ),
inference(avatar_component_clause,[],[f13859]) ).
fof(f22157,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1994 ),
inference(avatar_component_clause,[],[f22156]) ).
fof(f22158,plain,
spl0_1994,
inference(avatar_split_clause,[],[f3246,f22156]) ).
fof(f3246,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f3037,f2156]) ).
fof(f3037,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1319,f2129]) ).
fof(f1319,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f22117,plain,
spl0_1993,
inference(avatar_split_clause,[],[f3244,f22115]) ).
fof(f22115,plain,
( spl0_1993
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f3244,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3035,f2156]) ).
fof(f3035,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1315,f2129]) ).
fof(f1315,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f22113,plain,
spl0_1992,
inference(avatar_split_clause,[],[f3242,f22111]) ).
fof(f22111,plain,
( spl0_1992
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f3242,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f3033,f2156]) ).
fof(f3033,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1327,f2129]) ).
fof(f1327,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f22092,plain,
( spl0_1991
| ~ spl0_1578
| ~ spl0_1990 ),
inference(avatar_split_clause,[],[f22088,f22085,f13859,f22090]) ).
fof(f22090,plain,
( spl0_1991
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f22085,plain,
( spl0_1990
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f22088,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1578
| ~ spl0_1990 ),
inference(forward_demodulation,[],[f22086,f13861]) ).
fof(f22086,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1990 ),
inference(avatar_component_clause,[],[f22085]) ).
fof(f22087,plain,
spl0_1990,
inference(avatar_split_clause,[],[f3239,f22085]) ).
fof(f3239,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3031,f2156]) ).
fof(f3031,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1323,f2129]) ).
fof(f1323,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f22066,plain,
( spl0_1989
| ~ spl0_1578
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f22062,f22059,f13859,f22064]) ).
fof(f22064,plain,
( spl0_1989
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f22059,plain,
( spl0_1988
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f22062,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1578
| ~ spl0_1988 ),
inference(forward_demodulation,[],[f22060,f13861]) ).
fof(f22060,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1988 ),
inference(avatar_component_clause,[],[f22059]) ).
fof(f22061,plain,
spl0_1988,
inference(avatar_split_clause,[],[f3236,f22059]) ).
fof(f3236,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f3029,f2156]) ).
fof(f3029,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1318,f2129]) ).
fof(f1318,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f22057,plain,
spl0_1987,
inference(avatar_split_clause,[],[f3234,f22055]) ).
fof(f22055,plain,
( spl0_1987
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f3234,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3027,f2156]) ).
fof(f3027,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1314,f2129]) ).
fof(f1314,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f22053,plain,
spl0_1986,
inference(avatar_split_clause,[],[f3232,f22051]) ).
fof(f22051,plain,
( spl0_1986
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f3232,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f3025,f2156]) ).
fof(f3025,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1326,f2129]) ).
fof(f1326,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f22049,plain,
( spl0_1985
| ~ spl0_936
| ~ spl0_1031
| ~ spl0_1786 ),
inference(avatar_split_clause,[],[f21953,f17345,f8513,f8002,f22046]) ).
fof(f22046,plain,
( spl0_1985
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f8002,plain,
( spl0_936
<=> ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f8513,plain,
( spl0_1031
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f21953,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_936
| ~ spl0_1031
| ~ spl0_1786 ),
inference(forward_demodulation,[],[f21912,f8515]) ).
fof(f8515,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_1031 ),
inference(avatar_component_clause,[],[f8513]) ).
fof(f21912,plain,
( c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_936
| ~ spl0_1786 ),
inference(superposition,[],[f8003,f17347]) ).
fof(f8003,plain,
( ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_936 ),
inference(avatar_component_clause,[],[f8002]) ).
fof(f22035,plain,
( spl0_1984
| ~ spl0_1578
| ~ spl0_1983 ),
inference(avatar_split_clause,[],[f22031,f22028,f13859,f22033]) ).
fof(f22033,plain,
( spl0_1984
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f22028,plain,
( spl0_1983
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f22031,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1578
| ~ spl0_1983 ),
inference(forward_demodulation,[],[f22029,f13861]) ).
fof(f22029,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1983 ),
inference(avatar_component_clause,[],[f22028]) ).
fof(f22030,plain,
spl0_1983,
inference(avatar_split_clause,[],[f3229,f22028]) ).
fof(f3229,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3023,f2156]) ).
fof(f3023,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1322,f2129]) ).
fof(f1322,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f22009,plain,
( spl0_1982
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f22005,f22001,f10789,f3507,f22007]) ).
fof(f22007,plain,
( spl0_1982
<=> ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f22001,plain,
( spl0_1981
<=> ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f22005,plain,
( ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f22004,f11793]) ).
fof(f22004,plain,
( ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f22002,f11793]) ).
fof(f22002,plain,
( ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1981 ),
inference(avatar_component_clause,[],[f22001]) ).
fof(f22003,plain,
spl0_1981,
inference(avatar_split_clause,[],[f3187,f22001]) ).
fof(f3187,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3186,f2156]) ).
fof(f3186,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3185,f2154]) ).
fof(f3185,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3184,f2156]) ).
fof(f3184,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3183,f2156]) ).
fof(f3183,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3182,f2154]) ).
fof(f3182,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2308,f2156]) ).
fof(f2308,axiom,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).
fof(f21998,plain,
spl0_1980,
inference(avatar_split_clause,[],[f3018,f21996]) ).
fof(f3018,plain,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1855,f2129]) ).
fof(f1855,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f21993,plain,
spl0_1979,
inference(avatar_split_clause,[],[f3017,f21991]) ).
fof(f3017,plain,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1858,f2129]) ).
fof(f1858,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f21989,plain,
spl0_1978,
inference(avatar_split_clause,[],[f2352,f21987]) ).
fof(f21987,plain,
( spl0_1978
<=> ! [X15,X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| ~ c_less(c_1,X18,X1)
| c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f2352,axiom,
! [X21,X1,X18,X15] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| ~ c_less(c_1,X18,X1)
| c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f21985,plain,
spl0_1977,
inference(avatar_split_clause,[],[f2327,f21983]) ).
fof(f21983,plain,
( spl0_1977
<=> ! [X21,X1,X0] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f2327,axiom,
! [X21,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f21910,plain,
spl0_1976,
inference(avatar_split_clause,[],[f2320,f21908]) ).
fof(f21908,plain,
( spl0_1976
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| c_lessequals(X0,c_0,X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f2320,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| c_lessequals(X0,c_0,X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f21906,plain,
spl0_1975,
inference(avatar_split_clause,[],[f1973,f21904]) ).
fof(f21904,plain,
( spl0_1975
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f1973,axiom,
! [X2,X47,X18] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f21902,plain,
spl0_1974,
inference(avatar_split_clause,[],[f1972,f21900]) ).
fof(f21900,plain,
( spl0_1974
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f1972,axiom,
! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f21898,plain,
spl0_1973,
inference(avatar_split_clause,[],[f1969,f21896]) ).
fof(f21896,plain,
( spl0_1973
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f1969,axiom,
! [X2,X47,X18] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f21894,plain,
spl0_1972,
inference(avatar_split_clause,[],[f1968,f21892]) ).
fof(f21892,plain,
( spl0_1972
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f1968,axiom,
! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f21890,plain,
spl0_1971,
inference(avatar_split_clause,[],[f1962,f21888]) ).
fof(f21888,plain,
( spl0_1971
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f1962,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f21886,plain,
spl0_1970,
inference(avatar_split_clause,[],[f1961,f21884]) ).
fof(f21884,plain,
( spl0_1970
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f1961,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f21882,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1946,f21880]) ).
fof(f21880,plain,
( spl0_1969
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f1946,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f21878,plain,
spl0_1968,
inference(avatar_split_clause,[],[f1945,f21876]) ).
fof(f21876,plain,
( spl0_1968
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f1945,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f21874,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1876,f21872]) ).
fof(f21872,plain,
( spl0_1967
<=> ! [X11,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f1876,axiom,
! [X11,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f21869,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1755,f21867]) ).
fof(f21867,plain,
( spl0_1966
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f1755,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f21865,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1274,f21863]) ).
fof(f21863,plain,
( spl0_1965
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f1274,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f21861,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1256,f21859]) ).
fof(f21859,plain,
( spl0_1964
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f1256,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f21857,plain,
spl0_1963,
inference(avatar_split_clause,[],[f33,f21855]) ).
fof(f21855,plain,
( spl0_1963
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f33,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f21853,plain,
spl0_1962,
inference(avatar_split_clause,[],[f32,f21851]) ).
fof(f21851,plain,
( spl0_1962
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f32,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f21480,plain,
( spl0_1961
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1947 ),
inference(avatar_split_clause,[],[f21337,f21334,f17014,f7265,f7245,f21478]) ).
fof(f21478,plain,
( spl0_1961
<=> ! [X3,X23,X25,X1] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f21334,plain,
( spl0_1947
<=> ! [X3,X23,X25,X1] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f21337,plain,
( ! [X3,X1,X25,X23] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1947 ),
inference(forward_demodulation,[],[f21335,f17040]) ).
fof(f21335,plain,
( ! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 )
| ~ spl0_1947 ),
inference(avatar_component_clause,[],[f21334]) ).
fof(f21444,plain,
( spl0_1960
| ~ spl0_1786
| ~ spl0_1943 ),
inference(avatar_split_clause,[],[f21319,f21316,f17345,f21442]) ).
fof(f21442,plain,
( spl0_1960
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f21316,plain,
( spl0_1943
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f21319,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1786
| ~ spl0_1943 ),
inference(forward_demodulation,[],[f21317,f17347]) ).
fof(f21317,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1943 ),
inference(avatar_component_clause,[],[f21316]) ).
fof(f21386,plain,
spl0_1959,
inference(avatar_split_clause,[],[f3160,f21384]) ).
fof(f21384,plain,
( spl0_1959
<=> ! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f3160,plain,
! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2981,f2831]) ).
fof(f2831,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2016,f2544]) ).
fof(f2016,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2981,plain,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1872,f2544]) ).
fof(f1872,axiom,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f21382,plain,
spl0_1958,
inference(avatar_split_clause,[],[f2987,f21380]) ).
fof(f21380,plain,
( spl0_1958
<=> ! [X5,X1,X28] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f2987,plain,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f119,f2716]) ).
fof(f119,axiom,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f21378,plain,
spl0_1957,
inference(avatar_split_clause,[],[f2985,f21376]) ).
fof(f21376,plain,
( spl0_1957
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f2985,plain,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
inference(definition_unfolding,[],[f1557,f2373]) ).
fof(f1557,axiom,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f21373,plain,
spl0_1956,
inference(avatar_split_clause,[],[f2936,f21371]) ).
fof(f21371,plain,
( spl0_1956
<=> ! [X11,X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f2936,plain,
! [X48,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ),
inference(definition_unfolding,[],[f2165,f2129]) ).
fof(f2165,axiom,
! [X48,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f21369,plain,
spl0_1955,
inference(avatar_split_clause,[],[f2909,f21367]) ).
fof(f21367,plain,
( spl0_1955
<=> ! [X41,X0,X23,X25] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f2909,plain,
! [X41,X0,X25,X23] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41),
inference(definition_unfolding,[],[f1587,f1585,f1585]) ).
fof(f1585,axiom,
! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f1587,axiom,
! [X41,X0,X25,X23] : c_List_Oitrev(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Oitrev(X23,c_List_Olist_OCons(X0,X25,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f21365,plain,
spl0_1954,
inference(avatar_split_clause,[],[f2795,f21363]) ).
fof(f21363,plain,
( spl0_1954
<=> ! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f2795,axiom,
! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
fof(f21361,plain,
spl0_1953,
inference(avatar_split_clause,[],[f2786,f21359]) ).
fof(f21359,plain,
( spl0_1953
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f2786,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
fof(f21357,plain,
spl0_1952,
inference(avatar_split_clause,[],[f2122,f21355]) ).
fof(f21355,plain,
( spl0_1952
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f2122,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f21353,plain,
spl0_1951,
inference(avatar_split_clause,[],[f1864,f21351]) ).
fof(f21351,plain,
( spl0_1951
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f1864,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f21349,plain,
spl0_1950,
inference(avatar_split_clause,[],[f1800,f21347]) ).
fof(f21347,plain,
( spl0_1950
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f1800,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f21345,plain,
spl0_1949,
inference(avatar_split_clause,[],[f1796,f21343]) ).
fof(f21343,plain,
( spl0_1949
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f1796,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f21341,plain,
spl0_1948,
inference(avatar_split_clause,[],[f1795,f21339]) ).
fof(f21339,plain,
( spl0_1948
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f1795,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f21336,plain,
spl0_1947,
inference(avatar_split_clause,[],[f1726,f21334]) ).
fof(f1726,axiom,
! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f21332,plain,
( ~ spl0_1946
| ~ spl0_640
| ~ spl0_1727 ),
inference(avatar_split_clause,[],[f21254,f16605,f5911,f21329]) ).
fof(f21329,plain,
( spl0_1946
<=> c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f16605,plain,
( spl0_1727
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f21254,plain,
( ~ c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1727 ),
inference(superposition,[],[f16606,f5913]) ).
fof(f16606,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1727 ),
inference(avatar_component_clause,[],[f16605]) ).
fof(f21327,plain,
spl0_1945,
inference(avatar_split_clause,[],[f1714,f21325]) ).
fof(f21325,plain,
( spl0_1945
<=> ! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f1714,axiom,
! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f21323,plain,
spl0_1944,
inference(avatar_split_clause,[],[f1617,f21321]) ).
fof(f21321,plain,
( spl0_1944
<=> ! [X61,X5,X1,X24] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f1617,axiom,
! [X1,X24,X5,X61] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f21318,plain,
spl0_1943,
inference(avatar_split_clause,[],[f1453,f21316]) ).
fof(f1453,axiom,
! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f21314,plain,
spl0_1942,
inference(avatar_split_clause,[],[f1219,f21312]) ).
fof(f21312,plain,
( spl0_1942
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f1219,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f21310,plain,
spl0_1941,
inference(avatar_split_clause,[],[f1218,f21308]) ).
fof(f21308,plain,
( spl0_1941
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f1218,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f21306,plain,
spl0_1940,
inference(avatar_split_clause,[],[f57,f21304]) ).
fof(f21304,plain,
( spl0_1940
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f57,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f21302,plain,
spl0_1939,
inference(avatar_split_clause,[],[f56,f21300]) ).
fof(f21300,plain,
( spl0_1939
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f56,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f20778,plain,
( ~ spl0_1938
| ~ spl0_640
| ~ spl0_1716 ),
inference(avatar_split_clause,[],[f20511,f16561,f5911,f20775]) ).
fof(f20775,plain,
( spl0_1938
<=> c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f16561,plain,
( spl0_1716
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f20511,plain,
( ~ c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1716 ),
inference(superposition,[],[f16562,f5913]) ).
fof(f16562,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1716 ),
inference(avatar_component_clause,[],[f16561]) ).
fof(f20519,plain,
( spl0_1937
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1903 ),
inference(avatar_split_clause,[],[f20022,f20018,f17014,f7265,f7245,f20517]) ).
fof(f20517,plain,
( spl0_1937
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f20018,plain,
( spl0_1903
<=> ! [X23,X0,X3,X25,X1] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f20022,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1903 ),
inference(forward_demodulation,[],[f20021,f17040]) ).
fof(f20021,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X0 = X3 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1903 ),
inference(forward_demodulation,[],[f20019,f17040]) ).
fof(f20019,plain,
( ! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_1903 ),
inference(avatar_component_clause,[],[f20018]) ).
fof(f20510,plain,
( spl0_1936
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1902 ),
inference(avatar_split_clause,[],[f20016,f20012,f17014,f7265,f7245,f20508]) ).
fof(f20508,plain,
( spl0_1936
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f20012,plain,
( spl0_1902
<=> ! [X3,X0,X23,X25,X1] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f20016,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1902 ),
inference(forward_demodulation,[],[f20015,f17040]) ).
fof(f20015,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X23 = X25 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1762
| ~ spl0_1902 ),
inference(forward_demodulation,[],[f20013,f17040]) ).
fof(f20013,plain,
( ! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_1902 ),
inference(avatar_component_clause,[],[f20012]) ).
fof(f20189,plain,
( spl0_1935
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1934 ),
inference(avatar_split_clause,[],[f20185,f20181,f10767,f10447,f6846,f5911,f20187]) ).
fof(f20181,plain,
( spl0_1934
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f20185,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1934 ),
inference(forward_demodulation,[],[f20184,f11726]) ).
fof(f20184,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(c_1,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1934 ),
inference(forward_demodulation,[],[f20182,f11726]) ).
fof(f20182,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1934 ),
inference(avatar_component_clause,[],[f20181]) ).
fof(f20183,plain,
spl0_1934,
inference(avatar_split_clause,[],[f3084,f20181]) ).
fof(f20175,plain,
spl0_1933,
inference(avatar_split_clause,[],[f3011,f20173]) ).
fof(f20173,plain,
( spl0_1933
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f3011,plain,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2608,f2373]) ).
fof(f2608,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f20171,plain,
spl0_1932,
inference(avatar_split_clause,[],[f3006,f20169]) ).
fof(f20169,plain,
( spl0_1932
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f3006,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2142,f2129]) ).
fof(f2142,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f20167,plain,
spl0_1931,
inference(avatar_split_clause,[],[f3005,f20165]) ).
fof(f20165,plain,
( spl0_1931
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f3005,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2141,f2129]) ).
fof(f2141,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f20163,plain,
spl0_1930,
inference(avatar_split_clause,[],[f2957,f20161]) ).
fof(f20161,plain,
( spl0_1930
<=> ! [X43,X23,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f2957,plain,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ),
inference(definition_unfolding,[],[f1703,f1766]) ).
fof(f1703,axiom,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Otake(X21,X23,X1),X43,X1) = c_List_Onth(X23,X43,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f20159,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2933,f20157]) ).
fof(f20157,plain,
( spl0_1929
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f2933,plain,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f2120,f2129]) ).
fof(f2120,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1) = c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f20155,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2807,f20153]) ).
fof(f2807,axiom,
! [X91,X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
fof(f20151,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2802,f20149]) ).
fof(f20149,plain,
( spl0_1927
<=> ! [X20,X88,X4] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f2802,axiom,
! [X88,X4,X20] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
fof(f20147,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2782,f20145]) ).
fof(f20145,plain,
( spl0_1926
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f2782,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
fof(f20143,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2781,f20141]) ).
fof(f20141,plain,
( spl0_1925
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f2781,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
fof(f20139,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2774,f20137]) ).
fof(f20137,plain,
( spl0_1924
<=> ! [X86,X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f2774,axiom,
! [X91,X88,X86] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
fof(f20121,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2773,f20119]) ).
fof(f20119,plain,
( spl0_1923
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f2773,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
fof(f20117,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2674,f20115]) ).
fof(f20115,plain,
( spl0_1922
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f2674,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f20113,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2647,f20111]) ).
fof(f20111,plain,
( spl0_1921
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f2647,axiom,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f20109,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2597,f20107]) ).
fof(f20107,plain,
( spl0_1920
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f2597,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f20105,plain,
spl0_1919,
inference(avatar_split_clause,[],[f2337,f20103]) ).
fof(f20103,plain,
( spl0_1919
<=> ! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f2337,axiom,
! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f20101,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2329,f20099]) ).
fof(f20099,plain,
( spl0_1918
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f2329,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f20097,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2326,f20095]) ).
fof(f20095,plain,
( spl0_1917
<=> ! [X21,X1,X0] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f2326,axiom,
! [X21,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f20093,plain,
spl0_1916,
inference(avatar_split_clause,[],[f2323,f20091]) ).
fof(f20091,plain,
( spl0_1916
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f2323,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f20089,plain,
spl0_1915,
inference(avatar_split_clause,[],[f2077,f20087]) ).
fof(f20087,plain,
( spl0_1915
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f2077,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f20085,plain,
spl0_1914,
inference(avatar_split_clause,[],[f2074,f20083]) ).
fof(f20083,plain,
( spl0_1914
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f2074,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f20073,plain,
spl0_1913,
inference(avatar_split_clause,[],[f2069,f20071]) ).
fof(f20071,plain,
( spl0_1913
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f2069,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f20069,plain,
spl0_1912,
inference(avatar_split_clause,[],[f2066,f20067]) ).
fof(f20067,plain,
( spl0_1912
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f2066,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f20065,plain,
spl0_1911,
inference(avatar_split_clause,[],[f1929,f20063]) ).
fof(f20063,plain,
( spl0_1911
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f1929,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f20061,plain,
spl0_1910,
inference(avatar_split_clause,[],[f1830,f20059]) ).
fof(f20059,plain,
( spl0_1910
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f1830,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f20057,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1829,f20055]) ).
fof(f20055,plain,
( spl0_1909
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f1829,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f20053,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1721,f20051]) ).
fof(f20051,plain,
( spl0_1908
<=> ! [X41,X0,X23,X3] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f1721,axiom,
! [X3,X41,X0,X23] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f20049,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1704,f20047]) ).
fof(f20047,plain,
( spl0_1907
<=> ! [X16,X59,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f1704,axiom,
! [X59,X16,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f20045,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1697,f20043]) ).
fof(f20043,plain,
( spl0_1906
<=> ! [X21,X23,X25,X1] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f1697,axiom,
! [X21,X1,X25,X23] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f20041,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1630,f20039]) ).
fof(f20039,plain,
( spl0_1905
<=> ! [X41,X60,X18,X65] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f1630,axiom,
! [X65,X41,X18,X60] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f20037,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1599,f20035]) ).
fof(f20035,plain,
( spl0_1904
<=> ! [X25,X1,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f1599,axiom,
! [X1,X25,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f20020,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1517,f20018]) ).
fof(f1517,axiom,
! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f20014,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1516,f20012]) ).
fof(f1516,axiom,
! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f20010,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1481,f20008]) ).
fof(f1481,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f20006,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1480,f20004]) ).
fof(f20004,plain,
( spl0_1900
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f1480,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f20002,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1473,f20000]) ).
fof(f20000,plain,
( spl0_1899
<=> ! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f1473,axiom,
! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f19998,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1472,f19996]) ).
fof(f19996,plain,
( spl0_1898
<=> ! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f1472,axiom,
! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f19994,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1292,f19992]) ).
fof(f19992,plain,
( spl0_1897
<=> ! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f1292,axiom,
! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f19990,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1288,f19988]) ).
fof(f19988,plain,
( spl0_1896
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f1288,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f19656,plain,
( spl0_1895
| ~ spl0_641
| ~ spl0_1676 ),
inference(avatar_split_clause,[],[f19341,f15365,f5916,f19653]) ).
fof(f19653,plain,
( spl0_1895
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f15365,plain,
( spl0_1676
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f19341,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1676 ),
inference(superposition,[],[f15366,f5918]) ).
fof(f15366,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1676 ),
inference(avatar_component_clause,[],[f15365]) ).
fof(f19529,plain,
( spl0_1894
| ~ spl0_640
| ~ spl0_1676 ),
inference(avatar_split_clause,[],[f19340,f15365,f5911,f19526]) ).
fof(f19526,plain,
( spl0_1894
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f19340,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1676 ),
inference(superposition,[],[f15366,f5913]) ).
fof(f19258,plain,
( spl0_1893
| ~ spl0_646
| ~ spl0_776
| ~ spl0_1540 ),
inference(avatar_split_clause,[],[f14236,f13707,f7273,f5938,f19255]) ).
fof(f19255,plain,
( spl0_1893
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f13707,plain,
( spl0_1540
<=> ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f14236,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_776
| ~ spl0_1540 ),
inference(forward_demodulation,[],[f14218,f7274]) ).
fof(f14218,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_1540 ),
inference(resolution,[],[f13708,f5940]) ).
fof(f13708,plain,
( ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) )
| ~ spl0_1540 ),
inference(avatar_component_clause,[],[f13707]) ).
fof(f19034,plain,
( spl0_1891
| spl0_1892
| ~ spl0_663
| ~ spl0_1533 ),
inference(avatar_split_clause,[],[f14123,f13679,f6777,f19032,f19029]) ).
fof(f19029,plain,
( spl0_1891
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f14123,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_663
| ~ spl0_1533 ),
inference(resolution,[],[f13680,f6778]) ).
fof(f18992,plain,
spl0_1890,
inference(avatar_split_clause,[],[f3245,f18990]) ).
fof(f18990,plain,
( spl0_1890
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f3245,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3036,f2114]) ).
fof(f2114,axiom,
! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f3036,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1313,f2129]) ).
fof(f1313,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f18988,plain,
spl0_1889,
inference(avatar_split_clause,[],[f3243,f18986]) ).
fof(f18986,plain,
( spl0_1889
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f3243,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3034,f2114]) ).
fof(f3034,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1325,f2129]) ).
fof(f1325,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f18984,plain,
spl0_1888,
inference(avatar_split_clause,[],[f3235,f18982]) ).
fof(f18982,plain,
( spl0_1888
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f3235,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3028,f2114]) ).
fof(f3028,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1312,f2129]) ).
fof(f1312,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f18980,plain,
spl0_1887,
inference(avatar_split_clause,[],[f3233,f18978]) ).
fof(f18978,plain,
( spl0_1887
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f3233,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3026,f2114]) ).
fof(f3026,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1324,f2129]) ).
fof(f1324,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f18976,plain,
spl0_1886,
inference(avatar_split_clause,[],[f3201,f18974]) ).
fof(f18974,plain,
( spl0_1886
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f3201,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3002,f2156]) ).
fof(f3002,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1336,f2129]) ).
fof(f1336,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f18967,plain,
( spl0_1885
| ~ spl0_1578
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f18959,f18956,f13859,f18965]) ).
fof(f18965,plain,
( spl0_1885
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f18956,plain,
( spl0_1883
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f18959,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1578
| ~ spl0_1883 ),
inference(forward_demodulation,[],[f18957,f13861]) ).
fof(f18957,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1883 ),
inference(avatar_component_clause,[],[f18956]) ).
fof(f18963,plain,
( spl0_1884
| ~ spl0_832
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f13627,f12347,f7510,f18961]) ).
fof(f18961,plain,
( spl0_1884
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f12347,plain,
( spl0_1516
<=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f13627,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_832
| ~ spl0_1516 ),
inference(superposition,[],[f7511,f12348]) ).
fof(f12348,plain,
( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3
| ~ spl0_1516 ),
inference(avatar_component_clause,[],[f12347]) ).
fof(f18958,plain,
spl0_1883,
inference(avatar_split_clause,[],[f3200,f18956]) ).
fof(f3200,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3001,f2156]) ).
fof(f3001,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1340,f2129]) ).
fof(f1340,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f18954,plain,
spl0_1882,
inference(avatar_split_clause,[],[f3195,f18952]) ).
fof(f18952,plain,
( spl0_1882
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f3195,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f2998,f2156]) ).
fof(f2998,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1335,f2129]) ).
fof(f1335,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f18941,plain,
( spl0_1881
| ~ spl0_1578
| ~ spl0_1880 ),
inference(avatar_split_clause,[],[f18937,f18934,f13859,f18939]) ).
fof(f18939,plain,
( spl0_1881
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f18934,plain,
( spl0_1880
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f18937,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1578
| ~ spl0_1880 ),
inference(forward_demodulation,[],[f18935,f13861]) ).
fof(f18935,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1880 ),
inference(avatar_component_clause,[],[f18934]) ).
fof(f18936,plain,
spl0_1880,
inference(avatar_split_clause,[],[f3194,f18934]) ).
fof(f3194,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2997,f2156]) ).
fof(f2997,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1339,f2129]) ).
fof(f1339,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f18930,plain,
( spl0_1879
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1878 ),
inference(avatar_split_clause,[],[f18926,f18923,f10789,f3507,f18928]) ).
fof(f18928,plain,
( spl0_1879
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f18923,plain,
( spl0_1878
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f18926,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1878 ),
inference(forward_demodulation,[],[f18924,f11793]) ).
fof(f18924,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1878 ),
inference(avatar_component_clause,[],[f18923]) ).
fof(f18925,plain,
spl0_1878,
inference(avatar_split_clause,[],[f3163,f18923]) ).
fof(f3163,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3162,f2156]) ).
fof(f3162,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3161,f2154]) ).
fof(f3161,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2273,f2156]) ).
fof(f2273,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f18919,plain,
( spl0_1877
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1875 ),
inference(avatar_split_clause,[],[f18911,f18908,f10789,f3507,f18917]) ).
fof(f18917,plain,
( spl0_1877
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f18908,plain,
( spl0_1875
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f18911,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1391
| ~ spl0_1875 ),
inference(forward_demodulation,[],[f18909,f11793]) ).
fof(f18909,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1875 ),
inference(avatar_component_clause,[],[f18908]) ).
fof(f18915,plain,
( spl0_1876
| ~ spl0_1177
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f13144,f12076,f9515,f18913]) ).
fof(f18913,plain,
( spl0_1876
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f9515,plain,
( spl0_1177
<=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f13144,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1177
| ~ spl0_1463 ),
inference(superposition,[],[f9516,f12077]) ).
fof(f9516,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1177 ),
inference(avatar_component_clause,[],[f9515]) ).
fof(f18910,plain,
spl0_1875,
inference(avatar_split_clause,[],[f3159,f18908]) ).
fof(f3159,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3158,f2156]) ).
fof(f3158,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3157,f2154]) ).
fof(f3157,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2272,f2156]) ).
fof(f2272,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f18905,plain,
( spl0_1874
| ~ spl0_1578
| ~ spl0_1873 ),
inference(avatar_split_clause,[],[f18901,f18898,f13859,f18903]) ).
fof(f18903,plain,
( spl0_1874
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f18898,plain,
( spl0_1873
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f18901,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1578
| ~ spl0_1873 ),
inference(forward_demodulation,[],[f18899,f13861]) ).
fof(f18899,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1873 ),
inference(avatar_component_clause,[],[f18898]) ).
fof(f18900,plain,
spl0_1873,
inference(avatar_split_clause,[],[f3128,f18898]) ).
fof(f3128,plain,
! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2935,f2156]) ).
fof(f2935,plain,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
inference(definition_unfolding,[],[f1332,f2129]) ).
fof(f1332,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f18896,plain,
spl0_1872,
inference(avatar_split_clause,[],[f3127,f18894]) ).
fof(f18894,plain,
( spl0_1872
<=> ! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f3127,plain,
! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2934,f2156]) ).
fof(f2934,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f1331,f2129]) ).
fof(f1331,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X11)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f18892,plain,
spl0_1871,
inference(avatar_split_clause,[],[f3097,f18890]) ).
fof(f3097,plain,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat),
inference(forward_demodulation,[],[f2917,f2831]) ).
fof(f2917,plain,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2765,f2544]) ).
fof(f2765,axiom,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__6_0) ).
fof(f18888,plain,
spl0_1870,
inference(avatar_split_clause,[],[f3088,f18886]) ).
fof(f18886,plain,
( spl0_1870
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f3088,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3087,f2156]) ).
fof(f3087,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3086,f2154]) ).
fof(f3086,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3085,f2156]) ).
fof(f3085,plain,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2905,f3084]) ).
fof(f2905,plain,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1881,f2544,f2544]) ).
fof(f1881,axiom,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Suc(c_Suc(X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f18866,plain,
( spl0_1869
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1868 ),
inference(avatar_split_clause,[],[f18862,f18859,f10767,f10447,f6846,f5911,f18864]) ).
fof(f18864,plain,
( spl0_1869
<=> ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f18859,plain,
( spl0_1868
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f18862,plain,
( ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1868 ),
inference(forward_demodulation,[],[f18860,f11726]) ).
fof(f18860,plain,
( ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1868 ),
inference(avatar_component_clause,[],[f18859]) ).
fof(f18861,plain,
spl0_1868,
inference(avatar_split_clause,[],[f2980,f18859]) ).
fof(f2980,plain,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1823,f2544]) ).
fof(f1823,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f18857,plain,
( spl0_1867
| ~ spl0_783
| ~ spl0_807
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10246,f9829,f7398,f7301,f18855]) ).
fof(f18855,plain,
( spl0_1867
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f7398,plain,
( spl0_807
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f10246,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_807
| ~ spl0_1254 ),
inference(forward_demodulation,[],[f10235,f7302]) ).
fof(f10235,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_807
| ~ spl0_1254 ),
inference(superposition,[],[f9830,f7399]) ).
fof(f7399,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_807 ),
inference(avatar_component_clause,[],[f7398]) ).
fof(f18853,plain,
spl0_1866,
inference(avatar_split_clause,[],[f2910,f18851]) ).
fof(f2910,plain,
! [X0,X1,X16,X43] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1),
inference(definition_unfolding,[],[f1775,f1766]) ).
fof(f1775,axiom,
! [X0,X1,X16,X43] : c_List_Otake(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f18849,plain,
spl0_1865,
inference(avatar_split_clause,[],[f2908,f18847]) ).
fof(f2908,plain,
! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)),
inference(definition_unfolding,[],[f1611,f1766]) ).
fof(f1611,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Otake(X21,X23,X1),tc_List_Olist(X1)) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f18845,plain,
spl0_1864,
inference(avatar_split_clause,[],[f2904,f18843]) ).
fof(f2904,plain,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1),
inference(definition_unfolding,[],[f2623,f2373]) ).
fof(f2623,axiom,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f18840,plain,
( spl0_1863
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1862 ),
inference(avatar_split_clause,[],[f18836,f18833,f10767,f10447,f6846,f5911,f18838]) ).
fof(f18838,plain,
( spl0_1863
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f18833,plain,
( spl0_1862
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f18836,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1862 ),
inference(forward_demodulation,[],[f18834,f11726]) ).
fof(f18834,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_1862 ),
inference(avatar_component_clause,[],[f18833]) ).
fof(f18835,plain,
spl0_1862,
inference(avatar_split_clause,[],[f2903,f18833]) ).
fof(f2903,plain,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1207,f2544]) ).
fof(f1207,axiom,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f18830,plain,
( spl0_1861
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1860 ),
inference(avatar_split_clause,[],[f18826,f18823,f10767,f10447,f6846,f5911,f18828]) ).
fof(f18828,plain,
( spl0_1861
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f18823,plain,
( spl0_1860
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f18826,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1860 ),
inference(forward_demodulation,[],[f18824,f11726]) ).
fof(f18824,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_1860 ),
inference(avatar_component_clause,[],[f18823]) ).
fof(f18825,plain,
spl0_1860,
inference(avatar_split_clause,[],[f2902,f18823]) ).
fof(f2902,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1206,f2544]) ).
fof(f1206,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f18820,plain,
( spl0_1859
| ~ spl0_783
| ~ spl0_808
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10245,f9829,f7402,f7301,f18818]) ).
fof(f18818,plain,
( spl0_1859
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f7402,plain,
( spl0_808
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f10245,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_808
| ~ spl0_1254 ),
inference(forward_demodulation,[],[f10234,f7302]) ).
fof(f10234,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_808
| ~ spl0_1254 ),
inference(superposition,[],[f9830,f7403]) ).
fof(f7403,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f7402]) ).
fof(f18816,plain,
( spl0_1858
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1857 ),
inference(avatar_split_clause,[],[f18812,f18809,f10767,f10447,f6846,f5911,f18814]) ).
fof(f18814,plain,
( spl0_1858
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f18809,plain,
( spl0_1857
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f18812,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1857 ),
inference(forward_demodulation,[],[f18810,f11726]) ).
fof(f18810,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_1857 ),
inference(avatar_component_clause,[],[f18809]) ).
fof(f18811,plain,
spl0_1857,
inference(avatar_split_clause,[],[f2901,f18809]) ).
fof(f2901,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1203,f2544]) ).
fof(f1203,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f18807,plain,
spl0_1856,
inference(avatar_split_clause,[],[f2889,f18805]) ).
fof(f2889,plain,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)),
inference(definition_unfolding,[],[f120,f2716]) ).
fof(f120,axiom,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f18803,plain,
spl0_1855,
inference(avatar_split_clause,[],[f2881,f18801]) ).
fof(f18801,plain,
( spl0_1855
<=> ! [X5,X1] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f2881,plain,
! [X1,X5] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2708,f2716]) ).
fof(f2708,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f18778,plain,
( spl0_1854
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1853 ),
inference(avatar_split_clause,[],[f18774,f18771,f10767,f10447,f6846,f5911,f18776]) ).
fof(f18771,plain,
( spl0_1853
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f18774,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1853 ),
inference(forward_demodulation,[],[f18772,f11726]) ).
fof(f18772,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1853 ),
inference(avatar_component_clause,[],[f18771]) ).
fof(f18773,plain,
spl0_1853,
inference(avatar_split_clause,[],[f2879,f18771]) ).
fof(f2879,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2027,f2544,f2544]) ).
fof(f2027,axiom,
! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f18688,plain,
( spl0_1852
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1851 ),
inference(avatar_split_clause,[],[f18684,f18680,f10767,f10447,f6846,f5911,f18686]) ).
fof(f18680,plain,
( spl0_1851
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f18684,plain,
( ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f18683,f11726]) ).
fof(f18683,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f18681,f11726]) ).
fof(f18681,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f18680]) ).
fof(f18682,plain,
spl0_1851,
inference(avatar_split_clause,[],[f2878,f18680]) ).
fof(f18678,plain,
( spl0_1850
| ~ spl0_783
| ~ spl0_809
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10244,f9829,f7406,f7301,f18676]) ).
fof(f18676,plain,
( spl0_1850
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f7406,plain,
( spl0_809
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f10244,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_809
| ~ spl0_1254 ),
inference(forward_demodulation,[],[f10233,f7302]) ).
fof(f10233,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_809
| ~ spl0_1254 ),
inference(superposition,[],[f9830,f7407]) ).
fof(f7407,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f7406]) ).
fof(f18652,plain,
( spl0_1849
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1848 ),
inference(avatar_split_clause,[],[f18648,f18644,f10767,f10447,f6846,f5911,f18650]) ).
fof(f18644,plain,
( spl0_1848
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f18648,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f18647,f11726]) ).
fof(f18647,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f18645,f11726]) ).
fof(f18645,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1848 ),
inference(avatar_component_clause,[],[f18644]) ).
fof(f18646,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2877,f18644]) ).
fof(f2877,plain,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2035,f2544,f2544]) ).
fof(f2035,axiom,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f18642,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2819,f18640]) ).
fof(f18640,plain,
( spl0_1847
<=> ! [X87,X86,X88] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f2819,axiom,
! [X88,X86,X87] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
fof(f18638,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2816,f18636]) ).
fof(f18636,plain,
( spl0_1846
<=> ! [X86,X91,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f2816,axiom,
! [X91,X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
fof(f18634,plain,
spl0_1845,
inference(avatar_split_clause,[],[f2694,f18632]) ).
fof(f18632,plain,
( spl0_1845
<=> ! [X12,X0,X1] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f2694,axiom,
! [X0,X1,X12] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
fof(f18630,plain,
spl0_1844,
inference(avatar_split_clause,[],[f2693,f18628]) ).
fof(f18628,plain,
( spl0_1844
<=> ! [X12,X27,X1,X18] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f2693,axiom,
! [X1,X18,X27,X12] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
fof(f18626,plain,
spl0_1843,
inference(avatar_split_clause,[],[f2690,f18624]) ).
fof(f18624,plain,
( spl0_1843
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f2690,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f18622,plain,
spl0_1842,
inference(avatar_split_clause,[],[f2573,f18620]) ).
fof(f18620,plain,
( spl0_1842
<=> ! [X16,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f2573,axiom,
! [X1,X16] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f18618,plain,
spl0_1841,
inference(avatar_split_clause,[],[f2565,f18616]) ).
fof(f18616,plain,
( spl0_1841
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f2565,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f18614,plain,
( spl0_1840
| ~ spl0_783
| ~ spl0_806
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10242,f9829,f7394,f7301,f18612]) ).
fof(f18612,plain,
( spl0_1840
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f7394,plain,
( spl0_806
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f10242,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_806
| ~ spl0_1254 ),
inference(forward_demodulation,[],[f10231,f7302]) ).
fof(f10231,plain,
( ! [X0] : c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) = c_plus(c_0,c_1,tc_nat)
| ~ spl0_806
| ~ spl0_1254 ),
inference(superposition,[],[f9830,f7395]) ).
fof(f7395,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_806 ),
inference(avatar_component_clause,[],[f7394]) ).
fof(f18610,plain,
spl0_1839,
inference(avatar_split_clause,[],[f2556,f18608]) ).
fof(f18608,plain,
( spl0_1839
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f2556,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f18606,plain,
spl0_1838,
inference(avatar_split_clause,[],[f2553,f18604]) ).
fof(f18604,plain,
( spl0_1838
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f2553,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f18602,plain,
spl0_1837,
inference(avatar_split_clause,[],[f2526,f18600]) ).
fof(f18600,plain,
( spl0_1837
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f2526,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f18598,plain,
spl0_1836,
inference(avatar_split_clause,[],[f2521,f18596]) ).
fof(f18596,plain,
( spl0_1836
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f2521,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f18594,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2324,f18592]) ).
fof(f18592,plain,
( spl0_1835
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f2324,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f18590,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2307,f18588]) ).
fof(f18588,plain,
( spl0_1834
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f2307,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f18586,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2305,f18584]) ).
fof(f18584,plain,
( spl0_1833
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f2305,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f18582,plain,
spl0_1832,
inference(avatar_split_clause,[],[f2266,f18580]) ).
fof(f18580,plain,
( spl0_1832
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f2266,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f18578,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2261,f18576]) ).
fof(f18576,plain,
( spl0_1831
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f2261,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f18574,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2258,f18572]) ).
fof(f18572,plain,
( spl0_1830
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f2258,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f18570,plain,
( spl0_1829
| ~ spl0_856
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10240,f9829,f7606,f18568]) ).
fof(f18568,plain,
( spl0_1829
<=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f10240,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_856
| ~ spl0_1254 ),
inference(superposition,[],[f7607,f9830]) ).
fof(f18566,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2255,f18564]) ).
fof(f18564,plain,
( spl0_1828
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f2255,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f18562,plain,
spl0_1827,
inference(avatar_split_clause,[],[f2237,f18560]) ).
fof(f18560,plain,
( spl0_1827
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f2237,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f18558,plain,
spl0_1826,
inference(avatar_split_clause,[],[f2228,f18556]) ).
fof(f18556,plain,
( spl0_1826
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f2228,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f18554,plain,
spl0_1825,
inference(avatar_split_clause,[],[f2214,f18552]) ).
fof(f2214,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f18550,plain,
spl0_1824,
inference(avatar_split_clause,[],[f1843,f18548]) ).
fof(f18548,plain,
( spl0_1824
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f1843,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f18546,plain,
spl0_1823,
inference(avatar_split_clause,[],[f1836,f18544]) ).
fof(f18544,plain,
( spl0_1823
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f1836,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f18542,plain,
spl0_1822,
inference(avatar_split_clause,[],[f1824,f18540]) ).
fof(f18540,plain,
( spl0_1822
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f1824,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f18538,plain,
spl0_1821,
inference(avatar_split_clause,[],[f1821,f18536]) ).
fof(f18536,plain,
( spl0_1821
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f1821,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f18534,plain,
spl0_1820,
inference(avatar_split_clause,[],[f1809,f18532]) ).
fof(f18532,plain,
( spl0_1820
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f1809,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f18530,plain,
spl0_1819,
inference(avatar_split_clause,[],[f1781,f18528]) ).
fof(f18528,plain,
( spl0_1819
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f1781,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f18526,plain,
( spl0_1818
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10230,f9825,f9069,f5916,f18524]) ).
fof(f9069,plain,
( spl0_1118
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f10230,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1253 ),
inference(forward_demodulation,[],[f10227,f9070]) ).
fof(f9070,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1118 ),
inference(avatar_component_clause,[],[f9069]) ).
fof(f10227,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1253 ),
inference(superposition,[],[f9826,f5918]) ).
fof(f18522,plain,
spl0_1817,
inference(avatar_split_clause,[],[f1699,f18520]) ).
fof(f18520,plain,
( spl0_1817
<=> ! [X43,X23,X3,X1] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f1699,axiom,
! [X3,X1,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f18518,plain,
spl0_1816,
inference(avatar_split_clause,[],[f1633,f18516]) ).
fof(f18516,plain,
( spl0_1816
<=> ! [X1,X43,X3] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f1633,axiom,
! [X3,X1,X43] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f18514,plain,
spl0_1815,
inference(avatar_split_clause,[],[f1592,f18512]) ).
fof(f18512,plain,
( spl0_1815
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f1592,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f18510,plain,
spl0_1814,
inference(avatar_split_clause,[],[f1525,f18508]) ).
fof(f18508,plain,
( spl0_1814
<=> ! [X12,X1,X23,X25] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f1525,axiom,
! [X1,X25,X12,X23] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f18506,plain,
spl0_1813,
inference(avatar_split_clause,[],[f1524,f18504]) ).
fof(f18504,plain,
( spl0_1813
<=> ! [X23,X12,X25,X1] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f1524,axiom,
! [X1,X12,X23,X25] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f18502,plain,
spl0_1812,
inference(avatar_split_clause,[],[f1417,f18500]) ).
fof(f18500,plain,
( spl0_1812
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f1417,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f18498,plain,
spl0_1811,
inference(avatar_split_clause,[],[f1403,f18496]) ).
fof(f18496,plain,
( spl0_1811
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f1403,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f18494,plain,
spl0_1810,
inference(avatar_split_clause,[],[f1402,f18492]) ).
fof(f18492,plain,
( spl0_1810
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f1402,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f18490,plain,
spl0_1809,
inference(avatar_split_clause,[],[f1366,f18488]) ).
fof(f18488,plain,
( spl0_1809
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f1366,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f18486,plain,
spl0_1808,
inference(avatar_split_clause,[],[f1365,f18484]) ).
fof(f18484,plain,
( spl0_1808
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f1365,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f18482,plain,
spl0_1807,
inference(avatar_split_clause,[],[f1362,f18480]) ).
fof(f18480,plain,
( spl0_1807
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f1362,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f18478,plain,
spl0_1806,
inference(avatar_split_clause,[],[f1360,f18476]) ).
fof(f18476,plain,
( spl0_1806
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f1360,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f18474,plain,
spl0_1805,
inference(avatar_split_clause,[],[f1359,f18472]) ).
fof(f18472,plain,
( spl0_1805
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f1359,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f18470,plain,
spl0_1804,
inference(avatar_split_clause,[],[f1306,f18468]) ).
fof(f18468,plain,
( spl0_1804
<=> ! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f1306,axiom,
! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f18466,plain,
spl0_1803,
inference(avatar_split_clause,[],[f1290,f18464]) ).
fof(f18464,plain,
( spl0_1803
<=> ! [X2,X5,X1] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f1290,axiom,
! [X2,X1,X5] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f18462,plain,
spl0_1802,
inference(avatar_split_clause,[],[f1289,f18460]) ).
fof(f18460,plain,
( spl0_1802
<=> ! [X2,X5,X1] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f1289,axiom,
! [X2,X1,X5] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f18458,plain,
spl0_1801,
inference(avatar_split_clause,[],[f114,f18456]) ).
fof(f18456,plain,
( spl0_1801
<=> ! [X13,X12,X27,X2,X1] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f114,axiom,
! [X2,X1,X27,X12,X13] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f18454,plain,
spl0_1800,
inference(avatar_split_clause,[],[f113,f18452]) ).
fof(f18452,plain,
( spl0_1800
<=> ! [X18,X13,X12,X2,X1] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f113,axiom,
! [X2,X18,X1,X12,X13] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f18450,plain,
spl0_1799,
inference(avatar_split_clause,[],[f76,f18448]) ).
fof(f76,axiom,
! [X2,X1,X18,X27,X5] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f18446,plain,
spl0_1798,
inference(avatar_split_clause,[],[f72,f18444]) ).
fof(f18444,plain,
( spl0_1798
<=> ! [X12,X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f72,axiom,
! [X2,X1,X27,X5,X12] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f18442,plain,
( spl0_1796
| ~ spl0_1797
| ~ spl0_112
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f10054,f9700,f3799,f18439,f18436]) ).
fof(f18436,plain,
( spl0_1796
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f18439,plain,
( spl0_1797
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f10054,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_112
| ~ spl0_1223 ),
inference(resolution,[],[f9701,f3800]) ).
fof(f18434,plain,
spl0_1795,
inference(avatar_split_clause,[],[f71,f18432]) ).
fof(f18432,plain,
( spl0_1795
<=> ! [X1,X28] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f71,axiom,
! [X28,X1] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f18430,plain,
spl0_1794,
inference(avatar_split_clause,[],[f70,f18428]) ).
fof(f70,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f18426,plain,
spl0_1793,
inference(avatar_split_clause,[],[f58,f18424]) ).
fof(f18424,plain,
( spl0_1793
<=> ! [X12,X0,X1,X26] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f58,axiom,
! [X0,X1,X26,X12] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f18422,plain,
spl0_1792,
inference(avatar_split_clause,[],[f46,f18420]) ).
fof(f18420,plain,
( spl0_1792
<=> ! [X24,X23,X12,X1] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f46,axiom,
! [X1,X24,X12,X23] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f18317,plain,
( spl0_1791
| ~ spl0_709
| ~ spl0_732
| ~ spl0_882
| ~ spl0_1218 ),
inference(avatar_split_clause,[],[f10035,f9680,f7711,f7083,f6984,f18314]) ).
fof(f18314,plain,
( spl0_1791
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f6984,plain,
( spl0_709
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f7083,plain,
( spl0_732
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f10035,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_709
| ~ spl0_732
| ~ spl0_882
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f10034,f6986]) ).
fof(f6986,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_709 ),
inference(avatar_component_clause,[],[f6984]) ).
fof(f10034,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_732
| ~ spl0_882
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f10030,f7713]) ).
fof(f10030,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OPls)
| ~ spl0_732
| ~ spl0_1218 ),
inference(superposition,[],[f9681,f7085]) ).
fof(f7085,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f7083]) ).
fof(f18045,plain,
( spl0_1790
| ~ spl0_646
| ~ spl0_1198 ),
inference(avatar_split_clause,[],[f9944,f9600,f5938,f18042]) ).
fof(f18042,plain,
( spl0_1790
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f9944,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_1198 ),
inference(resolution,[],[f9601,f5940]) ).
fof(f17734,plain,
( spl0_1789
| ~ spl0_784
| ~ spl0_1128 ),
inference(avatar_split_clause,[],[f9427,f9109,f7305,f17732]) ).
fof(f17732,plain,
( spl0_1789
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f7305,plain,
( spl0_784
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f9109,plain,
( spl0_1128
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f9427,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_784
| ~ spl0_1128 ),
inference(superposition,[],[f9110,f7306]) ).
fof(f7306,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f7305]) ).
fof(f9110,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f9109]) ).
fof(f17648,plain,
( spl0_1788
| ~ spl0_878
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f8868,f8586,f7694,f17646]) ).
fof(f17646,plain,
( spl0_1788
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f8868,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_878
| ~ spl0_1049 ),
inference(superposition,[],[f7695,f8587]) ).
fof(f17470,plain,
( spl0_1787
| ~ spl0_9
| ~ spl0_1038 ),
inference(avatar_split_clause,[],[f8855,f8542,f3292,f17468]) ).
fof(f17468,plain,
( spl0_1787
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f8542,plain,
( spl0_1038
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f8855,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_1038 ),
inference(resolution,[],[f8543,f3294]) ).
fof(f8543,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1038 ),
inference(avatar_component_clause,[],[f8542]) ).
fof(f17348,plain,
( spl0_1786
| ~ spl0_52
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f8847,f8526,f3507,f17345]) ).
fof(f17208,plain,
( spl0_1783
| spl0_1785 ),
inference(avatar_split_clause,[],[f3250,f17206,f17185]) ).
fof(f17185,plain,
( spl0_1783
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f17206,plain,
( spl0_1785
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f3250,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1) ),
inference(inner_rewriting,[],[f2334]) ).
fof(f2334,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f17194,plain,
( ~ spl0_707
| ~ spl0_1783 ),
inference(avatar_contradiction_clause,[],[f17193]) ).
fof(f17193,plain,
( $false
| ~ spl0_707
| ~ spl0_1783 ),
inference(trivial_inequality_removal,[],[f17191]) ).
fof(f17191,plain,
( c_0 != c_0
| ~ spl0_707
| ~ spl0_1783 ),
inference(superposition,[],[f17186,f6976]) ).
fof(f6976,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f6974]) ).
fof(f6974,plain,
( spl0_707
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f17186,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_1783 ),
inference(avatar_component_clause,[],[f17185]) ).
fof(f17190,plain,
( spl0_1783
| spl0_1784 ),
inference(avatar_split_clause,[],[f3249,f17188,f17185]) ).
fof(f17188,plain,
( spl0_1784
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f3249,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1) ),
inference(inner_rewriting,[],[f2317]) ).
fof(f2317,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f17157,plain,
( spl0_1782
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1670
| ~ spl0_1781 ),
inference(avatar_split_clause,[],[f17153,f17149,f15310,f10767,f10447,f7265,f6846,f5911,f17155]) ).
fof(f17155,plain,
( spl0_1782
<=> ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f17149,plain,
( spl0_1781
<=> ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f17153,plain,
( ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1670
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f17152,f15313]) ).
fof(f15313,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_1670 ),
inference(superposition,[],[f15311,f7266]) ).
fof(f17152,plain,
( ! [X3] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f17150,f11726]) ).
fof(f17150,plain,
( ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_1781 ),
inference(avatar_component_clause,[],[f17149]) ).
fof(f17151,plain,
spl0_1781,
inference(avatar_split_clause,[],[f3143,f17149]) ).
fof(f3143,plain,
! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ),
inference(forward_demodulation,[],[f2959,f2884]) ).
fof(f2959,plain,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X3 ),
inference(definition_unfolding,[],[f2024,f2544,f2544]) ).
fof(f2024,axiom,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Suc(c_minus(X3,c_Suc(c_0),tc_nat)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f17147,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2983,f17145]) ).
fof(f17145,plain,
( spl0_1780
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f2983,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2610,f2373]) ).
fof(f2610,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f17143,plain,
spl0_1779,
inference(avatar_split_clause,[],[f2982,f17141]) ).
fof(f2982,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2609,f2373]) ).
fof(f2609,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f17139,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2978,f17137]) ).
fof(f17137,plain,
( spl0_1778
<=> ! [X20,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f2978,plain,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f30,f2373]) ).
fof(f30,axiom,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f17135,plain,
spl0_1777,
inference(avatar_split_clause,[],[f2977,f17133]) ).
fof(f17133,plain,
( spl0_1777
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f2977,plain,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f31,f2373]) ).
fof(f31,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f17129,plain,
spl0_1776,
inference(avatar_split_clause,[],[f2970,f17127]) ).
fof(f17127,plain,
( spl0_1776
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f2970,plain,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2021,f2544,f2544]) ).
fof(f2021,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f17123,plain,
spl0_1775,
inference(avatar_split_clause,[],[f2966,f17121]) ).
fof(f17121,plain,
( spl0_1775
<=> ! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f2966,plain,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2019,f2544,f2544]) ).
fof(f2019,axiom,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f17119,plain,
( spl0_1774
| ~ spl0_878
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f8813,f8477,f7694,f17117]) ).
fof(f17117,plain,
( spl0_1774
<=> ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f8813,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_878
| ~ spl0_1022 ),
inference(superposition,[],[f7695,f8478]) ).
fof(f17115,plain,
spl0_1773,
inference(avatar_split_clause,[],[f2963,f17113]) ).
fof(f17113,plain,
( spl0_1773
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f2963,plain,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2677,f2373]) ).
fof(f2677,axiom,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
fof(f17111,plain,
spl0_1772,
inference(avatar_split_clause,[],[f2961,f17109]) ).
fof(f2961,plain,
! [X1,X27,X12,X13] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
inference(definition_unfolding,[],[f2664,f2373]) ).
fof(f2664,axiom,
! [X1,X27,X12,X13] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f17105,plain,
spl0_1771,
inference(avatar_split_clause,[],[f2956,f17103]) ).
fof(f17103,plain,
( spl0_1771
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f2956,plain,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2022,f2544,f2544]) ).
fof(f2022,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f17099,plain,
spl0_1770,
inference(avatar_split_clause,[],[f2951,f17097]) ).
fof(f17097,plain,
( spl0_1770
<=> ! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f2951,plain,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2020,f2544,f2544]) ).
fof(f2020,axiom,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f17091,plain,
( spl0_1769
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1768 ),
inference(avatar_split_clause,[],[f17087,f17084,f10767,f10447,f6846,f5911,f17089]) ).
fof(f17089,plain,
( spl0_1769
<=> ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f17084,plain,
( spl0_1768
<=> ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f17087,plain,
( ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1768 ),
inference(forward_demodulation,[],[f17085,f11726]) ).
fof(f17085,plain,
( ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) )
| ~ spl0_1768 ),
inference(avatar_component_clause,[],[f17084]) ).
fof(f17086,plain,
spl0_1768,
inference(avatar_split_clause,[],[f2939,f17084]) ).
fof(f2939,plain,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ),
inference(definition_unfolding,[],[f1802,f2544]) ).
fof(f1802,axiom,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_NatArith_Oof__nat(c_Suc(X15),X41) = c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f17078,plain,
( spl0_1767
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1766 ),
inference(avatar_split_clause,[],[f17074,f17071,f10767,f10447,f6846,f5911,f17076]) ).
fof(f17076,plain,
( spl0_1767
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f17071,plain,
( spl0_1766
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f17074,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1766 ),
inference(forward_demodulation,[],[f17072,f11726]) ).
fof(f17072,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1)
| ~ spl0_1766 ),
inference(avatar_component_clause,[],[f17071]) ).
fof(f17073,plain,
spl0_1766,
inference(avatar_split_clause,[],[f2898,f17071]) ).
fof(f2898,plain,
! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1),
inference(definition_unfolding,[],[f1693,f2544]) ).
fof(f1693,axiom,
! [X21,X0,X1,X23] : c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Suc(X21),X1) = c_List_Onth(X23,X21,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f17069,plain,
( spl0_1765
| ~ spl0_967
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f8309,f8132,f8127,f17066]) ).
fof(f17066,plain,
( spl0_1765
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f8309,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_967
| ~ spl0_968 ),
inference(superposition,[],[f8133,f8129]) ).
fof(f17051,plain,
( spl0_1764
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1763 ),
inference(avatar_split_clause,[],[f17047,f17044,f10767,f10447,f6846,f5911,f17049]) ).
fof(f17044,plain,
( spl0_1763
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f17047,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1763 ),
inference(forward_demodulation,[],[f17045,f11726]) ).
fof(f17045,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_1763 ),
inference(avatar_component_clause,[],[f17044]) ).
fof(f17046,plain,
spl0_1763,
inference(avatar_split_clause,[],[f2897,f17044]) ).
fof(f2897,plain,
! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1),
inference(definition_unfolding,[],[f1572,f2544]) ).
fof(f1572,axiom,
! [X21,X0,X1,X23] : c_List_Odrop(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(X21,X23,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f17016,plain,
( spl0_1762
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1761 ),
inference(avatar_split_clause,[],[f17012,f17009,f10767,f10447,f6846,f5911,f17014]) ).
fof(f17009,plain,
( spl0_1761
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f17012,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1761 ),
inference(forward_demodulation,[],[f17010,f11726]) ).
fof(f17010,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41)
| ~ spl0_1761 ),
inference(avatar_component_clause,[],[f17009]) ).
fof(f17011,plain,
spl0_1761,
inference(avatar_split_clause,[],[f2895,f17009]) ).
fof(f2895,plain,
! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41),
inference(definition_unfolding,[],[f1723,f2544]) ).
fof(f1723,axiom,
! [X21,X41,X0] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f16912,plain,
( spl0_1760
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1759 ),
inference(avatar_split_clause,[],[f16908,f16905,f10767,f10447,f6846,f5911,f16910]) ).
fof(f16905,plain,
( spl0_1759
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f16908,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1759 ),
inference(forward_demodulation,[],[f16906,f11726]) ).
fof(f16906,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1759 ),
inference(avatar_component_clause,[],[f16905]) ).
fof(f16907,plain,
spl0_1759,
inference(avatar_split_clause,[],[f2894,f16905]) ).
fof(f2894,plain,
! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2099,f2544]) ).
fof(f2099,axiom,
! [X21,X15] : c_times(c_Suc(X15),X21,tc_nat) = c_plus(X21,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f16812,plain,
( spl0_1758
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1757 ),
inference(avatar_split_clause,[],[f16808,f16805,f10767,f10447,f6846,f5911,f16810]) ).
fof(f16805,plain,
( spl0_1757
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f16808,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1757 ),
inference(forward_demodulation,[],[f16806,f11726]) ).
fof(f16806,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1757 ),
inference(avatar_component_clause,[],[f16805]) ).
fof(f16807,plain,
spl0_1757,
inference(avatar_split_clause,[],[f2893,f16805]) ).
fof(f2893,plain,
! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2057,f2544]) ).
fof(f2057,axiom,
! [X21,X15] : c_times(X15,c_Suc(X21),tc_nat) = c_plus(X15,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f16749,plain,
( spl0_1756
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1755 ),
inference(avatar_split_clause,[],[f16745,f16742,f10767,f10447,f6846,f5911,f16747]) ).
fof(f16742,plain,
( spl0_1755
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f16745,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1755 ),
inference(forward_demodulation,[],[f16743,f11726]) ).
fof(f16743,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1755 ),
inference(avatar_component_clause,[],[f16742]) ).
fof(f16744,plain,
spl0_1755,
inference(avatar_split_clause,[],[f2892,f16742]) ).
fof(f2892,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2345,f2544]) ).
fof(f2345,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_nat) = c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f16716,plain,
( spl0_1754
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1753 ),
inference(avatar_split_clause,[],[f16712,f16709,f10767,f10447,f6846,f5911,f16714]) ).
fof(f16709,plain,
( spl0_1753
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f16712,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1753 ),
inference(forward_demodulation,[],[f16710,f11726]) ).
fof(f16710,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1753 ),
inference(avatar_component_clause,[],[f16709]) ).
fof(f16711,plain,
spl0_1753,
inference(avatar_split_clause,[],[f2891,f16709]) ).
fof(f2891,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1465,f2544]) ).
fof(f1465,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_IntDef_Oint) = c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f16707,plain,
spl0_1752,
inference(avatar_split_clause,[],[f2890,f16705]) ).
fof(f2890,plain,
! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
inference(definition_unfolding,[],[f2586,f2373]) ).
fof(f2586,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f16703,plain,
spl0_1751,
inference(avatar_split_clause,[],[f2824,f16701]) ).
fof(f2824,axiom,
! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
fof(f16699,plain,
( spl0_1749
| ~ spl0_1750
| ~ spl0_853
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8276,f8046,f7594,f16696,f16693]) ).
fof(f16693,plain,
( spl0_1749
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f16696,plain,
( spl0_1750
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f8276,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_853
| ~ spl0_947 ),
inference(resolution,[],[f8047,f7595]) ).
fof(f16691,plain,
spl0_1748,
inference(avatar_split_clause,[],[f2776,f16689]) ).
fof(f16689,plain,
( spl0_1748
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f2776,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
fof(f16687,plain,
spl0_1747,
inference(avatar_split_clause,[],[f2675,f16685]) ).
fof(f16685,plain,
( spl0_1747
<=> ! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f2675,axiom,
! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f16683,plain,
spl0_1746,
inference(avatar_split_clause,[],[f2650,f16681]) ).
fof(f16681,plain,
( spl0_1746
<=> ! [X13,X12,X1] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f2650,axiom,
! [X1,X12,X13] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f16679,plain,
spl0_1745,
inference(avatar_split_clause,[],[f2596,f16677]) ).
fof(f16677,plain,
( spl0_1745
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f2596,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f16675,plain,
spl0_1744,
inference(avatar_split_clause,[],[f2585,f16673]) ).
fof(f16673,plain,
( spl0_1744
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f2585,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f16671,plain,
spl0_1743,
inference(avatar_split_clause,[],[f2584,f16669]) ).
fof(f16669,plain,
( spl0_1743
<=> ! [X13,X12,X1] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f2584,axiom,
! [X1,X12,X13] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f16667,plain,
spl0_1742,
inference(avatar_split_clause,[],[f2574,f16665]) ).
fof(f2574,axiom,
! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f16663,plain,
spl0_1741,
inference(avatar_split_clause,[],[f2360,f16661]) ).
fof(f16661,plain,
( spl0_1741
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f2360,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f16659,plain,
spl0_1740,
inference(avatar_split_clause,[],[f2359,f16657]) ).
fof(f16657,plain,
( spl0_1740
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f2359,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f16655,plain,
spl0_1739,
inference(avatar_split_clause,[],[f2194,f16653]) ).
fof(f16653,plain,
( spl0_1739
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f2194,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f16651,plain,
( spl0_1738
| ~ spl0_640
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8219,f7913,f5911,f16649]) ).
fof(f16649,plain,
( spl0_1738
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f7913,plain,
( spl0_914
<=> ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f8219,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5913]) ).
fof(f7914,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f7913]) ).
fof(f16647,plain,
spl0_1737,
inference(avatar_split_clause,[],[f2193,f16645]) ).
fof(f2193,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f16643,plain,
spl0_1736,
inference(avatar_split_clause,[],[f2192,f16641]) ).
fof(f2192,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f16639,plain,
spl0_1735,
inference(avatar_split_clause,[],[f2191,f16637]) ).
fof(f16637,plain,
( spl0_1735
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f2191,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f16635,plain,
spl0_1734,
inference(avatar_split_clause,[],[f2189,f16633]) ).
fof(f16633,plain,
( spl0_1734
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f2189,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f16631,plain,
spl0_1733,
inference(avatar_split_clause,[],[f2188,f16629]) ).
fof(f2188,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f16627,plain,
spl0_1732,
inference(avatar_split_clause,[],[f2187,f16625]) ).
fof(f2187,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f16623,plain,
spl0_1731,
inference(avatar_split_clause,[],[f2186,f16621]) ).
fof(f16621,plain,
( spl0_1731
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f2186,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f16619,plain,
spl0_1730,
inference(avatar_split_clause,[],[f2146,f16617]) ).
fof(f16617,plain,
( spl0_1730
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f2146,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f16615,plain,
spl0_1729,
inference(avatar_split_clause,[],[f2145,f16613]) ).
fof(f16613,plain,
( spl0_1729
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f2145,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f16611,plain,
spl0_1728,
inference(avatar_split_clause,[],[f2138,f16609]) ).
fof(f16609,plain,
( spl0_1728
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f2138,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f16607,plain,
( spl0_1727
| ~ spl0_641
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8218,f7913,f5916,f16605]) ).
fof(f8218,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5918]) ).
fof(f16603,plain,
spl0_1726,
inference(avatar_split_clause,[],[f2137,f16601]) ).
fof(f16601,plain,
( spl0_1726
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f2137,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f16599,plain,
spl0_1725,
inference(avatar_split_clause,[],[f2119,f16597]) ).
fof(f2119,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f16595,plain,
spl0_1724,
inference(avatar_split_clause,[],[f2116,f16593]) ).
fof(f2116,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f16591,plain,
spl0_1723,
inference(avatar_split_clause,[],[f1971,f16589]) ).
fof(f16589,plain,
( spl0_1723
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f1971,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f16587,plain,
spl0_1722,
inference(avatar_split_clause,[],[f1970,f16585]) ).
fof(f16585,plain,
( spl0_1722
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f1970,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f16583,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1967,f16581]) ).
fof(f16581,plain,
( spl0_1721
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f1967,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f16579,plain,
spl0_1720,
inference(avatar_split_clause,[],[f1966,f16577]) ).
fof(f16577,plain,
( spl0_1720
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f1966,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f16575,plain,
spl0_1719,
inference(avatar_split_clause,[],[f1960,f16573]) ).
fof(f16573,plain,
( spl0_1719
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f1960,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f16571,plain,
spl0_1718,
inference(avatar_split_clause,[],[f1959,f16569]) ).
fof(f16569,plain,
( spl0_1718
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f1959,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f16567,plain,
spl0_1717,
inference(avatar_split_clause,[],[f1944,f16565]) ).
fof(f16565,plain,
( spl0_1717
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f1944,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f16563,plain,
( spl0_1716
| ~ spl0_640
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8217,f7913,f5911,f16561]) ).
fof(f8217,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5913]) ).
fof(f16559,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1943,f16557]) ).
fof(f16557,plain,
( spl0_1715
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f1943,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f16555,plain,
spl0_1714,
inference(avatar_split_clause,[],[f1869,f16553]) ).
fof(f16553,plain,
( spl0_1714
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f1869,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f16551,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1780,f16549]) ).
fof(f16549,plain,
( spl0_1713
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f1780,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f16547,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1764,f16545]) ).
fof(f16545,plain,
( spl0_1712
<=> ! [X0,X12,X1] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f1764,axiom,
! [X0,X1,X12] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f16542,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1727,f16540]) ).
fof(f16540,plain,
( spl0_1711
<=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f1727,axiom,
! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f16538,plain,
spl0_1710,
inference(avatar_split_clause,[],[f1724,f16536]) ).
fof(f1724,axiom,
! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f16534,plain,
spl0_1709,
inference(avatar_split_clause,[],[f1713,f16532]) ).
fof(f16532,plain,
( spl0_1709
<=> ! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f1713,axiom,
! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f16530,plain,
spl0_1708,
inference(avatar_split_clause,[],[f1701,f16528]) ).
fof(f16528,plain,
( spl0_1708
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f1701,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f16526,plain,
spl0_1707,
inference(avatar_split_clause,[],[f1700,f16524]) ).
fof(f16524,plain,
( spl0_1707
<=> ! [X59,X0,X23,X43,X1] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f1700,axiom,
! [X59,X0,X1,X23,X43] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f16522,plain,
spl0_1706,
inference(avatar_split_clause,[],[f1618,f16520]) ).
fof(f16520,plain,
( spl0_1706
<=> ! [X5,X1,X0] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f1618,axiom,
! [X0,X1,X5] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f16503,plain,
spl0_1705,
inference(avatar_split_clause,[],[f1605,f16501]) ).
fof(f16501,plain,
( spl0_1705
<=> ! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f1605,axiom,
! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f16499,plain,
spl0_1704,
inference(avatar_split_clause,[],[f1545,f16497]) ).
fof(f16497,plain,
( spl0_1704
<=> ! [X25,X1,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f1545,axiom,
! [X1,X25,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f16495,plain,
spl0_1703,
inference(avatar_split_clause,[],[f1538,f16493]) ).
fof(f16493,plain,
( spl0_1703
<=> ! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f1538,axiom,
! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f16491,plain,
spl0_1702,
inference(avatar_split_clause,[],[f1519,f16489]) ).
fof(f16489,plain,
( spl0_1702
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f1519,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f16487,plain,
spl0_1701,
inference(avatar_split_clause,[],[f1515,f16485]) ).
fof(f16485,plain,
( spl0_1701
<=> ! [X25,X5,X1] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f1515,axiom,
! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f16483,plain,
spl0_1700,
inference(avatar_split_clause,[],[f1507,f16481]) ).
fof(f16481,plain,
( spl0_1700
<=> ! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f1507,axiom,
! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f16479,plain,
spl0_1699,
inference(avatar_split_clause,[],[f1506,f16477]) ).
fof(f16477,plain,
( spl0_1699
<=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f1506,axiom,
! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f16475,plain,
spl0_1698,
inference(avatar_split_clause,[],[f1311,f16473]) ).
fof(f16473,plain,
( spl0_1698
<=> ! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f1311,axiom,
! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f16471,plain,
spl0_1697,
inference(avatar_split_clause,[],[f1303,f16469]) ).
fof(f16469,plain,
( spl0_1697
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f1303,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f16467,plain,
spl0_1696,
inference(avatar_split_clause,[],[f1302,f16465]) ).
fof(f16465,plain,
( spl0_1696
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f1302,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f16463,plain,
( spl0_1695
| ~ spl0_799
| ~ spl0_1663 ),
inference(avatar_split_clause,[],[f16126,f15247,f7366,f16461]) ).
fof(f16126,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_799
| ~ spl0_1663 ),
inference(forward_demodulation,[],[f16097,f7367]) ).
fof(f16097,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_799
| ~ spl0_1663 ),
inference(superposition,[],[f15248,f7367]) ).
fof(f16459,plain,
spl0_1694,
inference(avatar_split_clause,[],[f1301,f16457]) ).
fof(f16457,plain,
( spl0_1694
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f1301,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f16455,plain,
spl0_1693,
inference(avatar_split_clause,[],[f1272,f16453]) ).
fof(f16453,plain,
( spl0_1693
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f1272,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f16451,plain,
spl0_1692,
inference(avatar_split_clause,[],[f1257,f16449]) ).
fof(f16449,plain,
( spl0_1692
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f1257,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f16447,plain,
spl0_1691,
inference(avatar_split_clause,[],[f81,f16445]) ).
fof(f81,axiom,
! [X18,X1,X12] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f16443,plain,
spl0_1690,
inference(avatar_split_clause,[],[f47,f16441]) ).
fof(f47,axiom,
! [X1,X12,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f16091,plain,
( spl0_1689
| ~ spl0_663
| ~ spl0_1656 ),
inference(avatar_split_clause,[],[f16006,f15219,f6777,f16089]) ).
fof(f16089,plain,
( spl0_1689
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f15219,plain,
( spl0_1656
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f16006,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_663
| ~ spl0_1656 ),
inference(resolution,[],[f15220,f6778]) ).
fof(f15220,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| c_lessequals(X3,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1656 ),
inference(avatar_component_clause,[],[f15219]) ).
fof(f15976,plain,
( spl0_1688
| ~ spl0_640
| ~ spl0_911 ),
inference(avatar_split_clause,[],[f8208,f7901,f5911,f15974]) ).
fof(f15974,plain,
( spl0_1688
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f7901,plain,
( spl0_911
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f8208,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_640
| ~ spl0_911 ),
inference(superposition,[],[f7902,f5913]) ).
fof(f7902,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_911 ),
inference(avatar_component_clause,[],[f7901]) ).
fof(f15816,plain,
( spl0_1687
| ~ spl0_745
| ~ spl0_1630 ),
inference(avatar_split_clause,[],[f15756,f15106,f7148,f15814]) ).
fof(f15814,plain,
( spl0_1687
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f15756,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_745
| ~ spl0_1630 ),
inference(trivial_inequality_removal,[],[f15746]) ).
fof(f15746,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_745
| ~ spl0_1630 ),
inference(superposition,[],[f15107,f7149]) ).
fof(f15558,plain,
( spl0_1686
| ~ spl0_641
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8200,f7818,f5916,f15556]) ).
fof(f15556,plain,
( spl0_1686
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f7818,plain,
( spl0_891
<=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f8200,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5918]) ).
fof(f7819,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_891 ),
inference(avatar_component_clause,[],[f7818]) ).
fof(f15406,plain,
( spl0_1685
| ~ spl0_640
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8199,f7818,f5911,f15404]) ).
fof(f15404,plain,
( spl0_1685
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f8199,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5913]) ).
fof(f15399,plain,
spl0_1684,
inference(avatar_split_clause,[],[f3248,f15397]) ).
fof(f15397,plain,
( spl0_1684
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f3248,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3247,f2115]) ).
fof(f2115,axiom,
! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3247,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3038,f2830]) ).
fof(f2830,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f2126,f2129]) ).
fof(f2126,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f3038,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1317,f2129]) ).
fof(f1317,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f15395,plain,
spl0_1683,
inference(avatar_split_clause,[],[f3241,f15393]) ).
fof(f15393,plain,
( spl0_1683
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f3241,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3240,f2115]) ).
fof(f3240,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3032,f2830]) ).
fof(f3032,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1321,f2129]) ).
fof(f1321,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f15391,plain,
spl0_1682,
inference(avatar_split_clause,[],[f3238,f15389]) ).
fof(f15389,plain,
( spl0_1682
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f3238,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3237,f2115]) ).
fof(f3237,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3030,f2830]) ).
fof(f3030,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1316,f2129]) ).
fof(f1316,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f15387,plain,
spl0_1681,
inference(avatar_split_clause,[],[f3231,f15385]) ).
fof(f15385,plain,
( spl0_1681
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f3231,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3230,f2115]) ).
fof(f3230,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3024,f2830]) ).
fof(f3024,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1320,f2129]) ).
fof(f1320,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f15383,plain,
spl0_1680,
inference(avatar_split_clause,[],[f3212,f15381]) ).
fof(f15381,plain,
( spl0_1680
<=> ! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f3212,plain,
! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f3010,f2831]) ).
fof(f3010,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2097,f2544]) ).
fof(f2097,axiom,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f15379,plain,
spl0_1679,
inference(avatar_split_clause,[],[f3126,f15377]) ).
fof(f15377,plain,
( spl0_1679
<=> ! [X1,X47] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f3126,plain,
! [X47,X1] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1330,f2156]) ).
fof(f1330,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f15375,plain,
spl0_1678,
inference(avatar_split_clause,[],[f3125,f15373]) ).
fof(f15373,plain,
( spl0_1678
<=> ! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f3125,plain,
! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1329,f2156]) ).
fof(f1329,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X11),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f15371,plain,
spl0_1677,
inference(avatar_split_clause,[],[f3098,f15369]) ).
fof(f15369,plain,
( spl0_1677
<=> ! [X5,X1] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f3098,plain,
! [X1,X5] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
inference(forward_demodulation,[],[f1636,f1639]) ).
fof(f1639,axiom,
! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f1636,axiom,
! [X1,X5] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)),tc_List_Olist(X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f15367,plain,
( spl0_1676
| ~ spl0_640
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8197,f7818,f5911,f15365]) ).
fof(f8197,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5913]) ).
fof(f15363,plain,
spl0_1675,
inference(avatar_split_clause,[],[f3094,f15361]) ).
fof(f3094,plain,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat),
inference(forward_demodulation,[],[f2914,f2831]) ).
fof(f2914,plain,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1627,f2544]) ).
fof(f1627,axiom,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f15359,plain,
spl0_1674,
inference(avatar_split_clause,[],[f3090,f15357]) ).
fof(f15357,plain,
( spl0_1674
<=> ! [X18,X13,X32,X1] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f3090,plain,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1),
inference(forward_demodulation,[],[f2643,f2644]) ).
fof(f2644,axiom,
! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f2643,axiom,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_insert(X18,c_union(X13,X32,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f15355,plain,
spl0_1673,
inference(avatar_split_clause,[],[f2992,f15353]) ).
fof(f15353,plain,
( spl0_1673
<=> ! [X21,X1,X3] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f2992,plain,
! [X21,X3,X1] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
inference(definition_unfolding,[],[f1770,f1766]) ).
fof(f1770,axiom,
! [X21,X3,X1] :
( c_List_Otake(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f15335,plain,
( spl0_1672
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1671 ),
inference(avatar_split_clause,[],[f15331,f15328,f10767,f10447,f6846,f5911,f15333]) ).
fof(f15333,plain,
( spl0_1672
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f15328,plain,
( spl0_1671
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f15331,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1671 ),
inference(forward_demodulation,[],[f15329,f11726]) ).
fof(f15329,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat)
| ~ spl0_1671 ),
inference(avatar_component_clause,[],[f15328]) ).
fof(f15330,plain,
spl0_1671,
inference(avatar_split_clause,[],[f2885,f15328]) ).
fof(f15312,plain,
( spl0_1670
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1669 ),
inference(avatar_split_clause,[],[f15308,f15305,f10767,f10447,f6846,f5911,f15310]) ).
fof(f15305,plain,
( spl0_1669
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f15308,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1669 ),
inference(forward_demodulation,[],[f15306,f11726]) ).
fof(f15306,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat)
| ~ spl0_1669 ),
inference(avatar_component_clause,[],[f15305]) ).
fof(f15307,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2884,f15305]) ).
fof(f15270,plain,
( spl0_1668
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1667 ),
inference(avatar_split_clause,[],[f15266,f15263,f10767,f10447,f6846,f5911,f15268]) ).
fof(f15268,plain,
( spl0_1668
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f15263,plain,
( spl0_1667
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f15266,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1667 ),
inference(forward_demodulation,[],[f15264,f11726]) ).
fof(f15264,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1)
| ~ spl0_1667 ),
inference(avatar_component_clause,[],[f15263]) ).
fof(f15265,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2883,f15263]) ).
fof(f2883,plain,
! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1),
inference(definition_unfolding,[],[f1738,f2544]) ).
fof(f1738,axiom,
! [X21,X1,X23] : c_List_Orotate(c_Suc(X21),X23,X1) = c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f15261,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2722,f15259]) ).
fof(f15259,plain,
( spl0_1666
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f2722,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f15257,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2719,f15255]) ).
fof(f15255,plain,
( spl0_1665
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f2719,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f15253,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2657,f15251]) ).
fof(f15251,plain,
( spl0_1664
<=> ! [X24,X12,X32,X1] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f2657,axiom,
! [X1,X24,X12,X32] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f15249,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2644,f15247]) ).
fof(f15245,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2640,f15243]) ).
fof(f15243,plain,
( spl0_1662
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f2640,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f15241,plain,
spl0_1661,
inference(avatar_split_clause,[],[f2620,f15239]) ).
fof(f15239,plain,
( spl0_1661
<=> ! [X24,X12,X32,X1] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f2620,axiom,
! [X1,X24,X12,X32] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f15237,plain,
spl0_1660,
inference(avatar_split_clause,[],[f2593,f15235]) ).
fof(f15235,plain,
( spl0_1660
<=> ! [X13,X12,X1] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f2593,axiom,
! [X1,X12,X13] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f15233,plain,
spl0_1659,
inference(avatar_split_clause,[],[f2572,f15231]) ).
fof(f15231,plain,
( spl0_1659
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f2572,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f15229,plain,
spl0_1658,
inference(avatar_split_clause,[],[f2571,f15227]) ).
fof(f15227,plain,
( spl0_1658
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f2571,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f15225,plain,
spl0_1657,
inference(avatar_split_clause,[],[f2561,f15223]) ).
fof(f15223,plain,
( spl0_1657
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f2561,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f15221,plain,
spl0_1656,
inference(avatar_split_clause,[],[f2560,f15219]) ).
fof(f2560,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f15217,plain,
spl0_1655,
inference(avatar_split_clause,[],[f2548,f15215]) ).
fof(f15215,plain,
( spl0_1655
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f2548,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f15213,plain,
spl0_1654,
inference(avatar_split_clause,[],[f2541,f15211]) ).
fof(f15211,plain,
( spl0_1654
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f2541,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f15209,plain,
spl0_1653,
inference(avatar_split_clause,[],[f2539,f15207]) ).
fof(f15207,plain,
( spl0_1653
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f2539,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f15205,plain,
spl0_1652,
inference(avatar_split_clause,[],[f2538,f15203]) ).
fof(f15203,plain,
( spl0_1652
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f2538,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f15201,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2533,f15199]) ).
fof(f15199,plain,
( spl0_1651
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f2533,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f15197,plain,
spl0_1650,
inference(avatar_split_clause,[],[f2532,f15195]) ).
fof(f15195,plain,
( spl0_1650
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f2532,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f15193,plain,
spl0_1649,
inference(avatar_split_clause,[],[f2490,f15191]) ).
fof(f2490,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f15180,plain,
spl0_1648,
inference(avatar_split_clause,[],[f2489,f15178]) ).
fof(f2489,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f15176,plain,
spl0_1647,
inference(avatar_split_clause,[],[f2467,f15174]) ).
fof(f15174,plain,
( spl0_1647
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f2467,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f15172,plain,
spl0_1646,
inference(avatar_split_clause,[],[f2312,f15170]) ).
fof(f15170,plain,
( spl0_1646
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f2312,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f15168,plain,
spl0_1645,
inference(avatar_split_clause,[],[f2306,f15166]) ).
fof(f15166,plain,
( spl0_1645
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f2306,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f15164,plain,
spl0_1644,
inference(avatar_split_clause,[],[f2304,f15162]) ).
fof(f15162,plain,
( spl0_1644
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f2304,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f15160,plain,
spl0_1643,
inference(avatar_split_clause,[],[f2209,f15158]) ).
fof(f15158,plain,
( spl0_1643
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f2209,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f15156,plain,
spl0_1642,
inference(avatar_split_clause,[],[f2208,f15154]) ).
fof(f15154,plain,
( spl0_1642
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f2208,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f15152,plain,
spl0_1641,
inference(avatar_split_clause,[],[f2080,f15150]) ).
fof(f15150,plain,
( spl0_1641
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f2080,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f15148,plain,
spl0_1640,
inference(avatar_split_clause,[],[f2060,f15146]) ).
fof(f15146,plain,
( spl0_1640
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f2060,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f15144,plain,
spl0_1639,
inference(avatar_split_clause,[],[f2058,f15142]) ).
fof(f15142,plain,
( spl0_1639
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f2058,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f15140,plain,
spl0_1638,
inference(avatar_split_clause,[],[f2037,f15138]) ).
fof(f15136,plain,
spl0_1637,
inference(avatar_split_clause,[],[f2028,f15134]) ).
fof(f15134,plain,
( spl0_1637
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f2028,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f15132,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1863,f15130]) ).
fof(f15130,plain,
( spl0_1636
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f1863,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f15128,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1860,f15126]) ).
fof(f15126,plain,
( spl0_1635
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f1860,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f15124,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1847,f15122]) ).
fof(f15122,plain,
( spl0_1634
<=> ! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f1847,axiom,
! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f15120,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1827,f15118]) ).
fof(f15118,plain,
( spl0_1633
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f1827,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f15116,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1801,f15114]) ).
fof(f15114,plain,
( spl0_1632
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f1801,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f15112,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1749,f15110]) ).
fof(f1749,axiom,
! [X1,X25,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f15108,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1739,f15106]) ).
fof(f1739,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f15104,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1725,f15102]) ).
fof(f15102,plain,
( spl0_1629
<=> ! [X25,X1,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f1725,axiom,
! [X1,X25,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f15100,plain,
( ~ spl0_39
| ~ spl0_1628
| ~ spl0_1317
| spl0_1451 ),
inference(avatar_split_clause,[],[f13120,f12026,f10475,f15097,f3442]) ).
fof(f15097,plain,
( spl0_1628
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f12026,plain,
( spl0_1451
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f13120,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1317
| spl0_1451 ),
inference(resolution,[],[f12028,f10476]) ).
fof(f12028,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1451 ),
inference(avatar_component_clause,[],[f12026]) ).
fof(f15095,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1708,f15093]) ).
fof(f1708,axiom,
! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f15091,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1696,f15089]) ).
fof(f15089,plain,
( spl0_1626
<=> ! [X3,X23,X25,X1] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f1696,axiom,
! [X3,X1,X25,X23] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f15087,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1691,f15085]) ).
fof(f15085,plain,
( spl0_1625
<=> ! [X58,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f1691,axiom,
! [X58,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f15083,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1690,f15081]) ).
fof(f15081,plain,
( spl0_1624
<=> ! [X3,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f1690,axiom,
! [X3,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f15079,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1601,f15077]) ).
fof(f15077,plain,
( spl0_1623
<=> ! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f1601,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f15075,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1577,f15073]) ).
fof(f15073,plain,
( spl0_1622
<=> ! [X43,X0,X16,X1] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f1577,axiom,
! [X0,X1,X16,X43] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f15071,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1574,f15069]) ).
fof(f15069,plain,
( spl0_1621
<=> ! [X15,X23,X21,X1] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f1574,axiom,
! [X21,X1,X15,X23] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f15067,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1554,f15065]) ).
fof(f15065,plain,
( spl0_1620
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f1554,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f15063,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1547,f15061]) ).
fof(f15061,plain,
( spl0_1619
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f1547,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f15059,plain,
spl0_1618,
inference(avatar_split_clause,[],[f1518,f15057]) ).
fof(f15057,plain,
( spl0_1618
<=> ! [X51,X23,X25,X1] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f1518,axiom,
! [X51,X1,X25,X23] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f15055,plain,
( spl0_1617
| ~ spl0_813
| ~ spl0_1398 ),
inference(avatar_split_clause,[],[f12997,f11428,f7422,f15052]) ).
fof(f15052,plain,
( spl0_1617
<=> c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f7422,plain,
( spl0_813
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f11428,plain,
( spl0_1398
<=> c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f12997,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset))
| ~ spl0_813
| ~ spl0_1398 ),
inference(superposition,[],[f7423,f11430]) ).
fof(f11430,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_1398 ),
inference(avatar_component_clause,[],[f11428]) ).
fof(f7423,plain,
( ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88))
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f7422]) ).
fof(f15050,plain,
spl0_1616,
inference(avatar_split_clause,[],[f1508,f15048]) ).
fof(f15048,plain,
( spl0_1616
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f1508,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f15046,plain,
spl0_1615,
inference(avatar_split_clause,[],[f1495,f15044]) ).
fof(f15044,plain,
( spl0_1615
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f1495,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f15042,plain,
spl0_1614,
inference(avatar_split_clause,[],[f1239,f15040]) ).
fof(f15040,plain,
( spl0_1614
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f1239,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f15038,plain,
spl0_1613,
inference(avatar_split_clause,[],[f1237,f15036]) ).
fof(f15036,plain,
( spl0_1613
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f1237,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f15034,plain,
spl0_1612,
inference(avatar_split_clause,[],[f1217,f15032]) ).
fof(f15032,plain,
( spl0_1612
<=> ! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f1217,axiom,
! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f15030,plain,
spl0_1611,
inference(avatar_split_clause,[],[f127,f15028]) ).
fof(f15028,plain,
( spl0_1611
<=> ! [X35,X36,X2,X1] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f127,axiom,
! [X2,X36,X1,X35] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f15026,plain,
spl0_1610,
inference(avatar_split_clause,[],[f125,f15024]) ).
fof(f15024,plain,
( spl0_1610
<=> ! [X34,X33,X2,X1] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f125,axiom,
! [X2,X1,X34,X33] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f15022,plain,
spl0_1609,
inference(avatar_split_clause,[],[f80,f15020]) ).
fof(f15020,plain,
( spl0_1609
<=> ! [X12,X1,X4] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f80,axiom,
! [X1,X4,X12] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f15006,plain,
( spl0_1608
| ~ spl0_883
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f12208,f10487,f7716,f15003]) ).
fof(f15003,plain,
( spl0_1608
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f10487,plain,
( spl0_1320
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f12208,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_883
| ~ spl0_1320 ),
inference(superposition,[],[f10489,f7717]) ).
fof(f10489,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1320 ),
inference(avatar_component_clause,[],[f10487]) ).
fof(f14753,plain,
( ~ spl0_1607
| spl0_100
| ~ spl0_818
| ~ spl0_1127
| ~ spl0_1260 ),
inference(avatar_split_clause,[],[f12120,f9886,f9105,f7443,f3744,f14750]) ).
fof(f14750,plain,
( spl0_1607
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f7443,plain,
( spl0_818
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f9105,plain,
( spl0_1127
<=> ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f12120,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_818
| ~ spl0_1127
| ~ spl0_1260 ),
inference(forward_demodulation,[],[f12114,f7445]) ).
fof(f7445,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7443]) ).
fof(f12114,plain,
( ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_1127
| ~ spl0_1260 ),
inference(superposition,[],[f9106,f9888]) ).
fof(f9106,plain,
( ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) )
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9105]) ).
fof(f14621,plain,
( spl0_1606
| ~ spl0_1005
| ~ spl0_1236 ),
inference(avatar_split_clause,[],[f11939,f9752,f8408,f14619]) ).
fof(f14619,plain,
( spl0_1606
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f9752,plain,
( spl0_1236
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f11939,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1005
| ~ spl0_1236 ),
inference(superposition,[],[f8409,f9753]) ).
fof(f9753,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1236 ),
inference(avatar_component_clause,[],[f9752]) ).
fof(f13997,plain,
spl0_1605,
inference(avatar_split_clause,[],[f3204,f13995]) ).
fof(f13995,plain,
( spl0_1605
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f3204,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3004,f2114]) ).
fof(f3004,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1334,f2129]) ).
fof(f1334,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f13993,plain,
spl0_1604,
inference(avatar_split_clause,[],[f3199,f13991]) ).
fof(f13991,plain,
( spl0_1604
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f3199,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3000,f2114]) ).
fof(f3000,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1333,f2129]) ).
fof(f1333,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f13989,plain,
spl0_1603,
inference(avatar_split_clause,[],[f3089,f13987]) ).
fof(f13987,plain,
( spl0_1603
<=> ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f3089,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2907,f2831]) ).
fof(f2907,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1870,f2544]) ).
fof(f1870,axiom,
! [X83] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f13985,plain,
spl0_1602,
inference(avatar_split_clause,[],[f3009,f13983]) ).
fof(f13983,plain,
( spl0_1602
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f3009,plain,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ),
inference(definition_unfolding,[],[f1772,f1766]) ).
fof(f1772,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Otake(X21,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f13976,plain,
( spl0_1601
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f13972,f13969,f10767,f10447,f6846,f5911,f13974]) ).
fof(f13974,plain,
( spl0_1601
<=> ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f13969,plain,
( spl0_1600
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f13972,plain,
( ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1600 ),
inference(forward_demodulation,[],[f13970,f11726]) ).
fof(f13970,plain,
( ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1600 ),
inference(avatar_component_clause,[],[f13969]) ).
fof(f13971,plain,
spl0_1600,
inference(avatar_split_clause,[],[f2975,f13969]) ).
fof(f2975,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1822,f2544]) ).
fof(f1822,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f13946,plain,
spl0_1599,
inference(avatar_split_clause,[],[f2973,f13944]) ).
fof(f13944,plain,
( spl0_1599
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f2973,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2606,f2373]) ).
fof(f2606,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f13942,plain,
spl0_1598,
inference(avatar_split_clause,[],[f2972,f13940]) ).
fof(f13940,plain,
( spl0_1598
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f2972,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2607,f2373]) ).
fof(f2607,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f13938,plain,
spl0_1597,
inference(avatar_split_clause,[],[f2942,f13936]) ).
fof(f2942,plain,
! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2017,f2544,f2544]) ).
fof(f2017,axiom,
! [X21,X15] :
( X15 = X21
| c_Suc(X21) != c_Suc(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f13934,plain,
spl0_1596,
inference(avatar_split_clause,[],[f2888,f13932]) ).
fof(f2888,plain,
! [X21,X3,X1] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3,
inference(definition_unfolding,[],[f1535,f1766]) ).
fof(f1535,axiom,
! [X21,X3,X1] : c_append(c_List_Otake(X21,X3,X1),c_List_Odrop(X21,X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f13930,plain,
spl0_1595,
inference(avatar_split_clause,[],[f2745,f13928]) ).
fof(f13928,plain,
( spl0_1595
<=> ! [X86,X91,X88] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f2745,axiom,
! [X91,X88,X86] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
fof(f13926,plain,
spl0_1594,
inference(avatar_split_clause,[],[f2727,f13924]) ).
fof(f13924,plain,
( spl0_1594
<=> ! [X0,X3] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f2727,axiom,
! [X3,X0] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f13922,plain,
spl0_1593,
inference(avatar_split_clause,[],[f2726,f13920]) ).
fof(f13920,plain,
( spl0_1593
<=> ! [X0,X3] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f2726,axiom,
! [X3,X0] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f13918,plain,
spl0_1592,
inference(avatar_split_clause,[],[f2683,f13916]) ).
fof(f13916,plain,
( spl0_1592
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f2683,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f13914,plain,
spl0_1591,
inference(avatar_split_clause,[],[f2658,f13912]) ).
fof(f13912,plain,
( spl0_1591
<=> ! [X13,X18,X1] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f2658,axiom,
! [X18,X1,X13] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f13910,plain,
spl0_1590,
inference(avatar_split_clause,[],[f2655,f13908]) ).
fof(f13908,plain,
( spl0_1590
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f2655,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f13906,plain,
( spl0_1589
| ~ spl0_709
| ~ spl0_710
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(avatar_split_clause,[],[f13622,f12343,f7309,f6997,f6989,f6984,f13904]) ).
fof(f6997,plain,
( spl0_712
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f12343,plain,
( spl0_1515
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f13622,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_709
| ~ spl0_710
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13621,f6990]) ).
fof(f13621,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_709
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13620,f7311]) ).
fof(f13620,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0)
| ~ spl0_709
| ~ spl0_712
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13609,f6998]) ).
fof(f6998,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f6997]) ).
fof(f13609,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OPls,X0),X0)
| ~ spl0_709
| ~ spl0_1515 ),
inference(superposition,[],[f12344,f6986]) ).
fof(f12344,plain,
( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11)
| ~ spl0_1515 ),
inference(avatar_component_clause,[],[f12343]) ).
fof(f13902,plain,
spl0_1588,
inference(avatar_split_clause,[],[f2621,f13900]) ).
fof(f13900,plain,
( spl0_1588
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f2621,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f13898,plain,
spl0_1587,
inference(avatar_split_clause,[],[f2488,f13896]) ).
fof(f13896,plain,
( spl0_1587
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f2488,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f13894,plain,
spl0_1586,
inference(avatar_split_clause,[],[f2475,f13892]) ).
fof(f13892,plain,
( spl0_1586
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f2475,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
fof(f13890,plain,
spl0_1585,
inference(avatar_split_clause,[],[f2471,f13888]) ).
fof(f13888,plain,
( spl0_1585
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f2471,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f13886,plain,
spl0_1584,
inference(avatar_split_clause,[],[f2363,f13884]) ).
fof(f13884,plain,
( spl0_1584
<=> ! [X2,X42,X18,X84,X27,X1] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f2363,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f13882,plain,
spl0_1583,
inference(avatar_split_clause,[],[f2362,f13880]) ).
fof(f13880,plain,
( spl0_1583
<=> ! [X18,X42,X84,X27,X2,X1] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f2362,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f13878,plain,
spl0_1582,
inference(avatar_split_clause,[],[f2349,f13876]) ).
fof(f13876,plain,
( spl0_1582
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f2349,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f13874,plain,
spl0_1581,
inference(avatar_split_clause,[],[f2348,f13872]) ).
fof(f13872,plain,
( spl0_1581
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f2348,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f13870,plain,
spl0_1580,
inference(avatar_split_clause,[],[f2268,f13868]) ).
fof(f13868,plain,
( spl0_1580
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f2268,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f13866,plain,
spl0_1579,
inference(avatar_split_clause,[],[f2263,f13864]) ).
fof(f13864,plain,
( spl0_1579
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f2263,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f13862,plain,
( spl0_1578
| ~ spl0_708
| ~ spl0_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_883
| ~ spl0_1514 ),
inference(avatar_split_clause,[],[f13603,f12339,f7716,f7309,f7083,f6989,f6979,f13859]) ).
fof(f12339,plain,
( spl0_1514
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f13603,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_708
| ~ spl0_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_883
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13602,f6981]) ).
fof(f13602,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_883
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13601,f7311]) ).
fof(f13601,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))
| ~ spl0_710
| ~ spl0_732
| ~ spl0_883
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13600,f6990]) ).
fof(f13600,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_OMin),c_Numeral_Obit_OB1)
| ~ spl0_732
| ~ spl0_883
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13594,f7717]) ).
fof(f13594,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OPls),c_Numeral_Obit_OB1)
| ~ spl0_732
| ~ spl0_1514 ),
inference(superposition,[],[f12340,f7085]) ).
fof(f12340,plain,
( ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1)
| ~ spl0_1514 ),
inference(avatar_component_clause,[],[f12339]) ).
fof(f13857,plain,
spl0_1577,
inference(avatar_split_clause,[],[f2246,f13855]) ).
fof(f13855,plain,
( spl0_1577
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f2246,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f13853,plain,
spl0_1576,
inference(avatar_split_clause,[],[f2242,f13851]) ).
fof(f13851,plain,
( spl0_1576
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f2242,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f13849,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2236,f13847]) ).
fof(f13847,plain,
( spl0_1575
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f2236,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f13845,plain,
spl0_1574,
inference(avatar_split_clause,[],[f2235,f13843]) ).
fof(f13843,plain,
( spl0_1574
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f2235,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f13841,plain,
spl0_1573,
inference(avatar_split_clause,[],[f2232,f13839]) ).
fof(f13839,plain,
( spl0_1573
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f2232,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f13837,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2231,f13835]) ).
fof(f13835,plain,
( spl0_1572
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f2231,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f13833,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2195,f13831]) ).
fof(f13831,plain,
( spl0_1571
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f2195,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f13829,plain,
spl0_1570,
inference(avatar_split_clause,[],[f2190,f13827]) ).
fof(f13827,plain,
( spl0_1570
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f2190,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f13825,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2111,f13823]) ).
fof(f2111,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f13821,plain,
spl0_1568,
inference(avatar_split_clause,[],[f2085,f13819]) ).
fof(f13819,plain,
( spl0_1568
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f2085,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f13817,plain,
( spl0_1567
| ~ spl0_663
| ~ spl0_1498 ),
inference(avatar_split_clause,[],[f13540,f12238,f6777,f13815]) ).
fof(f13540,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
| ~ spl0_663
| ~ spl0_1498 ),
inference(resolution,[],[f12239,f6778]) ).
fof(f13813,plain,
spl0_1566,
inference(avatar_split_clause,[],[f2084,f13811]) ).
fof(f13811,plain,
( spl0_1566
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f2084,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f13809,plain,
spl0_1565,
inference(avatar_split_clause,[],[f2083,f13807]) ).
fof(f13807,plain,
( spl0_1565
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f2083,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f13805,plain,
spl0_1564,
inference(avatar_split_clause,[],[f2082,f13803]) ).
fof(f13803,plain,
( spl0_1564
<=> ! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f2082,axiom,
! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f13801,plain,
spl0_1563,
inference(avatar_split_clause,[],[f2076,f13799]) ).
fof(f13799,plain,
( spl0_1563
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f2076,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f13797,plain,
spl0_1562,
inference(avatar_split_clause,[],[f2075,f13795]) ).
fof(f13795,plain,
( spl0_1562
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f2075,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f13793,plain,
spl0_1561,
inference(avatar_split_clause,[],[f2073,f13791]) ).
fof(f13791,plain,
( spl0_1561
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f2073,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f13789,plain,
spl0_1560,
inference(avatar_split_clause,[],[f2072,f13787]) ).
fof(f13787,plain,
( spl0_1560
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f2072,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f13785,plain,
spl0_1559,
inference(avatar_split_clause,[],[f2071,f13783]) ).
fof(f13783,plain,
( spl0_1559
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f2071,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f13781,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2070,f13779]) ).
fof(f13779,plain,
( spl0_1558
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f2070,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f13777,plain,
spl0_1557,
inference(avatar_split_clause,[],[f2068,f13775]) ).
fof(f13775,plain,
( spl0_1557
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f2068,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f13773,plain,
( spl0_1556
| ~ spl0_663
| ~ spl0_1496 ),
inference(avatar_split_clause,[],[f13515,f12230,f6777,f13771]) ).
fof(f12230,plain,
( spl0_1496
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f13515,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_663
| ~ spl0_1496 ),
inference(resolution,[],[f12231,f6778]) ).
fof(f12231,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1496 ),
inference(avatar_component_clause,[],[f12230]) ).
fof(f13769,plain,
spl0_1555,
inference(avatar_split_clause,[],[f2067,f13767]) ).
fof(f13767,plain,
( spl0_1555
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f2067,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f13765,plain,
spl0_1554,
inference(avatar_split_clause,[],[f1927,f13763]) ).
fof(f13763,plain,
( spl0_1554
<=> ! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f1927,axiom,
! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f13761,plain,
spl0_1553,
inference(avatar_split_clause,[],[f1868,f13759]) ).
fof(f13759,plain,
( spl0_1553
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1868,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f13757,plain,
spl0_1552,
inference(avatar_split_clause,[],[f1820,f13755]) ).
fof(f13755,plain,
( spl0_1552
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f1820,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f13753,plain,
spl0_1551,
inference(avatar_split_clause,[],[f1819,f13751]) ).
fof(f13751,plain,
( spl0_1551
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f1819,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f13749,plain,
spl0_1550,
inference(avatar_split_clause,[],[f1817,f13747]) ).
fof(f13747,plain,
( spl0_1550
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f1817,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f13745,plain,
spl0_1549,
inference(avatar_split_clause,[],[f1816,f13743]) ).
fof(f13743,plain,
( spl0_1549
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f1816,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f13741,plain,
spl0_1548,
inference(avatar_split_clause,[],[f1760,f13739]) ).
fof(f13739,plain,
( spl0_1548
<=> ! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f1760,axiom,
! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
fof(f13737,plain,
spl0_1547,
inference(avatar_split_clause,[],[f1756,f13735]) ).
fof(f13735,plain,
( spl0_1547
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f1756,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f13733,plain,
spl0_1546,
inference(avatar_split_clause,[],[f1710,f13731]) ).
fof(f13731,plain,
( spl0_1546
<=> ! [X41,X0,X3,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f1710,axiom,
! [X3,X41,X0,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f13729,plain,
( spl0_1545
| ~ spl0_663
| ~ spl0_1488 ),
inference(avatar_split_clause,[],[f13395,f12193,f6777,f13727]) ).
fof(f13727,plain,
( spl0_1545
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f12193,plain,
( spl0_1488
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f13395,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_663
| ~ spl0_1488 ),
inference(resolution,[],[f12194,f6778]) ).
fof(f12194,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1488 ),
inference(avatar_component_clause,[],[f12193]) ).
fof(f13725,plain,
spl0_1544,
inference(avatar_split_clause,[],[f1640,f13723]) ).
fof(f13723,plain,
( spl0_1544
<=> ! [X41,X12,X66] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f1640,axiom,
! [X41,X66,X12] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f13721,plain,
spl0_1543,
inference(avatar_split_clause,[],[f1632,f13719]) ).
fof(f13719,plain,
( spl0_1543
<=> ! [X0,X3,X43,X1] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f1632,axiom,
! [X3,X0,X1,X43] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f13717,plain,
spl0_1542,
inference(avatar_split_clause,[],[f1612,f13715]) ).
fof(f13715,plain,
( spl0_1542
<=> ! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f1612,axiom,
! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f13713,plain,
spl0_1541,
inference(avatar_split_clause,[],[f1600,f13711]) ).
fof(f13711,plain,
( spl0_1541
<=> ! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f1600,axiom,
! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f13709,plain,
spl0_1540,
inference(avatar_split_clause,[],[f1596,f13707]) ).
fof(f1596,axiom,
! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f13705,plain,
spl0_1539,
inference(avatar_split_clause,[],[f1544,f13703]) ).
fof(f13703,plain,
( spl0_1539
<=> ! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f1544,axiom,
! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f13701,plain,
spl0_1538,
inference(avatar_split_clause,[],[f1456,f13699]) ).
fof(f13699,plain,
( spl0_1538
<=> ! [X5,X49] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f13697,plain,
spl0_1537,
inference(avatar_split_clause,[],[f1431,f13695]) ).
fof(f1431,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f13693,plain,
spl0_1536,
inference(avatar_split_clause,[],[f1415,f13691]) ).
fof(f1415,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f13689,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1414,f13687]) ).
fof(f13687,plain,
( spl0_1535
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f1414,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f13685,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1411,f13683]) ).
fof(f13683,plain,
( spl0_1534
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f1411,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f13681,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1410,f13679]) ).
fof(f1410,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f13677,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1281,f13675]) ).
fof(f13675,plain,
( spl0_1532
<=> ! [X13,X1,X46] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f1281,axiom,
! [X46,X1,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f13673,plain,
spl0_1531,
inference(avatar_split_clause,[],[f1198,f13671]) ).
fof(f13671,plain,
( spl0_1531
<=> ! [X9,X7,X8,X10,X2,X1] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f1198,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f13669,plain,
spl0_1530,
inference(avatar_split_clause,[],[f1197,f13667]) ).
fof(f13667,plain,
( spl0_1530
<=> ! [X7,X10,X8,X9,X2,X1] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f1197,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f13665,plain,
spl0_1529,
inference(avatar_split_clause,[],[f99,f13663]) ).
fof(f13663,plain,
( spl0_1529
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f99,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f13661,plain,
spl0_1528,
inference(avatar_split_clause,[],[f96,f13659]) ).
fof(f13659,plain,
( spl0_1528
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f96,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13657,plain,
spl0_1527,
inference(avatar_split_clause,[],[f59,f13655]) ).
fof(f13655,plain,
( spl0_1527
<=> ! [X0,X12,X1,X26] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f59,axiom,
! [X0,X1,X26,X12] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13653,plain,
spl0_1526,
inference(avatar_split_clause,[],[f48,f13651]) ).
fof(f48,axiom,
! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13649,plain,
spl0_1525,
inference(avatar_split_clause,[],[f43,f13647]) ).
fof(f43,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13645,plain,
spl0_1524,
inference(avatar_split_clause,[],[f27,f13643]) ).
fof(f27,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13568,plain,
( spl0_1523
| ~ spl0_114
| ~ spl0_1483 ),
inference(avatar_split_clause,[],[f13312,f12173,f3807,f13566]) ).
fof(f13312,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_114
| ~ spl0_1483 ),
inference(resolution,[],[f12174,f3808]) ).
fof(f13447,plain,
( spl0_1522
| ~ spl0_1146
| ~ spl0_1483 ),
inference(avatar_split_clause,[],[f13306,f12173,f9181,f13445]) ).
fof(f13445,plain,
( spl0_1522
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f9181,plain,
( spl0_1146
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f13306,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1146
| ~ spl0_1483 ),
inference(resolution,[],[f12174,f9182]) ).
fof(f9182,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1146 ),
inference(avatar_component_clause,[],[f9181]) ).
fof(f13207,plain,
( spl0_1521
| ~ spl0_767
| ~ spl0_1420 ),
inference(avatar_split_clause,[],[f12562,f11888,f7237,f13205]) ).
fof(f13205,plain,
( spl0_1521
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f12562,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_767
| ~ spl0_1420 ),
inference(superposition,[],[f7238,f11889]) ).
fof(f12580,plain,
( ~ spl0_1519
| spl0_1520
| ~ spl0_112
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f11115,f10471,f3799,f12578,f12574]) ).
fof(f12574,plain,
( spl0_1519
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f12578,plain,
( spl0_1520
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f10471,plain,
( spl0_1316
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f11115,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_112
| ~ spl0_1316 ),
inference(resolution,[],[f10472,f3800]) ).
fof(f10472,plain,
( ! [X18,X1] :
( ~ c_lessequals(c_0,c_uminus(X18,X1),X1)
| c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1316 ),
inference(avatar_component_clause,[],[f10471]) ).
fof(f12357,plain,
spl0_1518,
inference(avatar_split_clause,[],[f3156,f12355]) ).
fof(f12355,plain,
( spl0_1518
<=> ! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f3156,plain,
! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2976,f2831]) ).
fof(f2976,plain,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1871,f2544,f2544]) ).
fof(f1871,axiom,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f12353,plain,
spl0_1517,
inference(avatar_split_clause,[],[f3144,f12351]) ).
fof(f12351,plain,
( spl0_1517
<=> ! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f3144,plain,
! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ),
inference(forward_demodulation,[],[f2960,f2884]) ).
fof(f2960,plain,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X43,tc_nat),tc_nat),tc_nat),X21,tc_nat) ),
inference(definition_unfolding,[],[f2036,f2544]) ).
fof(f2036,axiom,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f12349,plain,
spl0_1516,
inference(avatar_split_clause,[],[f3093,f12347]) ).
fof(f3093,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3092,f2156]) ).
fof(f3092,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3091,f2154]) ).
fof(f3091,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f1883,f2156]) ).
fof(f1883,axiom,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f12345,plain,
spl0_1515,
inference(avatar_split_clause,[],[f3079,f12343]) ).
fof(f3079,plain,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
inference(forward_demodulation,[],[f2128,f2127]) ).
fof(f2127,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f2128,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f12341,plain,
spl0_1514,
inference(avatar_split_clause,[],[f3075,f12339]) ).
fof(f3075,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2873,f2846]) ).
fof(f2846,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
inference(definition_unfolding,[],[f2112,f2113]) ).
fof(f2113,axiom,
! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f2112,axiom,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2873,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2124,f2129,f2113,f2129]) ).
fof(f2124,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f12337,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2986,f12335]) ).
fof(f2986,plain,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1853,f2129]) ).
fof(f1853,axiom,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f12333,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2984,f12331]) ).
fof(f12331,plain,
( spl0_1512
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f2984,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1854,f2129]) ).
fof(f1854,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f12302,plain,
( spl0_1511
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1510 ),
inference(avatar_split_clause,[],[f12298,f12295,f10767,f10447,f6846,f5911,f12300]) ).
fof(f12295,plain,
( spl0_1510
<=> ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f12298,plain,
( ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1510 ),
inference(forward_demodulation,[],[f12296,f11726]) ).
fof(f12296,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_1510 ),
inference(avatar_component_clause,[],[f12295]) ).
fof(f12297,plain,
spl0_1510,
inference(avatar_split_clause,[],[f2967,f12295]) ).
fof(f2967,plain,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1783,f2544]) ).
fof(f1783,axiom,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f12293,plain,
spl0_1509,
inference(avatar_split_clause,[],[f2932,f12291]) ).
fof(f2932,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ),
inference(definition_unfolding,[],[f2117,f2129]) ).
fof(f2117,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f12285,plain,
( spl0_1508
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1507 ),
inference(avatar_split_clause,[],[f12281,f12278,f10767,f10447,f6846,f5911,f12283]) ).
fof(f12278,plain,
( spl0_1507
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f12281,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1507 ),
inference(forward_demodulation,[],[f12279,f11726]) ).
fof(f12279,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat)
| ~ spl0_1507 ),
inference(avatar_component_clause,[],[f12278]) ).
fof(f12280,plain,
spl0_1507,
inference(avatar_split_clause,[],[f2874,f12278]) ).
fof(f2874,plain,
! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2527,f2544]) ).
fof(f2527,axiom,
! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f12276,plain,
spl0_1506,
inference(avatar_split_clause,[],[f2872,f12274]) ).
fof(f12274,plain,
( spl0_1506
<=> ! [X13,X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f2872,plain,
! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2589,f2373]) ).
fof(f2589,axiom,
! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f12272,plain,
spl0_1505,
inference(avatar_split_clause,[],[f2861,f12270]) ).
fof(f2861,plain,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2706,f2716]) ).
fof(f2706,axiom,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f12268,plain,
spl0_1504,
inference(avatar_split_clause,[],[f2860,f12266]) ).
fof(f2860,plain,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2707,f2716]) ).
fof(f2707,axiom,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f12261,plain,
( ~ spl0_1502
| spl0_1503
| ~ spl0_112
| ~ spl0_1279 ),
inference(avatar_split_clause,[],[f10884,f10321,f3799,f12259,f12255]) ).
fof(f12255,plain,
( spl0_1502
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f12259,plain,
( spl0_1503
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f10321,plain,
( spl0_1279
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f10884,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_112
| ~ spl0_1279 ),
inference(resolution,[],[f10322,f3800]) ).
fof(f10322,plain,
( ! [X48,X1] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1279 ),
inference(avatar_component_clause,[],[f10321]) ).
fof(f12253,plain,
( spl0_1501
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1500 ),
inference(avatar_split_clause,[],[f12249,f12246,f10767,f10447,f6846,f5911,f12251]) ).
fof(f12251,plain,
( spl0_1501
<=> ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f12246,plain,
( spl0_1500
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f12249,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1387
| ~ spl0_1500 ),
inference(forward_demodulation,[],[f12247,f11726]) ).
fof(f12247,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21)
| ~ spl0_1500 ),
inference(avatar_component_clause,[],[f12246]) ).
fof(f12248,plain,
spl0_1500,
inference(avatar_split_clause,[],[f2856,f12246]) ).
fof(f2856,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21),
inference(definition_unfolding,[],[f1163,f2544,f2544]) ).
fof(f1163,axiom,
! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f12244,plain,
spl0_1499,
inference(avatar_split_clause,[],[f2821,f12242]) ).
fof(f12242,plain,
( spl0_1499
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f2821,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
fof(f12240,plain,
spl0_1498,
inference(avatar_split_clause,[],[f2820,f12238]) ).
fof(f2820,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
fof(f12236,plain,
spl0_1497,
inference(avatar_split_clause,[],[f2815,f12234]) ).
fof(f12234,plain,
( spl0_1497
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f2815,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
fof(f12232,plain,
spl0_1496,
inference(avatar_split_clause,[],[f2814,f12230]) ).
fof(f2814,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
fof(f12228,plain,
spl0_1495,
inference(avatar_split_clause,[],[f2812,f12226]) ).
fof(f2812,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
fof(f12224,plain,
spl0_1494,
inference(avatar_split_clause,[],[f2811,f12222]) ).
fof(f2811,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
fof(f12220,plain,
spl0_1493,
inference(avatar_split_clause,[],[f2809,f12218]) ).
fof(f2809,axiom,
! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
fof(f12216,plain,
spl0_1492,
inference(avatar_split_clause,[],[f2808,f12214]) ).
fof(f2808,axiom,
! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
fof(f12207,plain,
spl0_1491,
inference(avatar_split_clause,[],[f2806,f12205]) ).
fof(f2806,axiom,
! [X88,X102] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
fof(f12203,plain,
spl0_1490,
inference(avatar_split_clause,[],[f2804,f12201]) ).
fof(f12201,plain,
( spl0_1490
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2804,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
fof(f12199,plain,
spl0_1489,
inference(avatar_split_clause,[],[f2801,f12197]) ).
fof(f12197,plain,
( spl0_1489
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2801,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
fof(f12195,plain,
spl0_1488,
inference(avatar_split_clause,[],[f2800,f12193]) ).
fof(f2800,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
fof(f12191,plain,
spl0_1487,
inference(avatar_split_clause,[],[f2798,f12189]) ).
fof(f2798,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
fof(f12187,plain,
spl0_1486,
inference(avatar_split_clause,[],[f2797,f12185]) ).
fof(f2797,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
fof(f12183,plain,
spl0_1485,
inference(avatar_split_clause,[],[f2794,f12181]) ).
fof(f2794,axiom,
! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
fof(f12179,plain,
spl0_1484,
inference(avatar_split_clause,[],[f2793,f12177]) ).
fof(f2793,axiom,
! [X88,X102] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
fof(f12175,plain,
spl0_1483,
inference(avatar_split_clause,[],[f2725,f12173]) ).
fof(f2725,axiom,
! [X1,X18,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f12171,plain,
spl0_1482,
inference(avatar_split_clause,[],[f2689,f12169]) ).
fof(f2689,axiom,
! [X0,X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f12161,plain,
spl0_1481,
inference(avatar_split_clause,[],[f2656,f12159]) ).
fof(f12159,plain,
( spl0_1481
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f2656,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f12157,plain,
spl0_1480,
inference(avatar_split_clause,[],[f2652,f12155]) ).
fof(f12155,plain,
( spl0_1480
<=> ! [X12,X1,X24] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f2652,axiom,
! [X1,X24,X12] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f12153,plain,
spl0_1479,
inference(avatar_split_clause,[],[f2646,f12151]) ).
fof(f2646,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f12149,plain,
spl0_1478,
inference(avatar_split_clause,[],[f2645,f12147]) ).
fof(f2645,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f12145,plain,
spl0_1477,
inference(avatar_split_clause,[],[f2631,f12143]) ).
fof(f2631,axiom,
! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f12141,plain,
spl0_1476,
inference(avatar_split_clause,[],[f2630,f12139]) ).
fof(f2630,axiom,
! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f12137,plain,
spl0_1475,
inference(avatar_split_clause,[],[f2622,f12135]) ).
fof(f12135,plain,
( spl0_1475
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f2622,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f12133,plain,
spl0_1474,
inference(avatar_split_clause,[],[f2616,f12131]) ).
fof(f12131,plain,
( spl0_1474
<=> ! [X12,X1,X24] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f2616,axiom,
! [X1,X24,X12] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f12129,plain,
spl0_1473,
inference(avatar_split_clause,[],[f2555,f12127]) ).
fof(f12127,plain,
( spl0_1473
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f2555,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f12125,plain,
spl0_1472,
inference(avatar_split_clause,[],[f2554,f12123]) ).
fof(f12123,plain,
( spl0_1472
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f2554,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f12110,plain,
spl0_1471,
inference(avatar_split_clause,[],[f2552,f12108]) ).
fof(f12108,plain,
( spl0_1471
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f2552,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f12106,plain,
spl0_1470,
inference(avatar_split_clause,[],[f2551,f12104]) ).
fof(f12104,plain,
( spl0_1470
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f2551,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f12102,plain,
spl0_1469,
inference(avatar_split_clause,[],[f2525,f12100]) ).
fof(f12100,plain,
( spl0_1469
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f2525,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f12098,plain,
spl0_1468,
inference(avatar_split_clause,[],[f2524,f12096]) ).
fof(f12096,plain,
( spl0_1468
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f2524,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f12094,plain,
spl0_1467,
inference(avatar_split_clause,[],[f2520,f12092]) ).
fof(f12092,plain,
( spl0_1467
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f2520,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f12090,plain,
spl0_1466,
inference(avatar_split_clause,[],[f2519,f12088]) ).
fof(f12088,plain,
( spl0_1466
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f2519,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f12086,plain,
spl0_1465,
inference(avatar_split_clause,[],[f2387,f12084]) ).
fof(f12084,plain,
( spl0_1465
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f2387,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f12082,plain,
spl0_1464,
inference(avatar_split_clause,[],[f2367,f12080]) ).
fof(f2367,axiom,
! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f12078,plain,
spl0_1463,
inference(avatar_split_clause,[],[f2365,f12076]) ).
fof(f2365,axiom,
! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f12074,plain,
spl0_1462,
inference(avatar_split_clause,[],[f2361,f12072]) ).
fof(f12072,plain,
( spl0_1462
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f2361,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f12069,plain,
spl0_1461,
inference(avatar_split_clause,[],[f2358,f12067]) ).
fof(f12067,plain,
( spl0_1461
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f2358,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f12065,plain,
spl0_1460,
inference(avatar_split_clause,[],[f2347,f12063]) ).
fof(f12063,plain,
( spl0_1460
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f2347,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f12061,plain,
spl0_1459,
inference(avatar_split_clause,[],[f2339,f12059]) ).
fof(f12059,plain,
( spl0_1459
<=> ! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f2339,axiom,
! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f12057,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2295,f12055]) ).
fof(f12055,plain,
( spl0_1458
<=> ! [X0,X21] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f2295,axiom,
! [X21,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f12053,plain,
spl0_1457,
inference(avatar_split_clause,[],[f2282,f12051]) ).
fof(f12051,plain,
( spl0_1457
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f2282,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f12049,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2265,f12047]) ).
fof(f12047,plain,
( spl0_1456
<=> ! [X2,X48,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2265,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f12045,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2264,f12043]) ).
fof(f12043,plain,
( spl0_1455
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2264,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f12041,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2260,f12039]) ).
fof(f12039,plain,
( spl0_1454
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f2260,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f12037,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2259,f12035]) ).
fof(f2259,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f12033,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2257,f12031]) ).
fof(f12031,plain,
( spl0_1452
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f2257,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f12029,plain,
( ~ spl0_1451
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1250 ),
inference(avatar_split_clause,[],[f9815,f9809,f9069,f5916,f12026]) ).
fof(f9815,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1250 ),
inference(forward_demodulation,[],[f9814,f9070]) ).
fof(f9814,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1250 ),
inference(superposition,[],[f9810,f5918]) ).
fof(f12024,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2256,f12022]) ).
fof(f12022,plain,
( spl0_1450
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f2256,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f12020,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2254,f12018]) ).
fof(f12018,plain,
( spl0_1449
<=> ! [X48,X1,X0,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2254,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f12016,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2253,f12014]) ).
fof(f2253,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f12012,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2249,f12010]) ).
fof(f12010,plain,
( spl0_1447
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2249,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f12008,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2248,f12006]) ).
fof(f12006,plain,
( spl0_1446
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f2248,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f12004,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2215,f12002]) ).
fof(f12002,plain,
( spl0_1445
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f2215,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f12000,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2212,f11998]) ).
fof(f11998,plain,
( spl0_1444
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2212,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11996,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2210,f11994]) ).
fof(f11994,plain,
( spl0_1443
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f2210,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11992,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2207,f11990]) ).
fof(f11990,plain,
( spl0_1442
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f2207,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11988,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2206,f11986]) ).
fof(f11986,plain,
( spl0_1441
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f2206,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11979,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2204,f11977]) ).
fof(f11977,plain,
( spl0_1440
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f2204,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11975,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2203,f11973]) ).
fof(f11973,plain,
( spl0_1439
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f2203,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11971,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2202,f11969]) ).
fof(f11969,plain,
( spl0_1438
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f2202,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11967,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2201,f11965]) ).
fof(f11965,plain,
( spl0_1437
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f2201,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11963,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2200,f11961]) ).
fof(f11961,plain,
( spl0_1436
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2200,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11959,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2184,f11957]) ).
fof(f2184,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11955,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2110,f11953]) ).
fof(f2110,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11951,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2109,f11949]) ).
fof(f2109,axiom,
! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11947,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2045,f11945]) ).
fof(f11945,plain,
( spl0_1432
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f2045,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11943,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2044,f11941]) ).
fof(f11941,plain,
( spl0_1431
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f2044,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11934,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1852,f11932]) ).
fof(f11932,plain,
( spl0_1430
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1852,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11930,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1799,f11928]) ).
fof(f11928,plain,
( spl0_1429
<=> ! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1799,axiom,
! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11926,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1765,f11924]) ).
fof(f11924,plain,
( spl0_1428
<=> ! [X0,X12,X1] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1765,axiom,
! [X0,X1,X12] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11922,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1748,f11920]) ).
fof(f1748,axiom,
! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11918,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1742,f11916]) ).
fof(f11916,plain,
( spl0_1426
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f1742,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11914,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1702,f11912]) ).
fof(f1702,axiom,
! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11910,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1604,f11908]) ).
fof(f11908,plain,
( spl0_1424
<=> ! [X43,X0,X23,X1] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f1604,axiom,
! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11906,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1591,f11904]) ).
fof(f11904,plain,
( spl0_1423
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f1591,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11902,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1589,f11900]) ).
fof(f11900,plain,
( spl0_1422
<=> ! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1589,axiom,
! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11898,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1581,f11896]) ).
fof(f11896,plain,
( spl0_1421
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1581,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11890,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1580,f11888]) ).
fof(f1580,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11886,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1578,f11884]) ).
fof(f11884,plain,
( spl0_1419
<=> ! [X59,X43,X15] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1578,axiom,
! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11882,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1576,f11880]) ).
fof(f11880,plain,
( spl0_1418
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1576,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11878,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1575,f11876]) ).
fof(f1575,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11874,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1475,f11872]) ).
fof(f11872,plain,
( spl0_1416
<=> ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1475,axiom,
! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11870,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1416,f11868]) ).
fof(f11868,plain,
( spl0_1415
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1416,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11866,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1305,f11864]) ).
fof(f11864,plain,
( spl0_1414
<=> ! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1305,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11862,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1304,f11860]) ).
fof(f1304,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11858,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1291,f11856]) ).
fof(f11856,plain,
( spl0_1412
<=> ! [X12,X1,X18] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1291,axiom,
! [X1,X18,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11854,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1287,f11852]) ).
fof(f11852,plain,
( spl0_1411
<=> ! [X20,X1,X19] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1287,axiom,
! [X1,X19,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11848,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1286,f11846]) ).
fof(f1286,axiom,
! [X1,X19,X20] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11844,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1285,f11842]) ).
fof(f11842,plain,
( spl0_1409
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1285,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11840,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1284,f11838]) ).
fof(f11838,plain,
( spl0_1408
<=> ! [X12,X1] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1284,axiom,
! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11836,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1276,f11834]) ).
fof(f11834,plain,
( spl0_1407
<=> ! [X12,X1] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1276,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11832,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1223,f11830]) ).
fof(f11830,plain,
( spl0_1406
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1223,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11828,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1221,f11826]) ).
fof(f11826,plain,
( spl0_1405
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1221,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11824,plain,
spl0_1404,
inference(avatar_split_clause,[],[f111,f11822]) ).
fof(f111,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11820,plain,
spl0_1403,
inference(avatar_split_clause,[],[f108,f11818]) ).
fof(f11818,plain,
( spl0_1403
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f108,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11816,plain,
spl0_1402,
inference(avatar_split_clause,[],[f104,f11814]) ).
fof(f104,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11812,plain,
spl0_1401,
inference(avatar_split_clause,[],[f100,f11810]) ).
fof(f11810,plain,
( spl0_1401
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f100,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11808,plain,
spl0_1400,
inference(avatar_split_clause,[],[f97,f11806]) ).
fof(f11806,plain,
( spl0_1400
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f97,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11804,plain,
spl0_1399,
inference(avatar_split_clause,[],[f29,f11802]) ).
fof(f11802,plain,
( spl0_1399
<=> ! [X12,X1,X18] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f29,axiom,
! [X1,X18,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11431,plain,
( spl0_1398
| ~ spl0_653
| ~ spl0_802
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9491,f9225,f7378,f5969,f11428]) ).
fof(f5969,plain,
( spl0_653
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f9491,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_653
| ~ spl0_802
| ~ spl0_1157 ),
inference(forward_demodulation,[],[f9486,f7379]) ).
fof(f9486,plain,
( c_Message_Oparts(c_Message_Osynth(c_emptyset)) = c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg)
| ~ spl0_653
| ~ spl0_1157 ),
inference(superposition,[],[f9226,f5971]) ).
fof(f5971,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f5969]) ).
fof(f11260,plain,
( spl0_1397
| ~ spl0_718
| ~ spl0_1145 ),
inference(avatar_split_clause,[],[f9474,f9177,f7023,f11258]) ).
fof(f11258,plain,
( spl0_1397
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f9177,plain,
( spl0_1145
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f9474,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_718
| ~ spl0_1145 ),
inference(superposition,[],[f9178,f7024]) ).
fof(f9178,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f9177]) ).
fof(f11037,plain,
( spl0_1396
| ~ spl0_644
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9391,f9057,f5930,f11035]) ).
fof(f11035,plain,
( spl0_1396
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f5930,plain,
( spl0_644
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f9391,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1115 ),
inference(resolution,[],[f9058,f5931]) ).
fof(f5931,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5930]) ).
fof(f10971,plain,
( spl0_1395
| ~ spl0_644
| ~ spl0_1112 ),
inference(avatar_split_clause,[],[f9381,f9044,f5930,f10969]) ).
fof(f10969,plain,
( spl0_1395
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f9044,plain,
( spl0_1112
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f9381,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1112 ),
inference(resolution,[],[f9045,f5931]) ).
fof(f9045,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1112 ),
inference(avatar_component_clause,[],[f9044]) ).
fof(f10834,plain,
( spl0_1394
| ~ spl0_1064
| ~ spl0_1267 ),
inference(avatar_split_clause,[],[f10824,f10273,f8646,f10832]) ).
fof(f10273,plain,
( spl0_1267
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f10824,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1064
| ~ spl0_1267 ),
inference(resolution,[],[f10274,f8647]) ).
fof(f10274,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1267 ),
inference(avatar_component_clause,[],[f10273]) ).
fof(f10799,plain,
spl0_1393,
inference(avatar_split_clause,[],[f3203,f10797]) ).
fof(f10797,plain,
( spl0_1393
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f3203,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3202,f2115]) ).
fof(f3202,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3003,f2830]) ).
fof(f3003,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1338,f2129]) ).
fof(f1338,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10795,plain,
spl0_1392,
inference(avatar_split_clause,[],[f3131,f10793]) ).
fof(f3131,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3130,f2156]) ).
fof(f3130,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3129,f2154]) ).
fof(f3129,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f1878,f2156]) ).
fof(f1878,axiom,
! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10791,plain,
spl0_1391,
inference(avatar_split_clause,[],[f3124,f10789]) ).
fof(f3124,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3123,f2156]) ).
fof(f3123,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3122,f2154]) ).
fof(f3122,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1328,f2156]) ).
fof(f1328,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10781,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2944,f10779]) ).
fof(f2944,plain,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2598,f2373]) ).
fof(f2598,axiom,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10777,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2943,f10775]) ).
fof(f2943,plain,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2599,f2373]) ).
fof(f2599,axiom,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10773,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2938,f10771]) ).
fof(f2938,plain,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
inference(definition_unfolding,[],[f2346,f2544]) ).
fof(f2346,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10769,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2867,f10767]) ).
fof(f2867,plain,
! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1372,f2544]) ).
fof(f1372,axiom,
! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10765,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2864,f10763]) ).
fof(f2864,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1),
inference(definition_unfolding,[],[f2578,f2373]) ).
fof(f2578,axiom,
! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10761,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2863,f10759]) ).
fof(f2863,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2579,f2373]) ).
fof(f2579,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10757,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2823,f10755]) ).
fof(f2823,axiom,
! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
fof(f10753,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2780,f10751]) ).
fof(f10751,plain,
( spl0_1383
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f2780,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
fof(f10749,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2779,f10747]) ).
fof(f10747,plain,
( spl0_1382
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2779,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
fof(f10745,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2771,f10743]) ).
fof(f10743,plain,
( spl0_1381
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f2771,axiom,
! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
fof(f10738,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2768,f10736]) ).
fof(f10736,plain,
( spl0_1380
<=> ! [X20,X88] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f2768,axiom,
! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
fof(f10734,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2742,f10732]) ).
fof(f10732,plain,
( spl0_1379
<=> ! [X93,X88] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f2742,axiom,
! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
fof(f10730,plain,
spl0_1378,
inference(avatar_split_clause,[],[f2729,f10728]) ).
fof(f10728,plain,
( spl0_1378
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2729,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
fof(f10726,plain,
spl0_1377,
inference(avatar_split_clause,[],[f2728,f10724]) ).
fof(f10724,plain,
( spl0_1377
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f2728,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
fof(f10722,plain,
spl0_1376,
inference(avatar_split_clause,[],[f2703,f10720]) ).
fof(f10720,plain,
( spl0_1376
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f2703,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10718,plain,
spl0_1375,
inference(avatar_split_clause,[],[f2701,f10716]) ).
fof(f10716,plain,
( spl0_1375
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f2701,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10714,plain,
spl0_1374,
inference(avatar_split_clause,[],[f2692,f10712]) ).
fof(f10712,plain,
( spl0_1374
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2692,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f10710,plain,
spl0_1373,
inference(avatar_split_clause,[],[f2688,f10708]) ).
fof(f10708,plain,
( spl0_1373
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2688,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10706,plain,
spl0_1372,
inference(avatar_split_clause,[],[f2676,f10704]) ).
fof(f2676,axiom,
! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10702,plain,
spl0_1371,
inference(avatar_split_clause,[],[f2670,f10700]) ).
fof(f10700,plain,
( spl0_1371
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f2670,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10697,plain,
spl0_1370,
inference(avatar_split_clause,[],[f2653,f10695]) ).
fof(f10695,plain,
( spl0_1370
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f2653,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10693,plain,
spl0_1369,
inference(avatar_split_clause,[],[f2628,f10691]) ).
fof(f10691,plain,
( spl0_1369
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f2628,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10689,plain,
spl0_1368,
inference(avatar_split_clause,[],[f2627,f10687]) ).
fof(f10687,plain,
( spl0_1368
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f2627,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10685,plain,
spl0_1367,
inference(avatar_split_clause,[],[f2617,f10683]) ).
fof(f10683,plain,
( spl0_1367
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f2617,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10681,plain,
spl0_1366,
inference(avatar_split_clause,[],[f2614,f10679]) ).
fof(f10679,plain,
( spl0_1366
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f2614,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10677,plain,
spl0_1365,
inference(avatar_split_clause,[],[f2595,f10675]) ).
fof(f10675,plain,
( spl0_1365
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f2595,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10673,plain,
spl0_1364,
inference(avatar_split_clause,[],[f2594,f10671]) ).
fof(f10671,plain,
( spl0_1364
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f2594,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10669,plain,
spl0_1363,
inference(avatar_split_clause,[],[f2592,f10667]) ).
fof(f2592,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10665,plain,
spl0_1362,
inference(avatar_split_clause,[],[f2591,f10663]) ).
fof(f2591,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10661,plain,
spl0_1361,
inference(avatar_split_clause,[],[f2581,f10659]) ).
fof(f2581,axiom,
! [X1,X12,X13] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10653,plain,
spl0_1360,
inference(avatar_split_clause,[],[f2570,f10651]) ).
fof(f10651,plain,
( spl0_1360
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f2570,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10649,plain,
spl0_1359,
inference(avatar_split_clause,[],[f2569,f10647]) ).
fof(f10647,plain,
( spl0_1359
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f2569,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10645,plain,
spl0_1358,
inference(avatar_split_clause,[],[f2568,f10643]) ).
fof(f2568,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10641,plain,
spl0_1357,
inference(avatar_split_clause,[],[f2559,f10639]) ).
fof(f10639,plain,
( spl0_1357
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f2559,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10637,plain,
spl0_1356,
inference(avatar_split_clause,[],[f2558,f10635]) ).
fof(f10635,plain,
( spl0_1356
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f2558,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10633,plain,
spl0_1355,
inference(avatar_split_clause,[],[f2557,f10631]) ).
fof(f10631,plain,
( spl0_1355
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f2557,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10629,plain,
spl0_1354,
inference(avatar_split_clause,[],[f2550,f10627]) ).
fof(f2550,axiom,
! [X1,X26,X16] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10625,plain,
spl0_1353,
inference(avatar_split_clause,[],[f2546,f10623]) ).
fof(f10623,plain,
( spl0_1353
<=> ! [X14,X26] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f2546,axiom,
! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10621,plain,
spl0_1352,
inference(avatar_split_clause,[],[f2543,f10619]) ).
fof(f10619,plain,
( spl0_1352
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f2543,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10617,plain,
spl0_1351,
inference(avatar_split_clause,[],[f2537,f10615]) ).
fof(f10615,plain,
( spl0_1351
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f2537,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10613,plain,
spl0_1350,
inference(avatar_split_clause,[],[f2536,f10611]) ).
fof(f10611,plain,
( spl0_1350
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f2536,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10609,plain,
spl0_1349,
inference(avatar_split_clause,[],[f2535,f10607]) ).
fof(f10607,plain,
( spl0_1349
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f2535,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10605,plain,
spl0_1348,
inference(avatar_split_clause,[],[f2531,f10603]) ).
fof(f10603,plain,
( spl0_1348
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f2531,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10601,plain,
spl0_1347,
inference(avatar_split_clause,[],[f2530,f10599]) ).
fof(f10599,plain,
( spl0_1347
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f2530,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10597,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2529,f10595]) ).
fof(f2529,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10593,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2523,f10591]) ).
fof(f2523,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10589,plain,
spl0_1344,
inference(avatar_split_clause,[],[f2518,f10587]) ).
fof(f2518,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10585,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2517,f10583]) ).
fof(f2517,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10581,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2516,f10579]) ).
fof(f2516,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10577,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2515,f10575]) ).
fof(f2515,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10570,plain,
spl0_1340,
inference(avatar_split_clause,[],[f2514,f10568]) ).
fof(f2514,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10566,plain,
spl0_1339,
inference(avatar_split_clause,[],[f2302,f10564]) ).
fof(f10564,plain,
( spl0_1339
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f2302,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10562,plain,
spl0_1338,
inference(avatar_split_clause,[],[f2301,f10560]) ).
fof(f10560,plain,
( spl0_1338
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f2301,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10558,plain,
spl0_1337,
inference(avatar_split_clause,[],[f2300,f10556]) ).
fof(f10556,plain,
( spl0_1337
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f2300,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10554,plain,
spl0_1336,
inference(avatar_split_clause,[],[f2299,f10552]) ).
fof(f10552,plain,
( spl0_1336
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2299,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10550,plain,
spl0_1335,
inference(avatar_split_clause,[],[f2296,f10548]) ).
fof(f10548,plain,
( spl0_1335
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f2296,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10546,plain,
spl0_1334,
inference(avatar_split_clause,[],[f2289,f10544]) ).
fof(f10544,plain,
( spl0_1334
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f2289,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10542,plain,
spl0_1333,
inference(avatar_split_clause,[],[f2288,f10540]) ).
fof(f10540,plain,
( spl0_1333
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f2288,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10538,plain,
spl0_1332,
inference(avatar_split_clause,[],[f2287,f10536]) ).
fof(f10536,plain,
( spl0_1332
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f2287,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10534,plain,
spl0_1331,
inference(avatar_split_clause,[],[f2286,f10532]) ).
fof(f10532,plain,
( spl0_1331
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f2286,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10530,plain,
spl0_1330,
inference(avatar_split_clause,[],[f2283,f10528]) ).
fof(f10528,plain,
( spl0_1330
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f2283,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10526,plain,
spl0_1329,
inference(avatar_split_clause,[],[f2277,f10524]) ).
fof(f10524,plain,
( spl0_1329
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f2277,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10522,plain,
spl0_1328,
inference(avatar_split_clause,[],[f2276,f10520]) ).
fof(f10520,plain,
( spl0_1328
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f2276,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10518,plain,
spl0_1327,
inference(avatar_split_clause,[],[f2275,f10516]) ).
fof(f10516,plain,
( spl0_1327
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f2275,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10514,plain,
spl0_1326,
inference(avatar_split_clause,[],[f2274,f10512]) ).
fof(f10512,plain,
( spl0_1326
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f2274,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10510,plain,
spl0_1325,
inference(avatar_split_clause,[],[f2234,f10508]) ).
fof(f10508,plain,
( spl0_1325
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2234,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10506,plain,
spl0_1324,
inference(avatar_split_clause,[],[f2233,f10504]) ).
fof(f10504,plain,
( spl0_1324
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f2233,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10502,plain,
spl0_1323,
inference(avatar_split_clause,[],[f2230,f10500]) ).
fof(f10500,plain,
( spl0_1323
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f2230,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10498,plain,
spl0_1322,
inference(avatar_split_clause,[],[f2229,f10496]) ).
fof(f10496,plain,
( spl0_1322
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f2229,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10494,plain,
spl0_1321,
inference(avatar_split_clause,[],[f2227,f10492]) ).
fof(f10492,plain,
( spl0_1321
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f2227,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10490,plain,
( spl0_1320
| ~ spl0_709
| ~ spl0_785
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f8905,f8674,f7309,f6984,f10487]) ).
fof(f8905,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_709
| ~ spl0_785
| ~ spl0_1071 ),
inference(forward_demodulation,[],[f8902,f6986]) ).
fof(f8902,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_785
| ~ spl0_1071 ),
inference(superposition,[],[f8675,f7311]) ).
fof(f10485,plain,
spl0_1319,
inference(avatar_split_clause,[],[f2224,f10483]) ).
fof(f10483,plain,
( spl0_1319
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f2224,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10481,plain,
spl0_1318,
inference(avatar_split_clause,[],[f2223,f10479]) ).
fof(f10479,plain,
( spl0_1318
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f2223,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10477,plain,
spl0_1317,
inference(avatar_split_clause,[],[f2222,f10475]) ).
fof(f2222,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10473,plain,
spl0_1316,
inference(avatar_split_clause,[],[f2221,f10471]) ).
fof(f2221,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10469,plain,
spl0_1315,
inference(avatar_split_clause,[],[f2167,f10467]) ).
fof(f2167,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10465,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2166,f10463]) ).
fof(f2166,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10461,plain,
spl0_1313,
inference(avatar_split_clause,[],[f2086,f10459]) ).
fof(f2086,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10457,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2081,f10455]) ).
fof(f2081,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10453,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2065,f10451]) ).
fof(f10451,plain,
( spl0_1311
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f2065,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10449,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1850,f10447]) ).
fof(f1850,axiom,
! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10445,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1813,f10443]) ).
fof(f10443,plain,
( spl0_1309
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1813,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10441,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1807,f10439]) ).
fof(f10439,plain,
( spl0_1308
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1807,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10437,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1806,f10435]) ).
fof(f10435,plain,
( spl0_1307
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1806,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10433,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1784,f10431]) ).
fof(f10431,plain,
( spl0_1306
<=> ! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1784,axiom,
! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10429,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1743,f10427]) ).
fof(f1743,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10425,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1737,f10423]) ).
fof(f10423,plain,
( spl0_1304
<=> ! [X1,X3] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1737,axiom,
! [X3,X1] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10421,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1626,f10419]) ).
fof(f10419,plain,
( spl0_1303
<=> ! [X18,X42,X64,X63,X1] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1626,axiom,
! [X1,X18,X63,X42,X64] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10417,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1625,f10415]) ).
fof(f10415,plain,
( spl0_1302
<=> ! [X18,X42,X64,X63,X1] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1625,axiom,
! [X18,X1,X63,X42,X64] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10413,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1610,f10411]) ).
fof(f10411,plain,
( spl0_1301
<=> ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1610,axiom,
! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10409,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1552,f10407]) ).
fof(f10407,plain,
( spl0_1300
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1552,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10405,plain,
( spl0_1298
| ~ spl0_1299
| ~ spl0_787
| ~ spl0_1039 ),
inference(avatar_split_clause,[],[f8856,f8546,f7318,f10402,f10399]) ).
fof(f10399,plain,
( spl0_1298
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f10402,plain,
( spl0_1299
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f7318,plain,
( spl0_787
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f8546,plain,
( spl0_1039
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f8856,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_787
| ~ spl0_1039 ),
inference(superposition,[],[f8547,f7319]) ).
fof(f7319,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_787 ),
inference(avatar_component_clause,[],[f7318]) ).
fof(f8547,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1039 ),
inference(avatar_component_clause,[],[f8546]) ).
fof(f10397,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1530,f10395]) ).
fof(f1530,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10393,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1493,f10391]) ).
fof(f10391,plain,
( spl0_1296
<=> ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1493,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10389,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1492,f10387]) ).
fof(f10387,plain,
( spl0_1295
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1492,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10385,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1485,f10383]) ).
fof(f10383,plain,
( spl0_1294
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1485,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10380,plain,
( spl0_1293
| ~ spl0_888
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10376,f10373,f7790,f10378]) ).
fof(f10378,plain,
( spl0_1293
<=> ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f10373,plain,
( spl0_1292
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f10376,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_888
| ~ spl0_1292 ),
inference(forward_demodulation,[],[f10374,f7792]) ).
fof(f10374,plain,
( ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1292 ),
inference(avatar_component_clause,[],[f10373]) ).
fof(f10375,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1484,f10373]) ).
fof(f1484,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10371,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1477,f10369]) ).
fof(f10369,plain,
( spl0_1291
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1477,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10367,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1476,f10365]) ).
fof(f10365,plain,
( spl0_1290
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1476,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10363,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1457,f10361]) ).
fof(f10361,plain,
( spl0_1289
<=> ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1457,axiom,
! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10359,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1442,f10357]) ).
fof(f10357,plain,
( spl0_1288
<=> ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1442,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10355,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1413,f10353]) ).
fof(f10353,plain,
( spl0_1287
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1413,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10351,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1412,f10349]) ).
fof(f10349,plain,
( spl0_1286
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1412,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10347,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1409,f10345]) ).
fof(f10345,plain,
( spl0_1285
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1409,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10343,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1408,f10341]) ).
fof(f10341,plain,
( spl0_1284
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1408,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10339,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1406,f10337]) ).
fof(f10337,plain,
( spl0_1283
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1406,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10335,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1400,f10333]) ).
fof(f10333,plain,
( spl0_1282
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1400,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10331,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1399,f10329]) ).
fof(f10329,plain,
( spl0_1281
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1399,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10327,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1398,f10325]) ).
fof(f10325,plain,
( spl0_1280
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1398,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10323,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1397,f10321]) ).
fof(f1397,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10319,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1361,f10317]) ).
fof(f10317,plain,
( spl0_1278
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1361,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10315,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1356,f10313]) ).
fof(f10313,plain,
( spl0_1277
<=> ! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1356,axiom,
! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f10311,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1342,f10309]) ).
fof(f10309,plain,
( spl0_1276
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1342,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f10307,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1341,f10305]) ).
fof(f10305,plain,
( spl0_1275
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1341,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f10303,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1243,f10301]) ).
fof(f10301,plain,
( spl0_1274
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1243,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f10299,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1233,f10297]) ).
fof(f10297,plain,
( spl0_1273
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1233,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f10295,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1232,f10293]) ).
fof(f10293,plain,
( spl0_1272
<=> ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1232,axiom,
! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f10291,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1191,f10289]) ).
fof(f10289,plain,
( spl0_1271
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1191,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f10287,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1189,f10285]) ).
fof(f10285,plain,
( spl0_1270
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f1189,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f10283,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1185,f10281]) ).
fof(f10281,plain,
( spl0_1269
<=> ! [X2,X18,X27,X1] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f1185,axiom,
! [X2,X18,X1,X27] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f10279,plain,
( spl0_1268
| ~ spl0_753
| ~ spl0_1003 ),
inference(avatar_split_clause,[],[f8763,f8400,f7181,f10277]) ).
fof(f10277,plain,
( spl0_1268
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f7181,plain,
( spl0_753
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f8763,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_753
| ~ spl0_1003 ),
inference(superposition,[],[f8401,f7182]) ).
fof(f7182,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f7181]) ).
fof(f10275,plain,
spl0_1267,
inference(avatar_split_clause,[],[f110,f10273]) ).
fof(f110,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10271,plain,
spl0_1266,
inference(avatar_split_clause,[],[f109,f10269]) ).
fof(f10269,plain,
( spl0_1266
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f109,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10267,plain,
spl0_1265,
inference(avatar_split_clause,[],[f49,f10265]) ).
fof(f10265,plain,
( spl0_1265
<=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f49,axiom,
! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10263,plain,
spl0_1264,
inference(avatar_split_clause,[],[f2,f10261]) ).
fof(f10261,plain,
( spl0_1264
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10259,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1,f10257]) ).
fof(f10257,plain,
( spl0_1263
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10154,plain,
( ~ spl0_1261
| spl0_1262
| ~ spl0_775
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f10078,f9704,f7269,f10152,f10148]) ).
fof(f10148,plain,
( spl0_1261
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f10152,plain,
( spl0_1262
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f10078,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_775
| ~ spl0_1224 ),
inference(trivial_inequality_removal,[],[f10071]) ).
fof(f10071,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_775
| ~ spl0_1224 ),
inference(superposition,[],[f9705,f7270]) ).
fof(f9889,plain,
( spl0_1260
| ~ spl0_52
| ~ spl0_982 ),
inference(avatar_split_clause,[],[f8325,f8189,f3507,f9886]) ).
fof(f8189,plain,
( spl0_982
<=> ! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f8325,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_982 ),
inference(resolution,[],[f8190,f3509]) ).
fof(f8190,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_982 ),
inference(avatar_component_clause,[],[f8189]) ).
fof(f9882,plain,
( spl0_1259
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9542,f9539,f8526,f3507,f9880]) ).
fof(f9539,plain,
( spl0_1183
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f9542,plain,
( ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1183 ),
inference(forward_demodulation,[],[f9540,f8847]) ).
fof(f9540,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) )
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9539]) ).
fof(f9848,plain,
spl0_1258,
inference(avatar_split_clause,[],[f3148,f9846]) ).
fof(f9846,plain,
( spl0_1258
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f3148,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f2969,f2831]) ).
fof(f2969,plain,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2095,f2544]) ).
fof(f2095,axiom,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9844,plain,
( spl0_1257
| ~ spl0_878
| ~ spl0_967 ),
inference(avatar_split_clause,[],[f8307,f8127,f7694,f9841]) ).
fof(f9841,plain,
( spl0_1257
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f8307,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_878
| ~ spl0_967 ),
inference(superposition,[],[f7695,f8129]) ).
fof(f9839,plain,
spl0_1256,
inference(avatar_split_clause,[],[f3147,f9837]) ).
fof(f3147,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ),
inference(forward_demodulation,[],[f2968,f2831]) ).
fof(f2968,plain,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2096,f2544]) ).
fof(f2096,axiom,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9835,plain,
spl0_1255,
inference(avatar_split_clause,[],[f3141,f9833]) ).
fof(f9833,plain,
( spl0_1255
<=> ! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f3141,plain,
! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ),
inference(forward_demodulation,[],[f2955,f2831]) ).
fof(f2955,plain,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2340,f2544]) ).
fof(f2340,axiom,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9831,plain,
spl0_1254,
inference(avatar_split_clause,[],[f3078,f9829]) ).
fof(f3078,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2882,f2831]) ).
fof(f2882,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2764,f2544]) ).
fof(f2764,axiom,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).
fof(f9827,plain,
spl0_1253,
inference(avatar_split_clause,[],[f3074,f9825]) ).
fof(f3074,plain,
! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2871,f2867]) ).
fof(f2871,plain,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(definition_unfolding,[],[f38,f2544]) ).
fof(f38,axiom,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9823,plain,
spl0_1252,
inference(avatar_split_clause,[],[f3070,f9821]) ).
fof(f9821,plain,
( spl0_1252
<=> ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f3070,plain,
! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2869,f2846]) ).
fof(f2869,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2131,f2113,f2113]) ).
fof(f2131,axiom,
! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9819,plain,
spl0_1251,
inference(avatar_split_clause,[],[f2870,f9817]) ).
fof(f2870,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f2123,f2129,f2129]) ).
fof(f2123,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9811,plain,
( spl0_1250
| ~ spl0_1249 ),
inference(avatar_split_clause,[],[f9807,f9804,f9809]) ).
fof(f9804,plain,
( spl0_1249
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f9807,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1249 ),
inference(forward_demodulation,[],[f9805,f2867]) ).
fof(f9805,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1249 ),
inference(avatar_component_clause,[],[f9804]) ).
fof(f9806,plain,
spl0_1249,
inference(avatar_split_clause,[],[f2859,f9804]) ).
fof(f2859,plain,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1394,f2544]) ).
fof(f1394,axiom,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9802,plain,
spl0_1248,
inference(avatar_split_clause,[],[f2822,f9800]) ).
fof(f9800,plain,
( spl0_1248
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f2822,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
fof(f9798,plain,
( spl0_1247
| ~ spl0_87
| ~ spl0_955 ),
inference(avatar_split_clause,[],[f8290,f8078,f3682,f9796]) ).
fof(f9796,plain,
( spl0_1247
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f8078,plain,
( spl0_955
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f8290,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_87
| ~ spl0_955 ),
inference(resolution,[],[f8079,f3684]) ).
fof(f8079,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_955 ),
inference(avatar_component_clause,[],[f8078]) ).
fof(f9794,plain,
spl0_1246,
inference(avatar_split_clause,[],[f2817,f9792]) ).
fof(f9792,plain,
( spl0_1246
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f2817,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
fof(f9790,plain,
spl0_1245,
inference(avatar_split_clause,[],[f2783,f9788]) ).
fof(f9788,plain,
( spl0_1245
<=> ! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f2783,axiom,
! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
fof(f9786,plain,
spl0_1244,
inference(avatar_split_clause,[],[f2777,f9784]) ).
fof(f9784,plain,
( spl0_1244
<=> ! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f2777,axiom,
! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
fof(f9782,plain,
spl0_1243,
inference(avatar_split_clause,[],[f2715,f9780]) ).
fof(f2715,axiom,
! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9778,plain,
spl0_1242,
inference(avatar_split_clause,[],[f2713,f9776]) ).
fof(f2713,axiom,
! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9774,plain,
spl0_1241,
inference(avatar_split_clause,[],[f2685,f9772]) ).
fof(f9772,plain,
( spl0_1241
<=> ! [X18,X12,X27,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f2685,axiom,
! [X18,X1,X27,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9770,plain,
spl0_1240,
inference(avatar_split_clause,[],[f2642,f9768]) ).
fof(f9768,plain,
( spl0_1240
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f2642,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9766,plain,
spl0_1239,
inference(avatar_split_clause,[],[f2641,f9764]) ).
fof(f9764,plain,
( spl0_1239
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f2641,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9762,plain,
spl0_1238,
inference(avatar_split_clause,[],[f2583,f9760]) ).
fof(f9760,plain,
( spl0_1238
<=> ! [X12,X1,X4] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f2583,axiom,
! [X1,X4,X12] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9758,plain,
spl0_1237,
inference(avatar_split_clause,[],[f2582,f9756]) ).
fof(f9756,plain,
( spl0_1237
<=> ! [X12,X1,X4] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f2582,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9754,plain,
( spl0_1236
| ~ spl0_53
| ~ spl0_955 ),
inference(avatar_split_clause,[],[f8289,f8078,f3512,f9752]) ).
fof(f8289,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_53
| ~ spl0_955 ),
inference(resolution,[],[f8079,f3514]) ).
fof(f9750,plain,
spl0_1235,
inference(avatar_split_clause,[],[f2545,f9748]) ).
fof(f9748,plain,
( spl0_1235
<=> ! [X14,X26] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f2545,axiom,
! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9746,plain,
spl0_1234,
inference(avatar_split_clause,[],[f2542,f9744]) ).
fof(f9744,plain,
( spl0_1234
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f2542,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9742,plain,
spl0_1233,
inference(avatar_split_clause,[],[f2522,f9740]) ).
fof(f2522,axiom,
! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9738,plain,
spl0_1232,
inference(avatar_split_clause,[],[f2271,f9736]) ).
fof(f9736,plain,
( spl0_1232
<=> ! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f2271,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
fof(f9734,plain,
spl0_1231,
inference(avatar_split_clause,[],[f2270,f9732]) ).
fof(f9732,plain,
( spl0_1231
<=> ! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f2270,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
fof(f9730,plain,
spl0_1230,
inference(avatar_split_clause,[],[f2252,f9728]) ).
fof(f9728,plain,
( spl0_1230
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f2252,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9726,plain,
spl0_1229,
inference(avatar_split_clause,[],[f2245,f9724]) ).
fof(f2245,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9722,plain,
spl0_1228,
inference(avatar_split_clause,[],[f2244,f9720]) ).
fof(f2244,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9718,plain,
spl0_1227,
inference(avatar_split_clause,[],[f2240,f9716]) ).
fof(f2240,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9714,plain,
spl0_1226,
inference(avatar_split_clause,[],[f2239,f9712]) ).
fof(f2239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9710,plain,
( spl0_1225
| ~ spl0_87
| ~ spl0_954 ),
inference(avatar_split_clause,[],[f8288,f8074,f3682,f9708]) ).
fof(f9708,plain,
( spl0_1225
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f8074,plain,
( spl0_954
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f8288,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_87
| ~ spl0_954 ),
inference(resolution,[],[f8075,f3684]) ).
fof(f8075,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_954 ),
inference(avatar_component_clause,[],[f8074]) ).
fof(f9706,plain,
spl0_1224,
inference(avatar_split_clause,[],[f2199,f9704]) ).
fof(f2199,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9702,plain,
spl0_1223,
inference(avatar_split_clause,[],[f2183,f9700]) ).
fof(f2183,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9698,plain,
spl0_1222,
inference(avatar_split_clause,[],[f2181,f9696]) ).
fof(f2181,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9694,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2179,f9692]) ).
fof(f9692,plain,
( spl0_1221
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9690,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2178,f9688]) ).
fof(f2178,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9686,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2147,f9684]) ).
fof(f2147,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9682,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2127,f9680]) ).
fof(f9678,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2104,f9676]) ).
fof(f9676,plain,
( spl0_1217
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f2104,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9674,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2103,f9672]) ).
fof(f2103,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9670,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2079,f9668]) ).
fof(f2079,axiom,
! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9666,plain,
( spl0_1214
| ~ spl0_53
| ~ spl0_954 ),
inference(avatar_split_clause,[],[f8287,f8074,f3512,f9664]) ).
fof(f9664,plain,
( spl0_1214
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f8287,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_954 ),
inference(resolution,[],[f8075,f3514]) ).
fof(f9662,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2078,f9660]) ).
fof(f2078,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9658,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2030,f9656]) ).
fof(f9656,plain,
( spl0_1212
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9654,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2029,f9652]) ).
fof(f9652,plain,
( spl0_1211
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9650,plain,
spl0_1210,
inference(avatar_split_clause,[],[f1851,f9648]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9646,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1814,f9644]) ).
fof(f9644,plain,
( spl0_1209
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9642,plain,
spl0_1208,
inference(avatar_split_clause,[],[f1734,f9640]) ).
fof(f9640,plain,
( spl0_1208
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f1734,axiom,
! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9638,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1731,f9636]) ).
fof(f9636,plain,
( spl0_1207
<=> ! [X0,X1,X21] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1731,axiom,
! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9634,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1712,f9632]) ).
fof(f9632,plain,
( spl0_1206
<=> ! [X41,X0,X3,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1712,axiom,
! [X41,X3,X0,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9630,plain,
spl0_1205,
inference(avatar_split_clause,[],[f1613,f9628]) ).
fof(f9628,plain,
( spl0_1205
<=> ! [X43,X59] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1613,axiom,
! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9626,plain,
spl0_1204,
inference(avatar_split_clause,[],[f1609,f9624]) ).
fof(f9624,plain,
( spl0_1204
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1609,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9622,plain,
( spl0_1203
| ~ spl0_91
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8283,f8062,f3702,f9620]) ).
fof(f9620,plain,
( spl0_1203
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f8062,plain,
( spl0_951
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f8283,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_91
| ~ spl0_951 ),
inference(resolution,[],[f8063,f3704]) ).
fof(f8063,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f8062]) ).
fof(f9618,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1608,f9616]) ).
fof(f9616,plain,
( spl0_1202
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1608,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9614,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1595,f9612]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9610,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1594,f9608]) ).
fof(f9608,plain,
( spl0_1200
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9606,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1593,f9604]) ).
fof(f9604,plain,
( spl0_1199
<=> ! [X60,X1] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9602,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1584,f9600]) ).
fof(f1584,axiom,
! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9598,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1583,f9596]) ).
fof(f9596,plain,
( spl0_1197
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1583,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9594,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1582,f9592]) ).
fof(f9592,plain,
( spl0_1196
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1582,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9590,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1539,f9588]) ).
fof(f9588,plain,
( spl0_1195
<=> ! [X0,X1,X3] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1539,axiom,
! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9586,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1463,f9584]) ).
fof(f9584,plain,
( spl0_1194
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1463,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9582,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1462,f9580]) ).
fof(f9580,plain,
( spl0_1193
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1462,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9578,plain,
( spl0_1192
| ~ spl0_27
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8282,f8062,f3382,f9576]) ).
fof(f9576,plain,
( spl0_1192
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f8282,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_951 ),
inference(resolution,[],[f8063,f3384]) ).
fof(f9574,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1455,f9572]) ).
fof(f9572,plain,
( spl0_1191
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1455,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9570,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1454,f9568]) ).
fof(f9568,plain,
( spl0_1190
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9566,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1418,f9564]) ).
fof(f1418,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9562,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1354,f9560]) ).
fof(f9560,plain,
( spl0_1188
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9558,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1353,f9556]) ).
fof(f9556,plain,
( spl0_1187
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9554,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1352,f9552]) ).
fof(f9552,plain,
( spl0_1186
<=> ! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1352,axiom,
! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9550,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1351,f9548]) ).
fof(f9548,plain,
( spl0_1185
<=> ! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1351,axiom,
! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9546,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1348,f9544]) ).
fof(f1348,axiom,
! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9541,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1345,f9539]) ).
fof(f1345,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9537,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1310,f9535]) ).
fof(f1310,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9533,plain,
( spl0_1181
| ~ spl0_91
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8281,f8058,f3702,f9531]) ).
fof(f9531,plain,
( spl0_1181
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f8058,plain,
( spl0_950
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f8281,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_91
| ~ spl0_950 ),
inference(resolution,[],[f8059,f3704]) ).
fof(f8059,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_950 ),
inference(avatar_component_clause,[],[f8058]) ).
fof(f9529,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1307,f9527]) ).
fof(f9527,plain,
( spl0_1180
<=> ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1307,axiom,
! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9525,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1236,f9523]) ).
fof(f9523,plain,
( spl0_1179
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9521,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1234,f9519]) ).
fof(f9519,plain,
( spl0_1178
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9517,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1178,f9515]) ).
fof(f1178,axiom,
! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9513,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1166,f9511]) ).
fof(f9511,plain,
( spl0_1176
<=> ! [X0,X1,X40] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9498,plain,
( spl0_1175
| ~ spl0_27
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8280,f8058,f3382,f9496]) ).
fof(f9496,plain,
( spl0_1175
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f8280,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_950 ),
inference(resolution,[],[f8059,f3384]) ).
fof(f9481,plain,
( spl0_1174
| ~ spl0_64
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8275,f8042,f3567,f9479]) ).
fof(f9479,plain,
( spl0_1174
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f3567,plain,
( spl0_64
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f8042,plain,
( spl0_946
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f8275,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_64
| ~ spl0_946 ),
inference(resolution,[],[f8043,f3569]) ).
fof(f3569,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f8043,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f8042]) ).
fof(f9464,plain,
( spl0_1173
| ~ spl0_15
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8274,f8042,f3322,f9462]) ).
fof(f9462,plain,
( spl0_1173
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f3322,plain,
( spl0_15
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f8274,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_946 ),
inference(resolution,[],[f8043,f3324]) ).
fof(f3324,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f3322]) ).
fof(f9422,plain,
( spl0_1172
| ~ spl0_64
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8270,f8038,f3567,f9420]) ).
fof(f8038,plain,
( spl0_945
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f8270,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_64
| ~ spl0_945 ),
inference(resolution,[],[f8039,f3569]) ).
fof(f8039,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f8038]) ).
fof(f9390,plain,
( spl0_1171
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1114 ),
inference(avatar_split_clause,[],[f9055,f9052,f8526,f3507,f9388]) ).
fof(f9052,plain,
( spl0_1114
<=> ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f9055,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1114 ),
inference(forward_demodulation,[],[f9053,f8847]) ).
fof(f9053,plain,
( ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint)
| ~ spl0_1114 ),
inference(avatar_component_clause,[],[f9052]) ).
fof(f9340,plain,
( spl0_1170
| spl0_677
| ~ spl0_1100 ),
inference(avatar_split_clause,[],[f9327,f8995,f6837,f9337]) ).
fof(f8995,plain,
( spl0_1100
<=> ! [X12,X1] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f9327,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_677
| ~ spl0_1100 ),
inference(resolution,[],[f8996,f6839]) ).
fof(f8996,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f8995]) ).
fof(f9283,plain,
( spl0_1169
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1162 ),
inference(avatar_split_clause,[],[f9252,f9247,f9069,f5916,f9280]) ).
fof(f9280,plain,
( spl0_1169
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f9252,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1118
| ~ spl0_1162 ),
inference(forward_demodulation,[],[f9251,f9070]) ).
fof(f9251,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1162 ),
inference(superposition,[],[f9248,f5918]) ).
fof(f9276,plain,
spl0_1168,
inference(avatar_split_clause,[],[f3198,f9274]) ).
fof(f9274,plain,
( spl0_1168
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f3198,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(inner_rewriting,[],[f3197]) ).
fof(f3197,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3196,f2115]) ).
fof(f3196,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2999,f2830]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1337,f2129]) ).
fof(f1337,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9272,plain,
spl0_1167,
inference(avatar_split_clause,[],[f3081,f9270]) ).
fof(f9270,plain,
( spl0_1167
<=> ! [X96,X90] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f3081,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
inference(forward_demodulation,[],[f3080,f3078]) ).
fof(f3080,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2896,f2831]) ).
fof(f2896,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2766,f2544]) ).
fof(f2766,axiom,
! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).
fof(f9268,plain,
spl0_1166,
inference(avatar_split_clause,[],[f3077,f9266]) ).
fof(f9266,plain,
( spl0_1166
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f3077,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2876,f2831]) ).
fof(f2876,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1210,f2544]) ).
fof(f1210,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9264,plain,
spl0_1165,
inference(avatar_split_clause,[],[f3076,f9262]) ).
fof(f9262,plain,
( spl0_1165
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f3076,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2875,f2831]) ).
fof(f2875,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1209,f2544]) ).
fof(f1209,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9260,plain,
spl0_1164,
inference(avatar_split_clause,[],[f2950,f9258]) ).
fof(f9258,plain,
( spl0_1164
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f2950,plain,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2279,f2544]) ).
fof(f2279,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9256,plain,
spl0_1163,
inference(avatar_split_clause,[],[f2940,f9254]) ).
fof(f9254,plain,
( spl0_1163
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f2940,plain,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2278,f2544]) ).
fof(f2278,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9249,plain,
( spl0_1162
| ~ spl0_1160 ),
inference(avatar_split_clause,[],[f9241,f9238,f9247]) ).
fof(f9238,plain,
( spl0_1160
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f9241,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1160 ),
inference(forward_demodulation,[],[f9239,f2867]) ).
fof(f9239,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1160 ),
inference(avatar_component_clause,[],[f9238]) ).
fof(f9245,plain,
( spl0_1161
| ~ spl0_15
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8269,f8038,f3322,f9243]) ).
fof(f8269,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_945 ),
inference(resolution,[],[f8039,f3324]) ).
fof(f9240,plain,
spl0_1160,
inference(avatar_split_clause,[],[f2858,f9238]) ).
fof(f2858,plain,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1388,f2544]) ).
fof(f1388,axiom,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9236,plain,
( spl0_1159
| ~ spl0_802
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9232,f9229,f7378,f9234]) ).
fof(f9234,plain,
( spl0_1159
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f9229,plain,
( spl0_1158
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f9232,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_802
| ~ spl0_1158 ),
inference(forward_demodulation,[],[f9230,f7379]) ).
fof(f9230,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f9229]) ).
fof(f9231,plain,
spl0_1158,
inference(avatar_split_clause,[],[f2832,f9229]) ).
fof(f2832,plain,
! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2709,f2716]) ).
fof(f2709,axiom,
! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f9227,plain,
spl0_1157,
inference(avatar_split_clause,[],[f2825,f9225]) ).
fof(f2825,axiom,
! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
fof(f9223,plain,
spl0_1156,
inference(avatar_split_clause,[],[f2759,f9221]) ).
fof(f9221,plain,
( spl0_1156
<=> ! [X89,X96,X97,X90] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2759,axiom,
! [X90,X89,X96,X97] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
fof(f9219,plain,
spl0_1155,
inference(avatar_split_clause,[],[f2758,f9217]) ).
fof(f9217,plain,
( spl0_1155
<=> ! [X96,X97,X90,X89] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f2758,axiom,
! [X90,X89,X96,X97] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
fof(f9215,plain,
spl0_1154,
inference(avatar_split_clause,[],[f2757,f9213]) ).
fof(f9213,plain,
( spl0_1154
<=> ! [X100,X101,X98,X99] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
fof(f9211,plain,
spl0_1153,
inference(avatar_split_clause,[],[f2756,f9209]) ).
fof(f9209,plain,
( spl0_1153
<=> ! [X101,X98,X100,X99] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
fof(f9207,plain,
spl0_1152,
inference(avatar_split_clause,[],[f2748,f9205]) ).
fof(f9205,plain,
( spl0_1152
<=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f9203,plain,
( spl0_1151
| ~ spl0_9
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f8268,f8034,f3292,f9201]) ).
fof(f9201,plain,
( spl0_1151
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f8034,plain,
( spl0_944
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f8268,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_944 ),
inference(resolution,[],[f8035,f3294]) ).
fof(f8035,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f8034]) ).
fof(f9199,plain,
spl0_1150,
inference(avatar_split_clause,[],[f2671,f9197]) ).
fof(f9197,plain,
( spl0_1150
<=> ! [X12,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f9195,plain,
spl0_1149,
inference(avatar_split_clause,[],[f2654,f9193]) ).
fof(f9193,plain,
( spl0_1149
<=> ! [X12,X1] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2654,axiom,
! [X1,X12] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f9191,plain,
spl0_1148,
inference(avatar_split_clause,[],[f2618,f9189]) ).
fof(f9189,plain,
( spl0_1148
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2618,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f9187,plain,
spl0_1147,
inference(avatar_split_clause,[],[f2615,f9185]) ).
fof(f9185,plain,
( spl0_1147
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2615,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f9183,plain,
spl0_1146,
inference(avatar_split_clause,[],[f2388,f9181]) ).
fof(f2388,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f9179,plain,
spl0_1145,
inference(avatar_split_clause,[],[f2383,f9177]) ).
fof(f2383,axiom,
! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f9175,plain,
spl0_1144,
inference(avatar_split_clause,[],[f2366,f9173]) ).
fof(f2366,axiom,
! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f9171,plain,
spl0_1143,
inference(avatar_split_clause,[],[f2364,f9169]) ).
fof(f2364,axiom,
! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f9167,plain,
spl0_1142,
inference(avatar_split_clause,[],[f2342,f9165]) ).
fof(f9165,plain,
( spl0_1142
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f9163,plain,
spl0_1141,
inference(avatar_split_clause,[],[f2341,f9161]) ).
fof(f2341,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f9159,plain,
( spl0_1140
| ~ spl0_9
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8267,f8030,f3292,f9157]) ).
fof(f9157,plain,
( spl0_1140
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f8030,plain,
( spl0_943
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f8267,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_943 ),
inference(resolution,[],[f8031,f3294]) ).
fof(f8031,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_943 ),
inference(avatar_component_clause,[],[f8030]) ).
fof(f9155,plain,
spl0_1139,
inference(avatar_split_clause,[],[f2294,f9153]) ).
fof(f9153,plain,
( spl0_1139
<=> ! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f9151,plain,
spl0_1138,
inference(avatar_split_clause,[],[f2281,f9149]) ).
fof(f9149,plain,
( spl0_1138
<=> ! [X0,X3] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2281,axiom,
! [X3,X0] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f9147,plain,
spl0_1137,
inference(avatar_split_clause,[],[f2247,f9145]) ).
fof(f2247,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f9143,plain,
spl0_1136,
inference(avatar_split_clause,[],[f2225,f9141]) ).
fof(f9141,plain,
( spl0_1136
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f2225,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f9139,plain,
spl0_1135,
inference(avatar_split_clause,[],[f2213,f9137]) ).
fof(f9137,plain,
( spl0_1135
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f2213,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f9135,plain,
spl0_1134,
inference(avatar_split_clause,[],[f2211,f9133]) ).
fof(f9133,plain,
( spl0_1134
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2211,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f9131,plain,
spl0_1133,
inference(avatar_split_clause,[],[f2197,f9129]) ).
fof(f2197,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f9127,plain,
spl0_1132,
inference(avatar_split_clause,[],[f2172,f9125]) ).
fof(f9125,plain,
( spl0_1132
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f2172,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f9123,plain,
spl0_1131,
inference(avatar_split_clause,[],[f2171,f9121]) ).
fof(f2171,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f9119,plain,
spl0_1130,
inference(avatar_split_clause,[],[f2039,f9117]) ).
fof(f2039,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f9115,plain,
( spl0_1129
| ~ spl0_4
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8265,f8026,f3267,f9113]) ).
fof(f9113,plain,
( spl0_1129
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3267,plain,
( spl0_4
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f8026,plain,
( spl0_942
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8265,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_4
| ~ spl0_942 ),
inference(resolution,[],[f8027,f3269]) ).
fof(f3269,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3267]) ).
fof(f8027,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f8026]) ).
fof(f9111,plain,
spl0_1128,
inference(avatar_split_clause,[],[f2038,f9109]) ).
fof(f2038,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f9107,plain,
spl0_1127,
inference(avatar_split_clause,[],[f1849,f9105]) ).
fof(f1849,axiom,
! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f9103,plain,
spl0_1126,
inference(avatar_split_clause,[],[f1848,f9101]) ).
fof(f9101,plain,
( spl0_1126
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1848,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
fof(f9099,plain,
spl0_1125,
inference(avatar_split_clause,[],[f1803,f9097]) ).
fof(f9097,plain,
( spl0_1125
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1803,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f9095,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1759,f9093]) ).
fof(f9093,plain,
( spl0_1124
<=> ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f1759,axiom,
! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f9091,plain,
spl0_1123,
inference(avatar_split_clause,[],[f1730,f9089]) ).
fof(f1730,axiom,
! [X1,X25,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f9087,plain,
spl0_1122,
inference(avatar_split_clause,[],[f1603,f9085]) ).
fof(f1603,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f9083,plain,
spl0_1121,
inference(avatar_split_clause,[],[f1548,f9081]) ).
fof(f9081,plain,
( spl0_1121
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f9079,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1541,f9077]) ).
fof(f9077,plain,
( spl0_1120
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f9075,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1540,f9073]) ).
fof(f9073,plain,
( spl0_1119
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f9071,plain,
( spl0_1118
| ~ spl0_4
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8263,f8022,f3267,f9069]) ).
fof(f8022,plain,
( spl0_941
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f8263,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_4
| ~ spl0_941 ),
inference(resolution,[],[f8023,f3269]) ).
fof(f8023,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_941 ),
inference(avatar_component_clause,[],[f8022]) ).
fof(f9067,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1509,f9065]) ).
fof(f9065,plain,
( spl0_1117
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f9063,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1488,f9061]) ).
fof(f9061,plain,
( spl0_1116
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1488,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f9059,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1487,f9057]) ).
fof(f1487,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f9054,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1467,f9052]) ).
fof(f1467,axiom,
! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f9050,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1440,f9048]) ).
fof(f1440,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f9046,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1439,f9044]) ).
fof(f1439,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f9042,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1430,f9040]) ).
fof(f1430,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f9038,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1429,f9036]) ).
fof(f1429,axiom,
! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f9034,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1428,f9032]) ).
fof(f1428,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f9030,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1427,f9028]) ).
fof(f1427,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f9026,plain,
( spl0_1107
| ~ spl0_708
| ~ spl0_882
| ~ spl0_937 ),
inference(avatar_split_clause,[],[f8252,f8006,f7711,f6979,f9023]) ).
fof(f9023,plain,
( spl0_1107
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f8252,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_708
| ~ spl0_882
| ~ spl0_937 ),
inference(forward_demodulation,[],[f8250,f6981]) ).
fof(f8250,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_882
| ~ spl0_937 ),
inference(superposition,[],[f8007,f7713]) ).
fof(f9021,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1426,f9019]) ).
fof(f1426,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f9017,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1425,f9015]) ).
fof(f1425,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f9013,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1407,f9011]) ).
fof(f1407,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f9009,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1395,f9007]) ).
fof(f9007,plain,
( spl0_1103
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1395,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f9005,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1390,f9003]) ).
fof(f9003,plain,
( spl0_1102
<=> ! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1390,axiom,
! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f9001,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1389,f8999]) ).
fof(f1389,axiom,
! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8997,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1279,f8995]) ).
fof(f1279,axiom,
! [X1,X12] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8993,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1275,f8991]) ).
fof(f1275,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8989,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1265,f8987]) ).
fof(f1265,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8985,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1235,f8983]) ).
fof(f1235,axiom,
! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8981,plain,
( spl0_1096
| ~ spl0_82
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8226,f7929,f3657,f8979]) ).
fof(f8979,plain,
( spl0_1096
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f3657,plain,
( spl0_82
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f7929,plain,
( spl0_918
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8226,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_82
| ~ spl0_918 ),
inference(resolution,[],[f7930,f3659]) ).
fof(f3659,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f3657]) ).
fof(f7930,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7929]) ).
fof(f8977,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1224,f8975]) ).
fof(f1224,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8973,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1216,f8971]) ).
fof(f1216,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8969,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1201,f8967]) ).
fof(f8967,plain,
( spl0_1093
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1201,axiom,
! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f8965,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1200,f8963]) ).
fof(f8963,plain,
( spl0_1092
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1200,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f8961,plain,
spl0_1091,
inference(avatar_split_clause,[],[f1186,f8959]) ).
fof(f8959,plain,
( spl0_1091
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1186,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f8957,plain,
spl0_1090,
inference(avatar_split_clause,[],[f1180,f8955]) ).
fof(f8955,plain,
( spl0_1090
<=> ! [X2,X27,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f1180,axiom,
! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8953,plain,
spl0_1089,
inference(avatar_split_clause,[],[f1179,f8951]) ).
fof(f8951,plain,
( spl0_1089
<=> ! [X2,X1,X18] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1179,axiom,
! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8949,plain,
spl0_1088,
inference(avatar_split_clause,[],[f1175,f8947]) ).
fof(f8947,plain,
( spl0_1088
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8945,plain,
spl0_1087,
inference(avatar_split_clause,[],[f1170,f8943]) ).
fof(f8943,plain,
( spl0_1087
<=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8941,plain,
spl0_1086,
inference(avatar_split_clause,[],[f1169,f8939]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8936,plain,
spl0_1085,
inference(avatar_split_clause,[],[f1168,f8934]) ).
fof(f1168,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8932,plain,
spl0_1084,
inference(avatar_split_clause,[],[f105,f8930]) ).
fof(f105,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8928,plain,
spl0_1083,
inference(avatar_split_clause,[],[f103,f8926]) ).
fof(f8926,plain,
( spl0_1083
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8924,plain,
spl0_1082,
inference(avatar_split_clause,[],[f102,f8922]) ).
fof(f8922,plain,
( spl0_1082
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8891,plain,
( spl0_1081
| ~ spl0_804
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f8869,f8586,f7386,f8889]) ).
fof(f8889,plain,
( spl0_1081
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f8869,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_804
| ~ spl0_1049 ),
inference(superposition,[],[f7387,f8587]) ).
fof(f8866,plain,
( spl0_1080
| ~ spl0_886
| ~ spl0_1030 ),
inference(avatar_split_clause,[],[f8830,f8509,f7740,f8864]) ).
fof(f8864,plain,
( spl0_1080
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f7740,plain,
( spl0_886
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f8830,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_886
| ~ spl0_1030 ),
inference(resolution,[],[f8510,f7741]) ).
fof(f7741,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_886 ),
inference(avatar_component_clause,[],[f7740]) ).
fof(f8820,plain,
( spl0_1079
| ~ spl0_804
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f8814,f8477,f7386,f8818]) ).
fof(f8818,plain,
( spl0_1079
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f8814,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_804
| ~ spl0_1022 ),
inference(superposition,[],[f7387,f8478]) ).
fof(f8802,plain,
( spl0_1078
| ~ spl0_24
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8225,f7929,f3367,f8800]) ).
fof(f8800,plain,
( spl0_1078
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f3367,plain,
( spl0_24
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f8225,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_24
| ~ spl0_918 ),
inference(resolution,[],[f7930,f3369]) ).
fof(f3369,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f3367]) ).
fof(f8774,plain,
( spl0_1077
| ~ spl0_89
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8224,f7925,f3692,f8772]) ).
fof(f8772,plain,
( spl0_1077
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f3692,plain,
( spl0_89
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f7925,plain,
( spl0_917
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8224,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_89
| ~ spl0_917 ),
inference(resolution,[],[f7926,f3694]) ).
fof(f3694,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f3692]) ).
fof(f7926,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7925]) ).
fof(f8725,plain,
( spl0_1076
| ~ spl0_25
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8223,f7925,f3372,f8723]) ).
fof(f8723,plain,
( spl0_1076
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f3372,plain,
( spl0_25
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f8223,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_25
| ~ spl0_917 ),
inference(resolution,[],[f7926,f3374]) ).
fof(f3374,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f3372]) ).
fof(f8692,plain,
spl0_1075,
inference(avatar_split_clause,[],[f3149,f8690]) ).
fof(f3149,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2971,f2831]) ).
fof(f2971,plain,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1346,f2544]) ).
fof(f1346,axiom,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8688,plain,
spl0_1074,
inference(avatar_split_clause,[],[f3142,f8686]) ).
fof(f3142,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2958,f2831]) ).
fof(f2958,plain,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1347,f2544]) ).
fof(f1347,axiom,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8684,plain,
spl0_1073,
inference(avatar_split_clause,[],[f3134,f8682]) ).
fof(f8682,plain,
( spl0_1073
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f3134,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f2947,f2831]) ).
fof(f2947,plain,
! [X21,X15] :
( c_1 = X15
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2092,f2544]) ).
fof(f2092,axiom,
! [X21,X15] :
( c_1 = X15
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f8680,plain,
spl0_1072,
inference(avatar_split_clause,[],[f3132,f8678]) ).
fof(f8678,plain,
( spl0_1072
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f3132,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f2945,f2831]) ).
fof(f2945,plain,
! [X21,X15] :
( c_1 = X21
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2063,f2544]) ).
fof(f2063,axiom,
! [X21,X15] :
( c_1 = X21
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
fof(f8676,plain,
spl0_1071,
inference(avatar_split_clause,[],[f2862,f8674]) ).
fof(f2862,plain,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f2132,f2113]) ).
fof(f2132,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8672,plain,
spl0_1070,
inference(avatar_split_clause,[],[f2851,f8670]) ).
fof(f2851,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2603,f2373]) ).
fof(f2603,axiom,
! [X3,X1] : c_inter(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8668,plain,
spl0_1069,
inference(avatar_split_clause,[],[f2850,f8666]) ).
fof(f2850,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2601,f2373]) ).
fof(f2601,axiom,
! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8664,plain,
spl0_1068,
inference(avatar_split_clause,[],[f2849,f8662]) ).
fof(f2849,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3,
inference(definition_unfolding,[],[f2602,f2373]) ).
fof(f2602,axiom,
! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8660,plain,
spl0_1067,
inference(avatar_split_clause,[],[f2843,f8658]) ).
fof(f8658,plain,
( spl0_1067
<=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f2843,plain,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1160,f2544]) ).
fof(f1160,axiom,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8656,plain,
spl0_1066,
inference(avatar_split_clause,[],[f2818,f8654]) ).
fof(f8654,plain,
( spl0_1066
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f2818,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
fof(f8652,plain,
spl0_1065,
inference(avatar_split_clause,[],[f2787,f8650]) ).
fof(f8650,plain,
( spl0_1065
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2787,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
fof(f8648,plain,
( ~ spl0_74
| spl0_1064
| ~ spl0_675
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f8222,f7917,f6829,f8646,f3617]) ).
fof(f3617,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f7917,plain,
( spl0_915
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8222,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_675
| ~ spl0_915 ),
inference(superposition,[],[f7918,f6830]) ).
fof(f7918,plain,
( ! [X21,X1] :
( c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) )
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f7917]) ).
fof(f8644,plain,
spl0_1063,
inference(avatar_split_clause,[],[f2767,f8642]) ).
fof(f2767,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
fof(f8640,plain,
spl0_1062,
inference(avatar_split_clause,[],[f2750,f8638]) ).
fof(f8638,plain,
( spl0_1062
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f2750,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
fof(f8636,plain,
spl0_1061,
inference(avatar_split_clause,[],[f2749,f8634]) ).
fof(f8634,plain,
( spl0_1061
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f2749,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
fof(f8632,plain,
spl0_1060,
inference(avatar_split_clause,[],[f2747,f8630]) ).
fof(f8630,plain,
( spl0_1060
<=> ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f2747,axiom,
! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
fof(f8628,plain,
spl0_1059,
inference(avatar_split_clause,[],[f2746,f8626]) ).
fof(f8626,plain,
( spl0_1059
<=> ! [X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f2746,axiom,
! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
fof(f8624,plain,
spl0_1058,
inference(avatar_split_clause,[],[f2744,f8622]) ).
fof(f8622,plain,
( spl0_1058
<=> ! [X12,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f2744,axiom,
! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
fof(f8620,plain,
spl0_1057,
inference(avatar_split_clause,[],[f2718,f8618]) ).
fof(f8618,plain,
( spl0_1057
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f2718,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8616,plain,
spl0_1056,
inference(avatar_split_clause,[],[f2717,f8614]) ).
fof(f8614,plain,
( spl0_1056
<=> ! [X5,X1] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f2717,axiom,
! [X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8612,plain,
spl0_1055,
inference(avatar_split_clause,[],[f2702,f8610]) ).
fof(f8610,plain,
( spl0_1055
<=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f2702,axiom,
! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).
fof(f8608,plain,
spl0_1054,
inference(avatar_split_clause,[],[f2667,f8606]) ).
fof(f8606,plain,
( spl0_1054
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f2667,axiom,
! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8604,plain,
( spl0_1053
| ~ spl0_825
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7759,f7554,f7482,f8602]) ).
fof(f8602,plain,
( spl0_1053
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f7759,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_825
| ~ spl0_843 ),
inference(resolution,[],[f7555,f7483]) ).
fof(f8600,plain,
spl0_1052,
inference(avatar_split_clause,[],[f2659,f8598]) ).
fof(f2659,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8596,plain,
spl0_1051,
inference(avatar_split_clause,[],[f2636,f8594]) ).
fof(f2636,axiom,
! [X1,X12,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8592,plain,
spl0_1050,
inference(avatar_split_clause,[],[f2635,f8590]) ).
fof(f2635,axiom,
! [X1,X12,X13] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8588,plain,
spl0_1049,
inference(avatar_split_clause,[],[f2626,f8586]) ).
fof(f2626,axiom,
! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8584,plain,
spl0_1048,
inference(avatar_split_clause,[],[f2390,f8582]) ).
fof(f8582,plain,
( spl0_1048
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f2390,axiom,
! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8580,plain,
spl0_1047,
inference(avatar_split_clause,[],[f2389,f8578]) ).
fof(f8578,plain,
( spl0_1047
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f2389,axiom,
! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8576,plain,
spl0_1046,
inference(avatar_split_clause,[],[f2382,f8574]) ).
fof(f8574,plain,
( spl0_1046
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f2382,axiom,
! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8572,plain,
spl0_1045,
inference(avatar_split_clause,[],[f2298,f8570]) ).
fof(f8570,plain,
( spl0_1045
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f2298,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8568,plain,
spl0_1044,
inference(avatar_split_clause,[],[f2297,f8566]) ).
fof(f8566,plain,
( spl0_1044
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2297,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8564,plain,
spl0_1043,
inference(avatar_split_clause,[],[f2293,f8562]) ).
fof(f8562,plain,
( spl0_1043
<=> ! [X0,X21] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2293,axiom,
! [X21,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8560,plain,
( spl0_1042
| ~ spl0_824
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7758,f7554,f7478,f8558]) ).
fof(f8558,plain,
( spl0_1042
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f7758,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_824
| ~ spl0_843 ),
inference(resolution,[],[f7555,f7479]) ).
fof(f8556,plain,
spl0_1041,
inference(avatar_split_clause,[],[f2285,f8554]) ).
fof(f8554,plain,
( spl0_1041
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f2285,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8552,plain,
spl0_1040,
inference(avatar_split_clause,[],[f2284,f8550]) ).
fof(f8550,plain,
( spl0_1040
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f2284,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8548,plain,
spl0_1039,
inference(avatar_split_clause,[],[f2280,f8546]) ).
fof(f2280,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8544,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2216,f8542]) ).
fof(f2216,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8540,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2154,f8538]) ).
fof(f8536,plain,
spl0_1036,
inference(avatar_split_clause,[],[f2150,f8534]) ).
fof(f8534,plain,
( spl0_1036
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2150,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8532,plain,
spl0_1035,
inference(avatar_split_clause,[],[f2136,f8530]) ).
fof(f2136,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8528,plain,
spl0_1034,
inference(avatar_split_clause,[],[f2118,f8526]) ).
fof(f2118,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8524,plain,
spl0_1033,
inference(avatar_split_clause,[],[f2032,f8522]) ).
fof(f2032,axiom,
! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8520,plain,
spl0_1032,
inference(avatar_split_clause,[],[f2031,f8518]) ).
fof(f8518,plain,
( spl0_1032
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f2031,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8516,plain,
( spl0_1031
| ~ spl0_640
| ~ spl0_840 ),
inference(avatar_split_clause,[],[f7751,f7542,f5911,f8513]) ).
fof(f7542,plain,
( spl0_840
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f7751,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_640
| ~ spl0_840 ),
inference(superposition,[],[f7543,f5913]) ).
fof(f7543,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f7542]) ).
fof(f8511,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1786,f8509]) ).
fof(f1786,axiom,
! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8507,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1758,f8505]) ).
fof(f1758,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8503,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1757,f8501]) ).
fof(f1757,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8499,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1754,f8497]) ).
fof(f1754,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8495,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1744,f8493]) ).
fof(f8493,plain,
( spl0_1026
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1744,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8491,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1740,f8489]) ).
fof(f8489,plain,
( spl0_1025
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1740,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8487,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1720,f8485]) ).
fof(f8485,plain,
( spl0_1024
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1720,axiom,
! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8483,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1692,f8481]) ).
fof(f8481,plain,
( spl0_1023
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1692,axiom,
! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8479,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1639,f8477]) ).
fof(f8475,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1607,f8473]) ).
fof(f1607,axiom,
! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8471,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1597,f8469]) ).
fof(f1597,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8467,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1565,f8465]) ).
fof(f8465,plain,
( spl0_1019
<=> ! [X1,X23,X58] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1565,axiom,
! [X58,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8463,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1564,f8461]) ).
fof(f8461,plain,
( spl0_1018
<=> ! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1564,axiom,
! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8459,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1563,f8457]) ).
fof(f8457,plain,
( spl0_1017
<=> ! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1563,axiom,
! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8455,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1560,f8453]) ).
fof(f8453,plain,
( spl0_1016
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1560,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8451,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1559,f8449]) ).
fof(f8449,plain,
( spl0_1015
<=> ! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1559,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8447,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1556,f8445]) ).
fof(f8445,plain,
( spl0_1014
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1556,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8443,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1555,f8441]) ).
fof(f8441,plain,
( spl0_1013
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1555,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8439,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1553,f8437]) ).
fof(f8437,plain,
( spl0_1012
<=> ! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1553,axiom,
! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8435,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1533,f8433]) ).
fof(f8433,plain,
( spl0_1011
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1533,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8431,plain,
( ~ spl0_52
| spl0_1010
| ~ spl0_858
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8292,f8148,f7614,f8428,f3507]) ).
fof(f8428,plain,
( spl0_1010
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f7614,plain,
( spl0_858
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f8148,plain,
( spl0_972
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8292,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_858
| ~ spl0_972 ),
inference(superposition,[],[f7615,f8150]) ).
fof(f8150,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8148]) ).
fof(f7615,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7614]) ).
fof(f8426,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1528,f8424]) ).
fof(f1528,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f8422,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1527,f8420]) ).
fof(f8420,plain,
( spl0_1008
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1527,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8418,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1497,f8416]) ).
fof(f8416,plain,
( spl0_1007
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1497,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8414,plain,
spl0_1006,
inference(avatar_split_clause,[],[f1496,f8412]) ).
fof(f8412,plain,
( spl0_1006
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f1496,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8410,plain,
spl0_1005,
inference(avatar_split_clause,[],[f1483,f8408]) ).
fof(f1483,axiom,
! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8406,plain,
spl0_1004,
inference(avatar_split_clause,[],[f1471,f8404]) ).
fof(f8404,plain,
( spl0_1004
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1471,axiom,
! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8402,plain,
spl0_1003,
inference(avatar_split_clause,[],[f1441,f8400]) ).
fof(f1441,axiom,
! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8398,plain,
spl0_1002,
inference(avatar_split_clause,[],[f1423,f8396]) ).
fof(f8396,plain,
( spl0_1002
<=> ! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1423,axiom,
! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8394,plain,
spl0_1001,
inference(avatar_split_clause,[],[f1422,f8392]) ).
fof(f1422,axiom,
! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8390,plain,
spl0_1000,
inference(avatar_split_clause,[],[f1421,f8388]) ).
fof(f8388,plain,
( spl0_1000
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1421,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8386,plain,
spl0_999,
inference(avatar_split_clause,[],[f1420,f8384]) ).
fof(f8384,plain,
( spl0_999
<=> ! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f1420,axiom,
! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8382,plain,
spl0_998,
inference(avatar_split_clause,[],[f1380,f8380]) ).
fof(f1380,axiom,
! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8378,plain,
spl0_997,
inference(avatar_split_clause,[],[f1379,f8376]) ).
fof(f1379,axiom,
! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8374,plain,
spl0_996,
inference(avatar_split_clause,[],[f1349,f8372]) ).
fof(f1349,axiom,
! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8370,plain,
spl0_995,
inference(avatar_split_clause,[],[f1246,f8368]) ).
fof(f8368,plain,
( spl0_995
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1246,axiom,
! [X1,X5,X12] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8366,plain,
spl0_994,
inference(avatar_split_clause,[],[f1242,f8364]) ).
fof(f8364,plain,
( spl0_994
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f1242,axiom,
! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8362,plain,
spl0_993,
inference(avatar_split_clause,[],[f1240,f8360]) ).
fof(f8360,plain,
( spl0_993
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1240,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8358,plain,
spl0_992,
inference(avatar_split_clause,[],[f1238,f8356]) ).
fof(f8356,plain,
( spl0_992
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f1238,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8354,plain,
spl0_991,
inference(avatar_split_clause,[],[f1195,f8352]) ).
fof(f8352,plain,
( spl0_991
<=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f1195,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f8350,plain,
spl0_990,
inference(avatar_split_clause,[],[f1190,f8348]) ).
fof(f8348,plain,
( spl0_990
<=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f1190,axiom,
! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8346,plain,
( ~ spl0_989
| ~ spl0_804
| ~ spl0_967 ),
inference(avatar_split_clause,[],[f8308,f8127,f7386,f8343]) ).
fof(f8343,plain,
( spl0_989
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f8308,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_804
| ~ spl0_967 ),
inference(superposition,[],[f7387,f8129]) ).
fof(f8341,plain,
spl0_988,
inference(avatar_split_clause,[],[f63,f8339]) ).
fof(f8339,plain,
( spl0_988
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f63,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8337,plain,
spl0_987,
inference(avatar_split_clause,[],[f62,f8335]) ).
fof(f8335,plain,
( spl0_987
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f62,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8333,plain,
spl0_986,
inference(avatar_split_clause,[],[f35,f8331]) ).
fof(f35,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8329,plain,
spl0_985,
inference(avatar_split_clause,[],[f34,f8327]) ).
fof(f34,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8206,plain,
( spl0_984
| ~ spl0_40
| ~ spl0_868 ),
inference(avatar_split_clause,[],[f7798,f7654,f3447,f8203]) ).
fof(f8203,plain,
( spl0_984
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f7654,plain,
( spl0_868
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f7798,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_40
| ~ spl0_868 ),
inference(resolution,[],[f7655,f3449]) ).
fof(f3449,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f3447]) ).
fof(f7655,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_868 ),
inference(avatar_component_clause,[],[f7654]) ).
fof(f8196,plain,
( spl0_983
| ~ spl0_40
| ~ spl0_867 ),
inference(avatar_split_clause,[],[f7797,f7650,f3447,f8193]) ).
fof(f8193,plain,
( spl0_983
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f7650,plain,
( spl0_867
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f7797,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_40
| ~ spl0_867 ),
inference(resolution,[],[f7651,f3449]) ).
fof(f7651,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7650]) ).
fof(f8191,plain,
spl0_982,
inference(avatar_split_clause,[],[f3121,f8189]) ).
fof(f3121,plain,
! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2170,f2156]) ).
fof(f2170,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8187,plain,
spl0_981,
inference(avatar_split_clause,[],[f3069,f8185]) ).
fof(f8185,plain,
( spl0_981
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f3069,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2866,f2831]) ).
fof(f2866,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X15,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1300,f2544]) ).
fof(f1300,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8183,plain,
spl0_980,
inference(avatar_split_clause,[],[f3068,f8181]) ).
fof(f3068,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2865,f2831]) ).
fof(f2865,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1299,f2544]) ).
fof(f1299,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8179,plain,
spl0_979,
inference(avatar_split_clause,[],[f2837,f8177]) ).
fof(f2837,plain,
! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f67,f2544]) ).
fof(f67,axiom,
! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8175,plain,
spl0_978,
inference(avatar_split_clause,[],[f2835,f8173]) ).
fof(f2835,plain,
! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f65,f2544]) ).
fof(f65,axiom,
! [X21] : c_less(X21,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8171,plain,
spl0_977,
inference(avatar_split_clause,[],[f2755,f8169]) ).
fof(f8169,plain,
( spl0_977
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f2755,axiom,
! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
fof(f8167,plain,
spl0_976,
inference(avatar_split_clause,[],[f2754,f8165]) ).
fof(f8165,plain,
( spl0_976
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2754,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
fof(f8163,plain,
spl0_975,
inference(avatar_split_clause,[],[f2753,f8161]) ).
fof(f8161,plain,
( spl0_975
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2753,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
fof(f8159,plain,
spl0_974,
inference(avatar_split_clause,[],[f2752,f8157]) ).
fof(f8157,plain,
( spl0_974
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2752,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
fof(f8155,plain,
spl0_973,
inference(avatar_split_clause,[],[f2751,f8153]) ).
fof(f8153,plain,
( spl0_973
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2751,axiom,
! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
fof(f8151,plain,
( spl0_972
| ~ spl0_52
| ~ spl0_864 ),
inference(avatar_split_clause,[],[f7794,f7638,f3507,f8148]) ).
fof(f7638,plain,
( spl0_864
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f7794,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_864 ),
inference(resolution,[],[f7639,f3509]) ).
fof(f7639,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_864 ),
inference(avatar_component_clause,[],[f7638]) ).
fof(f8146,plain,
spl0_971,
inference(avatar_split_clause,[],[f2741,f8144]) ).
fof(f2741,axiom,
! [X91,X92] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
fof(f8142,plain,
spl0_970,
inference(avatar_split_clause,[],[f2736,f8140]) ).
fof(f8140,plain,
( spl0_970
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2736,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
fof(f8138,plain,
spl0_969,
inference(avatar_split_clause,[],[f2699,f8136]) ).
fof(f8136,plain,
( spl0_969
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2699,axiom,
! [X1,X12] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f8134,plain,
spl0_968,
inference(avatar_split_clause,[],[f2660,f8132]) ).
fof(f2660,axiom,
! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f8130,plain,
spl0_967,
inference(avatar_split_clause,[],[f2534,f8127]) ).
fof(f2534,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f8125,plain,
spl0_966,
inference(avatar_split_clause,[],[f2492,f8123]) ).
fof(f8123,plain,
( spl0_966
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2492,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f8121,plain,
spl0_965,
inference(avatar_split_clause,[],[f2491,f8119]) ).
fof(f8119,plain,
( spl0_965
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2491,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f8117,plain,
spl0_964,
inference(avatar_split_clause,[],[f2474,f8115]) ).
fof(f8115,plain,
( spl0_964
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2474,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f8113,plain,
spl0_963,
inference(avatar_split_clause,[],[f2473,f8111]) ).
fof(f8111,plain,
( spl0_963
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2473,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f8109,plain,
spl0_962,
inference(avatar_split_clause,[],[f2470,f8107]) ).
fof(f8107,plain,
( spl0_962
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2470,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f8104,plain,
spl0_961,
inference(avatar_split_clause,[],[f2469,f8102]) ).
fof(f8102,plain,
( spl0_961
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2469,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f8100,plain,
spl0_960,
inference(avatar_split_clause,[],[f2379,f8098]) ).
fof(f8098,plain,
( spl0_960
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2379,axiom,
! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f8096,plain,
spl0_959,
inference(avatar_split_clause,[],[f2377,f8094]) ).
fof(f8094,plain,
( spl0_959
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2377,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f8092,plain,
spl0_958,
inference(avatar_split_clause,[],[f2371,f8090]) ).
fof(f8090,plain,
( spl0_958
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2371,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f8088,plain,
spl0_957,
inference(avatar_split_clause,[],[f2369,f8086]) ).
fof(f8086,plain,
( spl0_957
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2369,axiom,
! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f8084,plain,
spl0_956,
inference(avatar_split_clause,[],[f2357,f8082]) ).
fof(f8082,plain,
( spl0_956
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2357,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f8080,plain,
spl0_955,
inference(avatar_split_clause,[],[f2354,f8078]) ).
fof(f2354,axiom,
! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f8076,plain,
spl0_954,
inference(avatar_split_clause,[],[f2353,f8074]) ).
fof(f2353,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f8072,plain,
spl0_953,
inference(avatar_split_clause,[],[f2292,f8070]) ).
fof(f8070,plain,
( spl0_953
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2292,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f8068,plain,
spl0_952,
inference(avatar_split_clause,[],[f2291,f8066]) ).
fof(f8066,plain,
( spl0_952
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2291,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f8064,plain,
spl0_951,
inference(avatar_split_clause,[],[f2267,f8062]) ).
fof(f2267,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f8060,plain,
spl0_950,
inference(avatar_split_clause,[],[f2262,f8058]) ).
fof(f2262,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f8056,plain,
spl0_949,
inference(avatar_split_clause,[],[f2251,f8054]) ).
fof(f8054,plain,
( spl0_949
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2251,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f8052,plain,
spl0_948,
inference(avatar_split_clause,[],[f2250,f8050]) ).
fof(f2250,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f8048,plain,
spl0_947,
inference(avatar_split_clause,[],[f2241,f8046]) ).
fof(f2241,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f8044,plain,
spl0_946,
inference(avatar_split_clause,[],[f2218,f8042]) ).
fof(f2218,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f8040,plain,
spl0_945,
inference(avatar_split_clause,[],[f2217,f8038]) ).
fof(f2217,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f8036,plain,
spl0_944,
inference(avatar_split_clause,[],[f2205,f8034]) ).
fof(f2205,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f8032,plain,
spl0_943,
inference(avatar_split_clause,[],[f2198,f8030]) ).
fof(f2198,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f8028,plain,
spl0_942,
inference(avatar_split_clause,[],[f2196,f8026]) ).
fof(f2196,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f8024,plain,
spl0_941,
inference(avatar_split_clause,[],[f2185,f8022]) ).
fof(f2185,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f8020,plain,
spl0_940,
inference(avatar_split_clause,[],[f2182,f8018]) ).
fof(f8018,plain,
( spl0_940
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f2182,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f8016,plain,
spl0_939,
inference(avatar_split_clause,[],[f2180,f8014]) ).
fof(f8014,plain,
( spl0_939
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f2180,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f8012,plain,
spl0_938,
inference(avatar_split_clause,[],[f2177,f8010]) ).
fof(f8010,plain,
( spl0_938
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f2177,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f8008,plain,
spl0_937,
inference(avatar_split_clause,[],[f2153,f8006]) ).
fof(f2153,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f8004,plain,
spl0_936,
inference(avatar_split_clause,[],[f1865,f8002]) ).
fof(f1865,axiom,
! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f8000,plain,
spl0_935,
inference(avatar_split_clause,[],[f1818,f7998]) ).
fof(f7998,plain,
( spl0_935
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1818,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7996,plain,
spl0_934,
inference(avatar_split_clause,[],[f1815,f7994]) ).
fof(f1815,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7992,plain,
spl0_933,
inference(avatar_split_clause,[],[f1805,f7990]) ).
fof(f7990,plain,
( spl0_933
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1805,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7988,plain,
spl0_932,
inference(avatar_split_clause,[],[f1779,f7986]) ).
fof(f7986,plain,
( spl0_932
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1779,axiom,
! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7984,plain,
( ~ spl0_930
| spl0_931
| ~ spl0_707
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f7788,f7614,f6974,f7981,f7977]) ).
fof(f7977,plain,
( spl0_930
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f7981,plain,
( spl0_931
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f7788,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_707
| ~ spl0_858 ),
inference(superposition,[],[f7615,f6976]) ).
fof(f7975,plain,
spl0_929,
inference(avatar_split_clause,[],[f1750,f7973]) ).
fof(f1750,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7971,plain,
spl0_928,
inference(avatar_split_clause,[],[f1735,f7969]) ).
fof(f7969,plain,
( spl0_928
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1735,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7967,plain,
spl0_927,
inference(avatar_split_clause,[],[f1717,f7965]) ).
fof(f7965,plain,
( spl0_927
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1717,axiom,
! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f7963,plain,
spl0_926,
inference(avatar_split_clause,[],[f1588,f7961]) ).
fof(f7961,plain,
( spl0_926
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1588,axiom,
! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7959,plain,
spl0_925,
inference(avatar_split_clause,[],[f1579,f7957]) ).
fof(f7957,plain,
( spl0_925
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f1579,axiom,
! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7955,plain,
spl0_924,
inference(avatar_split_clause,[],[f1562,f7953]) ).
fof(f7953,plain,
( spl0_924
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1562,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7951,plain,
spl0_923,
inference(avatar_split_clause,[],[f1561,f7949]) ).
fof(f7949,plain,
( spl0_923
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1561,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7947,plain,
spl0_922,
inference(avatar_split_clause,[],[f1550,f7945]) ).
fof(f7945,plain,
( spl0_922
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1550,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7943,plain,
spl0_921,
inference(avatar_split_clause,[],[f1549,f7941]) ).
fof(f7941,plain,
( spl0_921
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1549,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7939,plain,
spl0_920,
inference(avatar_split_clause,[],[f1537,f7937]) ).
fof(f7937,plain,
( spl0_920
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1537,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7935,plain,
spl0_919,
inference(avatar_split_clause,[],[f1513,f7933]) ).
fof(f1513,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7931,plain,
spl0_918,
inference(avatar_split_clause,[],[f1499,f7929]) ).
fof(f1499,axiom,
! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7927,plain,
spl0_917,
inference(avatar_split_clause,[],[f1498,f7925]) ).
fof(f1498,axiom,
! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7923,plain,
spl0_916,
inference(avatar_split_clause,[],[f1490,f7921]) ).
fof(f1490,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7919,plain,
spl0_915,
inference(avatar_split_clause,[],[f1419,f7917]) ).
fof(f1419,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7915,plain,
spl0_914,
inference(avatar_split_clause,[],[f1392,f7913]) ).
fof(f1392,axiom,
! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7911,plain,
spl0_913,
inference(avatar_split_clause,[],[f1385,f7909]) ).
fof(f1385,axiom,
! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7907,plain,
spl0_912,
inference(avatar_split_clause,[],[f1376,f7905]) ).
fof(f7905,plain,
( spl0_912
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1376,axiom,
! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7903,plain,
spl0_911,
inference(avatar_split_clause,[],[f1375,f7901]) ).
fof(f1375,axiom,
! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7899,plain,
spl0_910,
inference(avatar_split_clause,[],[f1308,f7897]) ).
fof(f7897,plain,
( spl0_910
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1308,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7895,plain,
( spl0_909
| ~ spl0_21
| ~ spl0_851 ),
inference(avatar_split_clause,[],[f7763,f7586,f3352,f7892]) ).
fof(f7892,plain,
( spl0_909
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f3352,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f7586,plain,
( spl0_851
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f7763,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_21
| ~ spl0_851 ),
inference(resolution,[],[f7587,f3354]) ).
fof(f3354,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f3352]) ).
fof(f7587,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_851 ),
inference(avatar_component_clause,[],[f7586]) ).
fof(f7890,plain,
spl0_908,
inference(avatar_split_clause,[],[f1298,f7888]) ).
fof(f7888,plain,
( spl0_908
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1298,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7886,plain,
spl0_907,
inference(avatar_split_clause,[],[f1297,f7884]) ).
fof(f7884,plain,
( spl0_907
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1297,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7882,plain,
spl0_906,
inference(avatar_split_clause,[],[f1177,f7880]) ).
fof(f1177,axiom,
! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7878,plain,
spl0_905,
inference(avatar_split_clause,[],[f1171,f7876]) ).
fof(f7876,plain,
( spl0_905
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1171,axiom,
! [X40,X1] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7873,plain,
spl0_904,
inference(avatar_split_clause,[],[f1167,f7871]) ).
fof(f7871,plain,
( spl0_904
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1167,axiom,
! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7869,plain,
spl0_903,
inference(avatar_split_clause,[],[f252,f7867]) ).
fof(f7867,plain,
( spl0_903
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f252,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f7865,plain,
spl0_902,
inference(avatar_split_clause,[],[f246,f7863]) ).
fof(f7863,plain,
( spl0_902
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f246,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7861,plain,
spl0_901,
inference(avatar_split_clause,[],[f196,f7859]) ).
fof(f7859,plain,
( spl0_901
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f196,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7857,plain,
spl0_900,
inference(avatar_split_clause,[],[f94,f7855]) ).
fof(f7855,plain,
( spl0_900
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f94,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f7853,plain,
spl0_899,
inference(avatar_split_clause,[],[f93,f7851]) ).
fof(f7851,plain,
( spl0_899
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f93,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7849,plain,
( spl0_898
| ~ spl0_48
| ~ spl0_850 ),
inference(avatar_split_clause,[],[f7761,f7582,f3487,f7846]) ).
fof(f7846,plain,
( spl0_898
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f3487,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f7582,plain,
( spl0_850
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f7761,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_48
| ~ spl0_850 ),
inference(resolution,[],[f7583,f3489]) ).
fof(f3489,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f3487]) ).
fof(f7583,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_850 ),
inference(avatar_component_clause,[],[f7582]) ).
fof(f7844,plain,
spl0_897,
inference(avatar_split_clause,[],[f92,f7842]) ).
fof(f7842,plain,
( spl0_897
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f92,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f7840,plain,
spl0_896,
inference(avatar_split_clause,[],[f91,f7838]) ).
fof(f7838,plain,
( spl0_896
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f91,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7836,plain,
spl0_895,
inference(avatar_split_clause,[],[f89,f7834]) ).
fof(f7834,plain,
( spl0_895
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f89,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7832,plain,
spl0_894,
inference(avatar_split_clause,[],[f88,f7830]) ).
fof(f88,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7828,plain,
spl0_893,
inference(avatar_split_clause,[],[f87,f7826]) ).
fof(f7826,plain,
( spl0_893
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f87,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7824,plain,
spl0_892,
inference(avatar_split_clause,[],[f86,f7822]) ).
fof(f7822,plain,
( spl0_892
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f86,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7820,plain,
spl0_891,
inference(avatar_split_clause,[],[f37,f7818]) ).
fof(f37,axiom,
! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7812,plain,
( spl0_890
| ~ spl0_50
| ~ spl0_842 ),
inference(avatar_split_clause,[],[f7755,f7550,f3497,f7809]) ).
fof(f7809,plain,
( spl0_890
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f7550,plain,
( spl0_842
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f7755,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_842 ),
inference(resolution,[],[f7551,f3499]) ).
fof(f7551,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_842 ),
inference(avatar_component_clause,[],[f7550]) ).
fof(f7805,plain,
( spl0_889
| ~ spl0_22
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f7754,f7546,f3357,f7802]) ).
fof(f7802,plain,
( spl0_889
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f7546,plain,
( spl0_841
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f7754,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_841 ),
inference(resolution,[],[f7547,f3359]) ).
fof(f7547,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f7546]) ).
fof(f7793,plain,
( spl0_888
| ~ spl0_641
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f7748,f7534,f5916,f7790]) ).
fof(f7748,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_838 ),
inference(superposition,[],[f7535,f5918]) ).
fof(f7772,plain,
( spl0_887
| ~ spl0_640
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f7747,f7534,f5911,f7769]) ).
fof(f7747,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_838 ),
inference(superposition,[],[f7535,f5913]) ).
fof(f7742,plain,
( spl0_886
| ~ spl0_821
| ~ spl0_832 ),
inference(avatar_split_clause,[],[f7737,f7510,f7457,f7740]) ).
fof(f7457,plain,
( spl0_821
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f7737,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_821
| ~ spl0_832 ),
inference(superposition,[],[f7511,f7458]) ).
fof(f7458,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7457]) ).
fof(f7726,plain,
spl0_885,
inference(avatar_split_clause,[],[f3146,f7724]) ).
fof(f7724,plain,
( spl0_885
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f3146,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3145,f2831]) ).
fof(f3145,plain,
! [X15] :
( c_1 = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2965,f2831]) ).
fof(f2965,plain,
! [X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1227,f2544,f2544]) ).
fof(f1227,axiom,
! [X15] :
( c_Suc(c_0) = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7722,plain,
spl0_884,
inference(avatar_split_clause,[],[f3056,f7720]) ).
fof(f3056,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
inference(forward_demodulation,[],[f2842,f2386]) ).
fof(f2386,axiom,
! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2842,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X1),X13,X1,X1),
inference(definition_unfolding,[],[f2604,f2373]) ).
fof(f2604,axiom,
! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7718,plain,
spl0_883,
inference(avatar_split_clause,[],[f2846,f7716]) ).
fof(f7714,plain,
spl0_882,
inference(avatar_split_clause,[],[f2844,f7711]) ).
fof(f2844,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2133,f2113]) ).
fof(f2133,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7709,plain,
spl0_881,
inference(avatar_split_clause,[],[f2831,f7706]) ).
fof(f7704,plain,
spl0_880,
inference(avatar_split_clause,[],[f2827,f7702]) ).
fof(f2827,plain,
! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2025,f2544]) ).
fof(f2025,axiom,
! [X15] : c_0 != c_Suc(X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
fof(f7700,plain,
spl0_879,
inference(avatar_split_clause,[],[f2705,f7698]) ).
fof(f7698,plain,
( spl0_879
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2705,axiom,
! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7696,plain,
spl0_878,
inference(avatar_split_clause,[],[f2684,f7694]) ).
fof(f2684,axiom,
! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7692,plain,
spl0_877,
inference(avatar_split_clause,[],[f2668,f7690]) ).
fof(f7690,plain,
( spl0_877
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2668,axiom,
! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7688,plain,
spl0_876,
inference(avatar_split_clause,[],[f2648,f7686]) ).
fof(f7686,plain,
( spl0_876
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2648,axiom,
! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7684,plain,
spl0_875,
inference(avatar_split_clause,[],[f2590,f7682]) ).
fof(f2590,axiom,
! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7680,plain,
spl0_874,
inference(avatar_split_clause,[],[f2588,f7678]) ).
fof(f2588,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7676,plain,
spl0_873,
inference(avatar_split_clause,[],[f2587,f7674]) ).
fof(f2587,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7672,plain,
spl0_872,
inference(avatar_split_clause,[],[f2549,f7670]) ).
fof(f7670,plain,
( spl0_872
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2549,axiom,
! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7668,plain,
spl0_871,
inference(avatar_split_clause,[],[f2394,f7666]) ).
fof(f7666,plain,
( spl0_871
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2394,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7664,plain,
spl0_870,
inference(avatar_split_clause,[],[f2374,f7662]) ).
fof(f7662,plain,
( spl0_870
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2374,axiom,
! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7660,plain,
spl0_869,
inference(avatar_split_clause,[],[f2372,f7658]) ).
fof(f7658,plain,
( spl0_869
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2372,axiom,
! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7656,plain,
spl0_868,
inference(avatar_split_clause,[],[f2243,f7654]) ).
fof(f2243,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7652,plain,
spl0_867,
inference(avatar_split_clause,[],[f2238,f7650]) ).
fof(f2238,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7648,plain,
spl0_866,
inference(avatar_split_clause,[],[f2226,f7646]) ).
fof(f7646,plain,
( spl0_866
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2226,axiom,
! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f7644,plain,
spl0_865,
inference(avatar_split_clause,[],[f2176,f7642]) ).
fof(f7642,plain,
( spl0_865
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2176,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7640,plain,
spl0_864,
inference(avatar_split_clause,[],[f2169,f7638]) ).
fof(f2169,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7636,plain,
spl0_863,
inference(avatar_split_clause,[],[f2162,f7634]) ).
fof(f7634,plain,
( spl0_863
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2162,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7632,plain,
spl0_862,
inference(avatar_split_clause,[],[f2161,f7630]) ).
fof(f7630,plain,
( spl0_862
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2161,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7628,plain,
spl0_861,
inference(avatar_split_clause,[],[f2158,f7626]) ).
fof(f7626,plain,
( spl0_861
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2158,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7624,plain,
spl0_860,
inference(avatar_split_clause,[],[f2157,f7622]) ).
fof(f7622,plain,
( spl0_860
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2157,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7620,plain,
spl0_859,
inference(avatar_split_clause,[],[f2144,f7618]) ).
fof(f2144,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7616,plain,
spl0_858,
inference(avatar_split_clause,[],[f2143,f7614]) ).
fof(f2143,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7612,plain,
spl0_857,
inference(avatar_split_clause,[],[f2089,f7610]) ).
fof(f2089,axiom,
! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7608,plain,
spl0_856,
inference(avatar_split_clause,[],[f2088,f7606]) ).
fof(f2088,axiom,
! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7604,plain,
spl0_855,
inference(avatar_split_clause,[],[f2087,f7602]) ).
fof(f2087,axiom,
! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7600,plain,
spl0_854,
inference(avatar_split_clause,[],[f2048,f7598]) ).
fof(f7598,plain,
( spl0_854
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2048,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7596,plain,
spl0_853,
inference(avatar_split_clause,[],[f2042,f7594]) ).
fof(f2042,axiom,
! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7592,plain,
spl0_852,
inference(avatar_split_clause,[],[f2040,f7590]) ).
fof(f2040,axiom,
! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7588,plain,
spl0_851,
inference(avatar_split_clause,[],[f1808,f7586]) ).
fof(f1808,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7584,plain,
spl0_850,
inference(avatar_split_clause,[],[f1804,f7582]) ).
fof(f1804,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
fof(f7580,plain,
spl0_849,
inference(avatar_split_clause,[],[f1790,f7578]) ).
fof(f7578,plain,
( spl0_849
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1790,axiom,
! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7576,plain,
spl0_848,
inference(avatar_split_clause,[],[f1788,f7574]) ).
fof(f7574,plain,
( spl0_848
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1788,axiom,
! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7572,plain,
spl0_847,
inference(avatar_split_clause,[],[f1732,f7570]) ).
fof(f1732,axiom,
! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7568,plain,
spl0_846,
inference(avatar_split_clause,[],[f1711,f7566]) ).
fof(f1711,axiom,
! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7564,plain,
spl0_845,
inference(avatar_split_clause,[],[f1631,f7562]) ).
fof(f7562,plain,
( spl0_845
<=> ! [X41,X43,X47] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1631,axiom,
! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7560,plain,
spl0_844,
inference(avatar_split_clause,[],[f1542,f7558]) ).
fof(f7558,plain,
( spl0_844
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1542,axiom,
! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7556,plain,
spl0_843,
inference(avatar_split_clause,[],[f1478,f7554]) ).
fof(f1478,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7552,plain,
spl0_842,
inference(avatar_split_clause,[],[f1405,f7550]) ).
fof(f1405,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
fof(f7548,plain,
spl0_841,
inference(avatar_split_clause,[],[f1401,f7546]) ).
fof(f1401,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7544,plain,
spl0_840,
inference(avatar_split_clause,[],[f1387,f7542]) ).
fof(f1387,axiom,
! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7540,plain,
spl0_839,
inference(avatar_split_clause,[],[f1373,f7538]) ).
fof(f7538,plain,
( spl0_839
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1373,axiom,
! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7536,plain,
spl0_838,
inference(avatar_split_clause,[],[f1367,f7534]) ).
fof(f1367,axiom,
! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7532,plain,
spl0_837,
inference(avatar_split_clause,[],[f1253,f7530]) ).
fof(f7530,plain,
( spl0_837
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1253,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7528,plain,
spl0_836,
inference(avatar_split_clause,[],[f1252,f7526]) ).
fof(f7526,plain,
( spl0_836
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f1252,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7524,plain,
spl0_835,
inference(avatar_split_clause,[],[f1249,f7522]) ).
fof(f7522,plain,
( spl0_835
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f1249,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7520,plain,
spl0_834,
inference(avatar_split_clause,[],[f1248,f7518]) ).
fof(f7518,plain,
( spl0_834
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f1248,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7516,plain,
spl0_833,
inference(avatar_split_clause,[],[f1225,f7514]) ).
fof(f7514,plain,
( spl0_833
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1225,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7512,plain,
spl0_832,
inference(avatar_split_clause,[],[f1215,f7510]) ).
fof(f1215,axiom,
! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7508,plain,
spl0_831,
inference(avatar_split_clause,[],[f1202,f7506]) ).
fof(f7506,plain,
( spl0_831
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1202,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7504,plain,
spl0_830,
inference(avatar_split_clause,[],[f1181,f7502]) ).
fof(f1181,axiom,
! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7500,plain,
spl0_829,
inference(avatar_split_clause,[],[f95,f7498]) ).
fof(f7498,plain,
( spl0_829
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f95,axiom,
! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7496,plain,
spl0_828,
inference(avatar_split_clause,[],[f90,f7494]) ).
fof(f7494,plain,
( spl0_828
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f90,axiom,
! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7492,plain,
spl0_827,
inference(avatar_split_clause,[],[f61,f7490]) ).
fof(f7490,plain,
( spl0_827
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f61,axiom,
! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7488,plain,
spl0_826,
inference(avatar_split_clause,[],[f45,f7486]) ).
fof(f7486,plain,
( spl0_826
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f45,axiom,
! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7484,plain,
spl0_825,
inference(avatar_split_clause,[],[f42,f7482]) ).
fof(f42,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7480,plain,
spl0_824,
inference(avatar_split_clause,[],[f41,f7478]) ).
fof(f41,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7476,plain,
spl0_823,
inference(avatar_split_clause,[],[f26,f7474]) ).
fof(f26,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7472,plain,
spl0_822,
inference(avatar_split_clause,[],[f25,f7470]) ).
fof(f25,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7459,plain,
spl0_821,
inference(avatar_split_clause,[],[f3066,f7457]) ).
fof(f3066,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f2857,f2831]) ).
fof(f2857,plain,
! [X3] : c_div(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X3,
inference(definition_unfolding,[],[f1214,f2544]) ).
fof(f1214,axiom,
! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7455,plain,
spl0_820,
inference(avatar_split_clause,[],[f3064,f7452]) ).
fof(f7452,plain,
( spl0_820
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f3064,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2854,f2831]) ).
fof(f2854,plain,
c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2064,f2544]) ).
fof(f2064,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
fof(f7450,plain,
spl0_819,
inference(avatar_split_clause,[],[f3062,f7448]) ).
fof(f3062,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f2853,f2831]) ).
fof(f2853,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1231,f2544]) ).
fof(f1231,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7446,plain,
spl0_818,
inference(avatar_split_clause,[],[f3061,f7443]) ).
fof(f3061,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f1867,f2156]) ).
fof(f1867,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7441,plain,
spl0_817,
inference(avatar_split_clause,[],[f3059,f7439]) ).
fof(f3059,plain,
! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
inference(forward_demodulation,[],[f2848,f1729]) ).
fof(f1729,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2848,plain,
! [X41,X3] : c_append(c_List_Orev(c_List_Olist_ONil,X41),X3,X41) = X3,
inference(definition_unfolding,[],[f1586,f1585]) ).
fof(f1586,axiom,
! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7437,plain,
spl0_816,
inference(avatar_split_clause,[],[f3057,f7434]) ).
fof(f3057,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2845,f2156]) ).
fof(f2845,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2125,f2129]) ).
fof(f2125,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7432,plain,
spl0_815,
inference(avatar_split_clause,[],[f2805,f7430]) ).
fof(f7430,plain,
( spl0_815
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2805,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
fof(f7428,plain,
spl0_814,
inference(avatar_split_clause,[],[f2803,f7426]) ).
fof(f2803,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
fof(f7424,plain,
spl0_813,
inference(avatar_split_clause,[],[f2799,f7422]) ).
fof(f2799,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
fof(f7420,plain,
spl0_812,
inference(avatar_split_clause,[],[f2792,f7418]) ).
fof(f2792,axiom,
! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
fof(f7416,plain,
spl0_811,
inference(avatar_split_clause,[],[f2785,f7414]) ).
fof(f7414,plain,
( spl0_811
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2785,axiom,
! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
fof(f7412,plain,
spl0_810,
inference(avatar_split_clause,[],[f2772,f7410]) ).
fof(f7410,plain,
( spl0_810
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2772,axiom,
! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
fof(f7408,plain,
spl0_809,
inference(avatar_split_clause,[],[f2763,f7406]) ).
fof(f2763,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
fof(f7404,plain,
spl0_808,
inference(avatar_split_clause,[],[f2762,f7402]) ).
fof(f2762,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
fof(f7400,plain,
spl0_807,
inference(avatar_split_clause,[],[f2761,f7398]) ).
fof(f2761,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
fof(f7396,plain,
spl0_806,
inference(avatar_split_clause,[],[f2760,f7394]) ).
fof(f2760,axiom,
! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
fof(f7392,plain,
spl0_805,
inference(avatar_split_clause,[],[f2738,f7390]) ).
fof(f7390,plain,
( spl0_805
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2738,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
fof(f7388,plain,
spl0_804,
inference(avatar_split_clause,[],[f2673,f7386]) ).
fof(f2673,axiom,
! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f7384,plain,
spl0_803,
inference(avatar_split_clause,[],[f2639,f7382]) ).
fof(f2639,axiom,
! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7380,plain,
spl0_802,
inference(avatar_split_clause,[],[f2638,f7378]) ).
fof(f2638,axiom,
! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7376,plain,
spl0_801,
inference(avatar_split_clause,[],[f2634,f7374]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7372,plain,
spl0_800,
inference(avatar_split_clause,[],[f2633,f7370]) ).
fof(f2633,axiom,
! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7368,plain,
spl0_799,
inference(avatar_split_clause,[],[f2632,f7366]) ).
fof(f2632,axiom,
! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7364,plain,
spl0_798,
inference(avatar_split_clause,[],[f2580,f7362]) ).
fof(f2580,axiom,
! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7360,plain,
spl0_797,
inference(avatar_split_clause,[],[f2576,f7358]) ).
fof(f2576,axiom,
! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7356,plain,
spl0_796,
inference(avatar_split_clause,[],[f2511,f7354]) ).
fof(f2511,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7352,plain,
spl0_795,
inference(avatar_split_clause,[],[f2499,f7350]) ).
fof(f2499,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7348,plain,
spl0_794,
inference(avatar_split_clause,[],[f2494,f7346]) ).
fof(f7346,plain,
( spl0_794
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2494,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7344,plain,
spl0_793,
inference(avatar_split_clause,[],[f2493,f7342]) ).
fof(f7342,plain,
( spl0_793
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2493,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7340,plain,
spl0_792,
inference(avatar_split_clause,[],[f2381,f7338]) ).
fof(f7338,plain,
( spl0_792
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2381,axiom,
! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7336,plain,
spl0_791,
inference(avatar_split_clause,[],[f2380,f7334]) ).
fof(f7334,plain,
( spl0_791
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2380,axiom,
! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7332,plain,
spl0_790,
inference(avatar_split_clause,[],[f2378,f7330]) ).
fof(f7330,plain,
( spl0_790
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2378,axiom,
! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7328,plain,
spl0_789,
inference(avatar_split_clause,[],[f2370,f7326]) ).
fof(f7326,plain,
( spl0_789
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2370,axiom,
! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7324,plain,
spl0_788,
inference(avatar_split_clause,[],[f2368,f7322]) ).
fof(f7322,plain,
( spl0_788
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2368,axiom,
! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7320,plain,
spl0_787,
inference(avatar_split_clause,[],[f2344,f7318]) ).
fof(f2344,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7316,plain,
spl0_786,
inference(avatar_split_clause,[],[f2269,f7314]) ).
fof(f2269,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7312,plain,
spl0_785,
inference(avatar_split_clause,[],[f2156,f7309]) ).
fof(f7307,plain,
spl0_784,
inference(avatar_split_clause,[],[f2102,f7305]) ).
fof(f2102,axiom,
! [X3] : c_minus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7303,plain,
spl0_783,
inference(avatar_split_clause,[],[f2100,f7301]) ).
fof(f2100,axiom,
! [X3] : c_plus(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7299,plain,
spl0_782,
inference(avatar_split_clause,[],[f2098,f7297]) ).
fof(f2098,axiom,
! [X21] : c_0 = c_times(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7295,plain,
spl0_781,
inference(avatar_split_clause,[],[f2056,f7293]) ).
fof(f7293,plain,
( spl0_781
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2056,axiom,
! [X15] : c_0 = c_times(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7291,plain,
spl0_780,
inference(avatar_split_clause,[],[f2054,f7289]) ).
fof(f2054,axiom,
! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7287,plain,
spl0_779,
inference(avatar_split_clause,[],[f2053,f7285]) ).
fof(f2053,axiom,
! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7283,plain,
spl0_778,
inference(avatar_split_clause,[],[f2051,f7281]) ).
fof(f7281,plain,
( spl0_778
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2051,axiom,
! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7279,plain,
spl0_777,
inference(avatar_split_clause,[],[f2050,f7277]) ).
fof(f2050,axiom,
! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7275,plain,
spl0_776,
inference(avatar_split_clause,[],[f2041,f7273]) ).
fof(f2041,axiom,
! [X15] : c_0 = c_minus(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7271,plain,
spl0_775,
inference(avatar_split_clause,[],[f2034,f7269]) ).
fof(f2034,axiom,
! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7267,plain,
spl0_774,
inference(avatar_split_clause,[],[f2026,f7265]) ).
fof(f2026,axiom,
! [X3] : c_plus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7263,plain,
spl0_773,
inference(avatar_split_clause,[],[f1763,f7261]) ).
fof(f7261,plain,
( spl0_773
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1763,axiom,
! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7259,plain,
spl0_772,
inference(avatar_split_clause,[],[f1762,f7257]) ).
fof(f7257,plain,
( spl0_772
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1762,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7255,plain,
spl0_771,
inference(avatar_split_clause,[],[f1747,f7253]) ).
fof(f1747,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7251,plain,
spl0_770,
inference(avatar_split_clause,[],[f1741,f7249]) ).
fof(f7249,plain,
( spl0_770
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f1741,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7247,plain,
spl0_769,
inference(avatar_split_clause,[],[f1722,f7245]) ).
fof(f1722,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7243,plain,
spl0_768,
inference(avatar_split_clause,[],[f1719,f7241]) ).
fof(f7241,plain,
( spl0_768
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1719,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7239,plain,
spl0_767,
inference(avatar_split_clause,[],[f1707,f7237]) ).
fof(f1707,axiom,
! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7235,plain,
spl0_766,
inference(avatar_split_clause,[],[f1689,f7233]) ).
fof(f1689,axiom,
! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
fof(f7231,plain,
spl0_765,
inference(avatar_split_clause,[],[f1628,f7229]) ).
fof(f7229,plain,
( spl0_765
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1628,axiom,
! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7227,plain,
spl0_764,
inference(avatar_split_clause,[],[f1624,f7225]) ).
fof(f1624,axiom,
! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7223,plain,
spl0_763,
inference(avatar_split_clause,[],[f1615,f7221]) ).
fof(f7221,plain,
( spl0_763
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1615,axiom,
! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7219,plain,
spl0_762,
inference(avatar_split_clause,[],[f1598,f7217]) ).
fof(f1598,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7215,plain,
spl0_761,
inference(avatar_split_clause,[],[f1569,f7213]) ).
fof(f1569,axiom,
! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7211,plain,
spl0_760,
inference(avatar_split_clause,[],[f1568,f7209]) ).
fof(f7209,plain,
( spl0_760
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1568,axiom,
! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7207,plain,
spl0_759,
inference(avatar_split_clause,[],[f1494,f7205]) ).
fof(f1494,axiom,
! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7203,plain,
spl0_758,
inference(avatar_split_clause,[],[f1491,f7201]) ).
fof(f1491,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7199,plain,
spl0_757,
inference(avatar_split_clause,[],[f1489,f7197]) ).
fof(f1489,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7195,plain,
spl0_756,
inference(avatar_split_clause,[],[f1474,f7193]) ).
fof(f7193,plain,
( spl0_756
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1474,axiom,
! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7191,plain,
spl0_755,
inference(avatar_split_clause,[],[f1466,f7189]) ).
fof(f7189,plain,
( spl0_755
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f1466,axiom,
! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7187,plain,
spl0_754,
inference(avatar_split_clause,[],[f1464,f7185]) ).
fof(f7185,plain,
( spl0_754
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1464,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7183,plain,
spl0_753,
inference(avatar_split_clause,[],[f1432,f7181]) ).
fof(f1432,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7179,plain,
spl0_752,
inference(avatar_split_clause,[],[f1364,f7177]) ).
fof(f7177,plain,
( spl0_752
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f1364,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7175,plain,
spl0_751,
inference(avatar_split_clause,[],[f1363,f7173]) ).
fof(f7173,plain,
( spl0_751
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1363,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7171,plain,
spl0_750,
inference(avatar_split_clause,[],[f1358,f7169]) ).
fof(f7169,plain,
( spl0_750
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1358,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7167,plain,
spl0_749,
inference(avatar_split_clause,[],[f1357,f7165]) ).
fof(f7165,plain,
( spl0_749
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f1357,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7163,plain,
spl0_748,
inference(avatar_split_clause,[],[f1350,f7160]) ).
fof(f7160,plain,
( spl0_748
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1350,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7158,plain,
spl0_747,
inference(avatar_split_clause,[],[f1247,f7156]) ).
fof(f7156,plain,
( spl0_747
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f1247,axiom,
! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
fof(f7154,plain,
spl0_746,
inference(avatar_split_clause,[],[f1241,f7152]) ).
fof(f1241,axiom,
! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7150,plain,
spl0_745,
inference(avatar_split_clause,[],[f1230,f7148]) ).
fof(f1230,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7146,plain,
spl0_744,
inference(avatar_split_clause,[],[f1213,f7144]) ).
fof(f7144,plain,
( spl0_744
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1213,axiom,
! [X15] : c_0 = c_div(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7142,plain,
spl0_743,
inference(avatar_split_clause,[],[f1212,f7140]) ).
fof(f7140,plain,
( spl0_743
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1212,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7138,plain,
spl0_742,
inference(avatar_split_clause,[],[f1211,f7136]) ).
fof(f7136,plain,
( spl0_742
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f1211,axiom,
! [X18] : c_0 = c_div(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7134,plain,
spl0_741,
inference(avatar_split_clause,[],[f1183,f7132]) ).
fof(f7132,plain,
( spl0_741
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1183,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7130,plain,
spl0_740,
inference(avatar_split_clause,[],[f1182,f7128]) ).
fof(f7128,plain,
( spl0_740
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1182,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7126,plain,
spl0_739,
inference(avatar_split_clause,[],[f1176,f7124]) ).
fof(f7124,plain,
( spl0_739
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1176,axiom,
! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7122,plain,
spl0_738,
inference(avatar_split_clause,[],[f68,f7120]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7118,plain,
( spl0_737
| ~ spl0_640
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f7100,f6850,f5911,f7115]) ).
fof(f7100,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_680 ),
inference(superposition,[],[f6851,f5913]) ).
fof(f7111,plain,
( ~ spl0_736
| ~ spl0_641
| ~ spl0_678 ),
inference(avatar_split_clause,[],[f7097,f6842,f5916,f7108]) ).
fof(f7108,plain,
( spl0_736
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f6842,plain,
( spl0_678
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f7097,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_678 ),
inference(superposition,[],[f6843,f5918]) ).
fof(f6843,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_678 ),
inference(avatar_component_clause,[],[f6842]) ).
fof(f7106,plain,
( ~ spl0_735
| ~ spl0_640
| ~ spl0_678 ),
inference(avatar_split_clause,[],[f7096,f6842,f5911,f7103]) ).
fof(f7103,plain,
( spl0_735
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f7096,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_678 ),
inference(superposition,[],[f6843,f5913]) ).
fof(f7095,plain,
spl0_734,
inference(avatar_split_clause,[],[f3063,f7092]) ).
fof(f7092,plain,
( spl0_734
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f3063,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1391,f1374]) ).
fof(f1374,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f1391,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f7090,plain,
spl0_733,
inference(avatar_split_clause,[],[f3058,f7088]) ).
fof(f7088,plain,
( spl0_733
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f3058,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f2847,f2831]) ).
fof(f2847,plain,
! [X3] : c_Binomial_Obinomial(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X3,
inference(definition_unfolding,[],[f1161,f2544]) ).
fof(f1161,axiom,
! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f7086,plain,
spl0_732,
inference(avatar_split_clause,[],[f2830,f7083]) ).
fof(f7081,plain,
spl0_731,
inference(avatar_split_clause,[],[f2740,f7079]) ).
fof(f2740,axiom,
! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f7077,plain,
spl0_730,
inference(avatar_split_clause,[],[f2739,f7074]) ).
fof(f7074,plain,
( spl0_730
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2739,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
fof(f7072,plain,
spl0_729,
inference(avatar_split_clause,[],[f2737,f7069]) ).
fof(f7069,plain,
( spl0_729
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2737,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
fof(f7067,plain,
spl0_728,
inference(avatar_split_clause,[],[f2714,f7065]) ).
fof(f7065,plain,
( spl0_728
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2714,axiom,
! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f7063,plain,
spl0_727,
inference(avatar_split_clause,[],[f2698,f7061]) ).
fof(f2698,axiom,
! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f7059,plain,
spl0_726,
inference(avatar_split_clause,[],[f2691,f7057]) ).
fof(f7057,plain,
( spl0_726
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2691,axiom,
! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f7055,plain,
spl0_725,
inference(avatar_split_clause,[],[f2651,f7053]) ).
fof(f7053,plain,
( spl0_725
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7051,plain,
spl0_724,
inference(avatar_split_clause,[],[f2649,f7049]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7047,plain,
spl0_723,
inference(avatar_split_clause,[],[f2625,f7045]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7043,plain,
spl0_722,
inference(avatar_split_clause,[],[f2619,f7041]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7039,plain,
spl0_721,
inference(avatar_split_clause,[],[f2612,f7037]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f7035,plain,
spl0_720,
inference(avatar_split_clause,[],[f2567,f7032]) ).
fof(f2567,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f7030,plain,
spl0_719,
inference(avatar_split_clause,[],[f2528,f7027]) ).
fof(f2528,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f7025,plain,
spl0_718,
inference(avatar_split_clause,[],[f2386,f7023]) ).
fof(f7021,plain,
spl0_717,
inference(avatar_split_clause,[],[f2164,f7018]) ).
fof(f7018,plain,
( spl0_717
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f2164,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f7016,plain,
spl0_716,
inference(avatar_split_clause,[],[f2163,f7013]) ).
fof(f7013,plain,
( spl0_716
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2163,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f7011,plain,
spl0_715,
inference(avatar_split_clause,[],[f2152,f7009]) ).
fof(f7009,plain,
( spl0_715
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2152,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f7007,plain,
spl0_714,
inference(avatar_split_clause,[],[f2151,f7005]) ).
fof(f7005,plain,
( spl0_714
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2151,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f7003,plain,
spl0_713,
inference(avatar_split_clause,[],[f2135,f7001]) ).
fof(f7001,plain,
( spl0_713
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2135,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6999,plain,
spl0_712,
inference(avatar_split_clause,[],[f2130,f6997]) ).
fof(f2130,axiom,
! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6995,plain,
spl0_711,
inference(avatar_split_clause,[],[f2115,f6993]) ).
fof(f6991,plain,
spl0_710,
inference(avatar_split_clause,[],[f2114,f6989]) ).
fof(f6987,plain,
spl0_709,
inference(avatar_split_clause,[],[f2106,f6984]) ).
fof(f2106,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f6982,plain,
spl0_708,
inference(avatar_split_clause,[],[f2105,f6979]) ).
fof(f2105,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f6977,plain,
spl0_707,
inference(avatar_split_clause,[],[f1866,f6974]) ).
fof(f1866,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f6972,plain,
spl0_706,
inference(avatar_split_clause,[],[f1785,f6970]) ).
fof(f1785,axiom,
! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6968,plain,
spl0_705,
inference(avatar_split_clause,[],[f1778,f6966]) ).
fof(f6966,plain,
( spl0_705
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1778,axiom,
! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6964,plain,
spl0_704,
inference(avatar_split_clause,[],[f1751,f6962]) ).
fof(f6962,plain,
( spl0_704
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1751,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f6960,plain,
spl0_703,
inference(avatar_split_clause,[],[f1736,f6958]) ).
fof(f6958,plain,
( spl0_703
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1736,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6956,plain,
spl0_702,
inference(avatar_split_clause,[],[f1729,f6954]) ).
fof(f6954,plain,
( spl0_702
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f6952,plain,
spl0_701,
inference(avatar_split_clause,[],[f1718,f6950]) ).
fof(f6950,plain,
( spl0_701
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1718,axiom,
! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
fof(f6948,plain,
spl0_700,
inference(avatar_split_clause,[],[f1688,f6945]) ).
fof(f6945,plain,
( spl0_700
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1688,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f6943,plain,
spl0_699,
inference(avatar_split_clause,[],[f1687,f6940]) ).
fof(f6940,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1687,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f6938,plain,
spl0_698,
inference(avatar_split_clause,[],[f1686,f6935]) ).
fof(f6935,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1686,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f6933,plain,
spl0_697,
inference(avatar_split_clause,[],[f1685,f6930]) ).
fof(f6930,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1685,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f6928,plain,
spl0_696,
inference(avatar_split_clause,[],[f1684,f6925]) ).
fof(f6925,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1684,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f6923,plain,
spl0_695,
inference(avatar_split_clause,[],[f1683,f6920]) ).
fof(f6920,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1683,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f6918,plain,
spl0_694,
inference(avatar_split_clause,[],[f1682,f6915]) ).
fof(f6915,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1682,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f6913,plain,
spl0_693,
inference(avatar_split_clause,[],[f1681,f6910]) ).
fof(f6910,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1681,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f6908,plain,
spl0_692,
inference(avatar_split_clause,[],[f1680,f6905]) ).
fof(f6905,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1680,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f6903,plain,
spl0_691,
inference(avatar_split_clause,[],[f1679,f6900]) ).
fof(f6900,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1679,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f6898,plain,
spl0_690,
inference(avatar_split_clause,[],[f1678,f6895]) ).
fof(f6895,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1678,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f6893,plain,
spl0_689,
inference(avatar_split_clause,[],[f1677,f6890]) ).
fof(f6890,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1677,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f6888,plain,
spl0_688,
inference(avatar_split_clause,[],[f1676,f6885]) ).
fof(f6885,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1676,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f6883,plain,
spl0_687,
inference(avatar_split_clause,[],[f1675,f6880]) ).
fof(f6880,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1675,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f6878,plain,
spl0_686,
inference(avatar_split_clause,[],[f1674,f6875]) ).
fof(f6875,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1674,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f6873,plain,
spl0_685,
inference(avatar_split_clause,[],[f1673,f6870]) ).
fof(f6870,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1673,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f6868,plain,
spl0_684,
inference(avatar_split_clause,[],[f1638,f6866]) ).
fof(f1638,axiom,
! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6864,plain,
spl0_683,
inference(avatar_split_clause,[],[f1567,f6862]) ).
fof(f6862,plain,
( spl0_683
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1567,axiom,
! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6860,plain,
spl0_682,
inference(avatar_split_clause,[],[f1543,f6858]) ).
fof(f6858,plain,
( spl0_682
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1543,axiom,
! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6856,plain,
spl0_681,
inference(avatar_split_clause,[],[f1536,f6854]) ).
fof(f6854,plain,
( spl0_681
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f1536,axiom,
! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6852,plain,
spl0_680,
inference(avatar_split_clause,[],[f1424,f6850]) ).
fof(f1424,axiom,
! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6848,plain,
spl0_679,
inference(avatar_split_clause,[],[f1384,f6846]) ).
fof(f1384,axiom,
! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6844,plain,
spl0_678,
inference(avatar_split_clause,[],[f1378,f6842]) ).
fof(f1378,axiom,
! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6840,plain,
~ spl0_677,
inference(avatar_split_clause,[],[f1309,f6837]) ).
fof(f1309,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f6835,plain,
spl0_676,
inference(avatar_split_clause,[],[f1296,f6833]) ).
fof(f6833,plain,
( spl0_676
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6831,plain,
spl0_675,
inference(avatar_split_clause,[],[f1295,f6829]) ).
fof(f1295,axiom,
! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6827,plain,
spl0_674,
inference(avatar_split_clause,[],[f1278,f6825]) ).
fof(f6825,plain,
( spl0_674
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1278,axiom,
! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6823,plain,
spl0_673,
inference(avatar_split_clause,[],[f1255,f6820]) ).
fof(f6820,plain,
( spl0_673
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1255,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f6818,plain,
spl0_672,
inference(avatar_split_clause,[],[f1254,f6815]) ).
fof(f6815,plain,
( spl0_672
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1254,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f6813,plain,
spl0_671,
inference(avatar_split_clause,[],[f1184,f6810]) ).
fof(f6810,plain,
( spl0_671
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1184,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f6808,plain,
spl0_670,
inference(avatar_split_clause,[],[f1174,f6806]) ).
fof(f6806,plain,
( spl0_670
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1174,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2_0) ).
fof(f6804,plain,
spl0_669,
inference(avatar_split_clause,[],[f1172,f6802]) ).
fof(f6802,plain,
( spl0_669
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1172,axiom,
! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6800,plain,
spl0_668,
inference(avatar_split_clause,[],[f1165,f6798]) ).
fof(f6798,plain,
( spl0_668
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1165,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6796,plain,
spl0_667,
inference(avatar_split_clause,[],[f1164,f6794]) ).
fof(f6794,plain,
( spl0_667
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f1164,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f6792,plain,
spl0_666,
inference(avatar_split_clause,[],[f250,f6790]) ).
fof(f6790,plain,
( spl0_666
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f250,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6788,plain,
spl0_665,
inference(avatar_split_clause,[],[f128,f6786]) ).
fof(f6786,plain,
( spl0_665
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f128,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6784,plain,
( ~ spl0_664
| ~ spl0_641
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6758,f5926,f5916,f6781]) ).
fof(f6781,plain,
( spl0_664
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f5926,plain,
( spl0_643
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f6758,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_643 ),
inference(superposition,[],[f5927,f5918]) ).
fof(f5927,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f5926]) ).
fof(f6779,plain,
spl0_663,
inference(avatar_split_clause,[],[f112,f6777]) ).
fof(f112,axiom,
! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6775,plain,
spl0_662,
inference(avatar_split_clause,[],[f101,f6773]) ).
fof(f101,axiom,
! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6771,plain,
spl0_661,
inference(avatar_split_clause,[],[f44,f6769]) ).
fof(f6769,plain,
( spl0_661
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f44,axiom,
! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6767,plain,
spl0_660,
inference(avatar_split_clause,[],[f28,f6765]) ).
fof(f6765,plain,
( spl0_660
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f28,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6763,plain,
( ~ spl0_659
| ~ spl0_640
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6757,f5926,f5911,f6760]) ).
fof(f6757,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_643 ),
inference(superposition,[],[f5927,f5913]) ).
fof(f5996,plain,
spl0_658,
inference(avatar_split_clause,[],[f3073,f5993]) ).
fof(f3073,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1486,f1464]) ).
fof(f1486,axiom,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f5991,plain,
spl0_657,
inference(avatar_split_clause,[],[f3054,f5988]) ).
fof(f5988,plain,
( spl0_657
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f3054,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1377,f1374]) ).
fof(f1377,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f5986,plain,
spl0_656,
inference(avatar_split_clause,[],[f3053,f5984]) ).
fof(f5984,plain,
( spl0_656
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f3053,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f2834,f2831]) ).
fof(f2834,plain,
! [X16] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X16,tc_nat),
inference(definition_unfolding,[],[f24,f2544]) ).
fof(f24,axiom,
! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5982,plain,
spl0_655,
inference(avatar_split_clause,[],[f3052,f5979]) ).
fof(f3052,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2833,f2831]) ).
fof(f2833,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1344,f2544]) ).
fof(f1344,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5977,plain,
spl0_654,
inference(avatar_split_clause,[],[f2791,f5974]) ).
fof(f5974,plain,
( spl0_654
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2791,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
fof(f5972,plain,
spl0_653,
inference(avatar_split_clause,[],[f2770,f5969]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f5967,plain,
spl0_652,
inference(avatar_split_clause,[],[f2743,f5964]) ).
fof(f5964,plain,
( spl0_652
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f5962,plain,
spl0_651,
inference(avatar_split_clause,[],[f2734,f5960]) ).
fof(f5960,plain,
( spl0_651
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2734,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).
fof(f5958,plain,
spl0_650,
inference(avatar_split_clause,[],[f2730,f5956]) ).
fof(f5956,plain,
( spl0_650
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2730,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
fof(f5954,plain,
spl0_649,
inference(avatar_split_clause,[],[f2672,f5952]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f5950,plain,
spl0_648,
inference(avatar_split_clause,[],[f2155,f5947]) ).
fof(f5947,plain,
( spl0_648
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2155,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f5945,plain,
spl0_647,
inference(avatar_split_clause,[],[f2091,f5943]) ).
fof(f5943,plain,
( spl0_647
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f5941,plain,
spl0_646,
inference(avatar_split_clause,[],[f2049,f5938]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f5936,plain,
spl0_645,
inference(avatar_split_clause,[],[f1709,f5934]) ).
fof(f5934,plain,
( spl0_645
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1709,axiom,
! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f5932,plain,
spl0_644,
inference(avatar_split_clause,[],[f1482,f5930]) ).
fof(f1482,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f5928,plain,
spl0_643,
inference(avatar_split_clause,[],[f1393,f5926]) ).
fof(f1393,axiom,
! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f5924,plain,
spl0_642,
inference(avatar_split_clause,[],[f1386,f5921]) ).
fof(f5921,plain,
( spl0_642
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f5919,plain,
spl0_641,
inference(avatar_split_clause,[],[f1374,f5916]) ).
fof(f5914,plain,
spl0_640,
inference(avatar_split_clause,[],[f1371,f5911]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f5909,plain,
spl0_639,
inference(avatar_split_clause,[],[f1229,f5907]) ).
fof(f5907,plain,
( spl0_639
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1229,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f5905,plain,
spl0_638,
inference(avatar_split_clause,[],[f1159,f5903]) ).
fof(f5903,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1159,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5901,plain,
spl0_637,
inference(avatar_split_clause,[],[f1158,f5899]) ).
fof(f5899,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1158,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5897,plain,
spl0_636,
inference(avatar_split_clause,[],[f1157,f5895]) ).
fof(f5895,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1157,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5893,plain,
spl0_635,
inference(avatar_split_clause,[],[f1156,f5891]) ).
fof(f5891,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1156,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5889,plain,
spl0_634,
inference(avatar_split_clause,[],[f1155,f5887]) ).
fof(f5887,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1155,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5885,plain,
spl0_633,
inference(avatar_split_clause,[],[f1154,f5883]) ).
fof(f5883,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1154,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5881,plain,
spl0_632,
inference(avatar_split_clause,[],[f1153,f5879]) ).
fof(f5879,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1153,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5877,plain,
spl0_631,
inference(avatar_split_clause,[],[f1148,f5875]) ).
fof(f5875,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1148,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5873,plain,
spl0_630,
inference(avatar_split_clause,[],[f1147,f5871]) ).
fof(f5871,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1147,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5869,plain,
spl0_629,
inference(avatar_split_clause,[],[f1146,f5867]) ).
fof(f5867,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1146,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5865,plain,
spl0_628,
inference(avatar_split_clause,[],[f1145,f5863]) ).
fof(f5863,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1145,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5861,plain,
spl0_627,
inference(avatar_split_clause,[],[f1144,f5859]) ).
fof(f5859,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1144,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5857,plain,
spl0_626,
inference(avatar_split_clause,[],[f1143,f5855]) ).
fof(f5855,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1143,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5853,plain,
spl0_625,
inference(avatar_split_clause,[],[f1140,f5851]) ).
fof(f5851,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1140,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5849,plain,
spl0_624,
inference(avatar_split_clause,[],[f1139,f5847]) ).
fof(f5847,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1139,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5845,plain,
spl0_623,
inference(avatar_split_clause,[],[f1138,f5843]) ).
fof(f5843,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1138,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5841,plain,
spl0_622,
inference(avatar_split_clause,[],[f1135,f5839]) ).
fof(f5839,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1135,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5837,plain,
spl0_621,
inference(avatar_split_clause,[],[f1132,f5835]) ).
fof(f5835,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1132,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5833,plain,
spl0_620,
inference(avatar_split_clause,[],[f1131,f5831]) ).
fof(f5831,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1131,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5829,plain,
spl0_619,
inference(avatar_split_clause,[],[f1130,f5827]) ).
fof(f5827,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1130,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5825,plain,
spl0_618,
inference(avatar_split_clause,[],[f1129,f5823]) ).
fof(f5823,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1129,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5821,plain,
spl0_617,
inference(avatar_split_clause,[],[f1126,f5819]) ).
fof(f5819,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1126,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5817,plain,
spl0_616,
inference(avatar_split_clause,[],[f1125,f5815]) ).
fof(f5815,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1125,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5813,plain,
spl0_615,
inference(avatar_split_clause,[],[f1120,f5811]) ).
fof(f5811,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1120,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5809,plain,
spl0_614,
inference(avatar_split_clause,[],[f1117,f5807]) ).
fof(f5807,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1117,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5805,plain,
spl0_613,
inference(avatar_split_clause,[],[f1116,f5803]) ).
fof(f5803,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1116,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5801,plain,
spl0_612,
inference(avatar_split_clause,[],[f1115,f5799]) ).
fof(f5799,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1115,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5797,plain,
spl0_611,
inference(avatar_split_clause,[],[f1113,f5795]) ).
fof(f5795,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1113,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5793,plain,
spl0_610,
inference(avatar_split_clause,[],[f1107,f5791]) ).
fof(f5791,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1107,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5789,plain,
spl0_609,
inference(avatar_split_clause,[],[f1099,f5787]) ).
fof(f5787,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1099,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5785,plain,
spl0_608,
inference(avatar_split_clause,[],[f1098,f5783]) ).
fof(f5783,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1098,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5781,plain,
spl0_607,
inference(avatar_split_clause,[],[f1097,f5779]) ).
fof(f5779,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1097,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5777,plain,
spl0_606,
inference(avatar_split_clause,[],[f1096,f5775]) ).
fof(f5775,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1096,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5773,plain,
spl0_605,
inference(avatar_split_clause,[],[f1095,f5771]) ).
fof(f5771,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1095,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5769,plain,
spl0_604,
inference(avatar_split_clause,[],[f1093,f5767]) ).
fof(f5767,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f1093,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5765,plain,
spl0_603,
inference(avatar_split_clause,[],[f1092,f5763]) ).
fof(f5763,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1092,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5761,plain,
spl0_602,
inference(avatar_split_clause,[],[f1091,f5759]) ).
fof(f5759,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1091,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5757,plain,
spl0_601,
inference(avatar_split_clause,[],[f1090,f5755]) ).
fof(f5755,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1090,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5753,plain,
spl0_600,
inference(avatar_split_clause,[],[f1089,f5751]) ).
fof(f5751,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1089,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5749,plain,
spl0_599,
inference(avatar_split_clause,[],[f1084,f5747]) ).
fof(f5747,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1084,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5745,plain,
spl0_598,
inference(avatar_split_clause,[],[f1083,f5743]) ).
fof(f5743,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1083,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5741,plain,
spl0_597,
inference(avatar_split_clause,[],[f1082,f5739]) ).
fof(f5739,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1082,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5737,plain,
spl0_596,
inference(avatar_split_clause,[],[f1080,f5735]) ).
fof(f5735,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1080,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5733,plain,
spl0_595,
inference(avatar_split_clause,[],[f1078,f5731]) ).
fof(f5731,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1078,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5729,plain,
spl0_594,
inference(avatar_split_clause,[],[f1073,f5727]) ).
fof(f5727,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1073,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5725,plain,
spl0_593,
inference(avatar_split_clause,[],[f1072,f5723]) ).
fof(f5723,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1072,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5721,plain,
spl0_592,
inference(avatar_split_clause,[],[f1071,f5719]) ).
fof(f5719,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1071,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5717,plain,
spl0_591,
inference(avatar_split_clause,[],[f1070,f5715]) ).
fof(f5715,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1070,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5713,plain,
spl0_590,
inference(avatar_split_clause,[],[f1068,f5711]) ).
fof(f5711,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1068,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5709,plain,
spl0_589,
inference(avatar_split_clause,[],[f1067,f5707]) ).
fof(f5707,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1067,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5705,plain,
spl0_588,
inference(avatar_split_clause,[],[f1062,f5703]) ).
fof(f5703,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1062,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5701,plain,
spl0_587,
inference(avatar_split_clause,[],[f1059,f5699]) ).
fof(f5699,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1059,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5697,plain,
spl0_586,
inference(avatar_split_clause,[],[f1058,f5695]) ).
fof(f5695,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1058,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5693,plain,
spl0_585,
inference(avatar_split_clause,[],[f1057,f5691]) ).
fof(f5691,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1057,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5689,plain,
spl0_584,
inference(avatar_split_clause,[],[f1056,f5687]) ).
fof(f5687,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1056,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5685,plain,
spl0_583,
inference(avatar_split_clause,[],[f1053,f5683]) ).
fof(f5683,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1053,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5681,plain,
spl0_582,
inference(avatar_split_clause,[],[f1052,f5679]) ).
fof(f5679,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1052,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5677,plain,
spl0_581,
inference(avatar_split_clause,[],[f1051,f5675]) ).
fof(f5675,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1051,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5673,plain,
spl0_580,
inference(avatar_split_clause,[],[f1050,f5671]) ).
fof(f5671,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1050,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5669,plain,
spl0_579,
inference(avatar_split_clause,[],[f1049,f5667]) ).
fof(f5667,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1049,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5665,plain,
spl0_578,
inference(avatar_split_clause,[],[f1048,f5663]) ).
fof(f5663,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1048,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5661,plain,
spl0_577,
inference(avatar_split_clause,[],[f1047,f5659]) ).
fof(f5659,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1047,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5657,plain,
spl0_576,
inference(avatar_split_clause,[],[f1046,f5655]) ).
fof(f5655,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1046,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5653,plain,
spl0_575,
inference(avatar_split_clause,[],[f1044,f5651]) ).
fof(f5651,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1044,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5649,plain,
spl0_574,
inference(avatar_split_clause,[],[f1043,f5647]) ).
fof(f5647,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1043,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5645,plain,
spl0_573,
inference(avatar_split_clause,[],[f1042,f5643]) ).
fof(f5643,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1042,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5641,plain,
spl0_572,
inference(avatar_split_clause,[],[f1041,f5639]) ).
fof(f5639,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1041,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5637,plain,
spl0_571,
inference(avatar_split_clause,[],[f1040,f5635]) ).
fof(f5635,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1040,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5633,plain,
spl0_570,
inference(avatar_split_clause,[],[f1035,f5631]) ).
fof(f5631,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1035,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5629,plain,
spl0_569,
inference(avatar_split_clause,[],[f1034,f5627]) ).
fof(f5627,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f1034,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5625,plain,
spl0_568,
inference(avatar_split_clause,[],[f1033,f5623]) ).
fof(f5623,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1033,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5621,plain,
spl0_567,
inference(avatar_split_clause,[],[f1030,f5619]) ).
fof(f5619,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1030,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5617,plain,
spl0_566,
inference(avatar_split_clause,[],[f1027,f5615]) ).
fof(f5615,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1027,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5613,plain,
spl0_565,
inference(avatar_split_clause,[],[f1026,f5611]) ).
fof(f5611,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1026,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5609,plain,
spl0_564,
inference(avatar_split_clause,[],[f1024,f5607]) ).
fof(f5607,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1024,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5605,plain,
spl0_563,
inference(avatar_split_clause,[],[f1023,f5603]) ).
fof(f5603,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f1023,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5601,plain,
spl0_562,
inference(avatar_split_clause,[],[f1022,f5599]) ).
fof(f5599,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1022,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5597,plain,
spl0_561,
inference(avatar_split_clause,[],[f1021,f5595]) ).
fof(f5595,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1021,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5593,plain,
spl0_560,
inference(avatar_split_clause,[],[f1018,f5591]) ).
fof(f5591,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1018,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5589,plain,
spl0_559,
inference(avatar_split_clause,[],[f1017,f5587]) ).
fof(f5587,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1017,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5585,plain,
spl0_558,
inference(avatar_split_clause,[],[f989,f5583]) ).
fof(f5583,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f989,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5581,plain,
spl0_557,
inference(avatar_split_clause,[],[f987,f5579]) ).
fof(f5579,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f987,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5577,plain,
spl0_556,
inference(avatar_split_clause,[],[f984,f5575]) ).
fof(f5575,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f984,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5573,plain,
spl0_555,
inference(avatar_split_clause,[],[f983,f5571]) ).
fof(f5571,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f983,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5569,plain,
spl0_554,
inference(avatar_split_clause,[],[f982,f5567]) ).
fof(f5567,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f982,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5565,plain,
spl0_553,
inference(avatar_split_clause,[],[f981,f5563]) ).
fof(f5563,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f981,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5561,plain,
spl0_552,
inference(avatar_split_clause,[],[f980,f5559]) ).
fof(f5559,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f980,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5557,plain,
spl0_551,
inference(avatar_split_clause,[],[f979,f5555]) ).
fof(f5555,plain,
( spl0_551
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f979,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5553,plain,
spl0_550,
inference(avatar_split_clause,[],[f977,f5551]) ).
fof(f5551,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f977,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5549,plain,
spl0_549,
inference(avatar_split_clause,[],[f976,f5547]) ).
fof(f5547,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f976,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5545,plain,
spl0_548,
inference(avatar_split_clause,[],[f974,f5543]) ).
fof(f5543,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f974,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5541,plain,
spl0_547,
inference(avatar_split_clause,[],[f971,f5539]) ).
fof(f5539,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f971,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5537,plain,
spl0_546,
inference(avatar_split_clause,[],[f970,f5535]) ).
fof(f5535,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f970,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5533,plain,
spl0_545,
inference(avatar_split_clause,[],[f968,f5531]) ).
fof(f5531,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f968,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5529,plain,
spl0_544,
inference(avatar_split_clause,[],[f967,f5527]) ).
fof(f5527,plain,
( spl0_544
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f967,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5525,plain,
spl0_543,
inference(avatar_split_clause,[],[f966,f5523]) ).
fof(f5523,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f966,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5521,plain,
spl0_542,
inference(avatar_split_clause,[],[f965,f5519]) ).
fof(f5519,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f965,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5517,plain,
spl0_541,
inference(avatar_split_clause,[],[f964,f5515]) ).
fof(f5515,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f964,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5513,plain,
spl0_540,
inference(avatar_split_clause,[],[f963,f5511]) ).
fof(f5511,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f963,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5509,plain,
spl0_539,
inference(avatar_split_clause,[],[f962,f5507]) ).
fof(f5507,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f962,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5505,plain,
spl0_538,
inference(avatar_split_clause,[],[f961,f5503]) ).
fof(f5503,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f961,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5501,plain,
spl0_537,
inference(avatar_split_clause,[],[f957,f5499]) ).
fof(f5499,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f957,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5497,plain,
spl0_536,
inference(avatar_split_clause,[],[f956,f5495]) ).
fof(f5495,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f956,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5493,plain,
spl0_535,
inference(avatar_split_clause,[],[f955,f5491]) ).
fof(f5491,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f955,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5489,plain,
spl0_534,
inference(avatar_split_clause,[],[f954,f5487]) ).
fof(f5487,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f954,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5485,plain,
spl0_533,
inference(avatar_split_clause,[],[f949,f5483]) ).
fof(f5483,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f949,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5481,plain,
spl0_532,
inference(avatar_split_clause,[],[f947,f5479]) ).
fof(f5479,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f947,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5477,plain,
spl0_531,
inference(avatar_split_clause,[],[f946,f5475]) ).
fof(f5475,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f946,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5473,plain,
spl0_530,
inference(avatar_split_clause,[],[f945,f5471]) ).
fof(f5471,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f945,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5469,plain,
spl0_529,
inference(avatar_split_clause,[],[f944,f5467]) ).
fof(f5467,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f944,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5465,plain,
spl0_528,
inference(avatar_split_clause,[],[f942,f5463]) ).
fof(f5463,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f942,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5461,plain,
spl0_527,
inference(avatar_split_clause,[],[f941,f5459]) ).
fof(f5459,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f941,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5457,plain,
spl0_526,
inference(avatar_split_clause,[],[f940,f5455]) ).
fof(f5455,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f940,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5453,plain,
spl0_525,
inference(avatar_split_clause,[],[f939,f5451]) ).
fof(f5451,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f939,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5449,plain,
spl0_524,
inference(avatar_split_clause,[],[f938,f5447]) ).
fof(f5447,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f938,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5445,plain,
spl0_523,
inference(avatar_split_clause,[],[f937,f5443]) ).
fof(f5443,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f937,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5441,plain,
spl0_522,
inference(avatar_split_clause,[],[f936,f5439]) ).
fof(f5439,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f936,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5437,plain,
spl0_521,
inference(avatar_split_clause,[],[f935,f5435]) ).
fof(f5435,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f935,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5433,plain,
spl0_520,
inference(avatar_split_clause,[],[f934,f5431]) ).
fof(f5431,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f934,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5429,plain,
spl0_519,
inference(avatar_split_clause,[],[f933,f5427]) ).
fof(f5427,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f933,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5425,plain,
spl0_518,
inference(avatar_split_clause,[],[f932,f5423]) ).
fof(f5423,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f932,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5421,plain,
spl0_517,
inference(avatar_split_clause,[],[f931,f5419]) ).
fof(f5419,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f931,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5417,plain,
spl0_516,
inference(avatar_split_clause,[],[f930,f5415]) ).
fof(f5415,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f930,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5413,plain,
spl0_515,
inference(avatar_split_clause,[],[f929,f5411]) ).
fof(f5411,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f929,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5409,plain,
spl0_514,
inference(avatar_split_clause,[],[f928,f5407]) ).
fof(f5407,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f928,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5405,plain,
spl0_513,
inference(avatar_split_clause,[],[f927,f5403]) ).
fof(f5403,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f927,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5401,plain,
spl0_512,
inference(avatar_split_clause,[],[f926,f5399]) ).
fof(f5399,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f926,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5397,plain,
spl0_511,
inference(avatar_split_clause,[],[f925,f5395]) ).
fof(f5395,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f925,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5393,plain,
spl0_510,
inference(avatar_split_clause,[],[f924,f5391]) ).
fof(f5391,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f924,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5389,plain,
spl0_509,
inference(avatar_split_clause,[],[f923,f5387]) ).
fof(f5387,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f923,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5385,plain,
spl0_508,
inference(avatar_split_clause,[],[f922,f5383]) ).
fof(f5383,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f922,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5381,plain,
spl0_507,
inference(avatar_split_clause,[],[f921,f5379]) ).
fof(f5379,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f921,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5377,plain,
spl0_506,
inference(avatar_split_clause,[],[f920,f5375]) ).
fof(f5375,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f920,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5373,plain,
spl0_505,
inference(avatar_split_clause,[],[f919,f5371]) ).
fof(f5371,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f919,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5369,plain,
spl0_504,
inference(avatar_split_clause,[],[f918,f5367]) ).
fof(f5367,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f918,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5365,plain,
spl0_503,
inference(avatar_split_clause,[],[f917,f5363]) ).
fof(f5363,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f917,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5361,plain,
spl0_502,
inference(avatar_split_clause,[],[f916,f5359]) ).
fof(f5359,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f916,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5357,plain,
spl0_501,
inference(avatar_split_clause,[],[f915,f5355]) ).
fof(f5355,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f915,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5353,plain,
spl0_500,
inference(avatar_split_clause,[],[f914,f5351]) ).
fof(f5351,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f914,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5349,plain,
spl0_499,
inference(avatar_split_clause,[],[f913,f5347]) ).
fof(f5347,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f913,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5345,plain,
spl0_498,
inference(avatar_split_clause,[],[f912,f5343]) ).
fof(f5343,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f912,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5341,plain,
spl0_497,
inference(avatar_split_clause,[],[f911,f5339]) ).
fof(f5339,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f911,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5337,plain,
spl0_496,
inference(avatar_split_clause,[],[f910,f5335]) ).
fof(f5335,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f910,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5333,plain,
spl0_495,
inference(avatar_split_clause,[],[f909,f5331]) ).
fof(f5331,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f909,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5329,plain,
spl0_494,
inference(avatar_split_clause,[],[f908,f5327]) ).
fof(f5327,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f908,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5325,plain,
spl0_493,
inference(avatar_split_clause,[],[f905,f5323]) ).
fof(f5323,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f905,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5321,plain,
spl0_492,
inference(avatar_split_clause,[],[f903,f5319]) ).
fof(f5319,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f903,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5317,plain,
spl0_491,
inference(avatar_split_clause,[],[f902,f5315]) ).
fof(f5315,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f902,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5313,plain,
spl0_490,
inference(avatar_split_clause,[],[f900,f5311]) ).
fof(f5311,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f900,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5309,plain,
spl0_489,
inference(avatar_split_clause,[],[f897,f5307]) ).
fof(f5307,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f897,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5305,plain,
spl0_488,
inference(avatar_split_clause,[],[f896,f5303]) ).
fof(f5303,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f896,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5301,plain,
spl0_487,
inference(avatar_split_clause,[],[f895,f5299]) ).
fof(f5299,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f895,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5297,plain,
spl0_486,
inference(avatar_split_clause,[],[f893,f5295]) ).
fof(f5295,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f893,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5293,plain,
spl0_485,
inference(avatar_split_clause,[],[f892,f5291]) ).
fof(f5291,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f892,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5289,plain,
spl0_484,
inference(avatar_split_clause,[],[f891,f5287]) ).
fof(f5287,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f891,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5285,plain,
spl0_483,
inference(avatar_split_clause,[],[f888,f5283]) ).
fof(f5283,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f888,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5281,plain,
spl0_482,
inference(avatar_split_clause,[],[f887,f5279]) ).
fof(f5279,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f887,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5277,plain,
spl0_481,
inference(avatar_split_clause,[],[f886,f5275]) ).
fof(f5275,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f886,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5273,plain,
spl0_480,
inference(avatar_split_clause,[],[f885,f5271]) ).
fof(f5271,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f885,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5269,plain,
spl0_479,
inference(avatar_split_clause,[],[f883,f5267]) ).
fof(f5267,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f883,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5265,plain,
spl0_478,
inference(avatar_split_clause,[],[f882,f5263]) ).
fof(f5263,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f882,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5261,plain,
spl0_477,
inference(avatar_split_clause,[],[f881,f5259]) ).
fof(f5259,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f881,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5257,plain,
spl0_476,
inference(avatar_split_clause,[],[f880,f5255]) ).
fof(f5255,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f880,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5253,plain,
spl0_475,
inference(avatar_split_clause,[],[f879,f5251]) ).
fof(f5251,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f879,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5249,plain,
spl0_474,
inference(avatar_split_clause,[],[f878,f5247]) ).
fof(f5247,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f878,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5245,plain,
spl0_473,
inference(avatar_split_clause,[],[f877,f5243]) ).
fof(f5243,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f877,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5241,plain,
spl0_472,
inference(avatar_split_clause,[],[f876,f5239]) ).
fof(f5239,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f876,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5237,plain,
spl0_471,
inference(avatar_split_clause,[],[f875,f5235]) ).
fof(f5235,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f875,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5233,plain,
spl0_470,
inference(avatar_split_clause,[],[f874,f5231]) ).
fof(f5231,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f874,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5229,plain,
spl0_469,
inference(avatar_split_clause,[],[f873,f5227]) ).
fof(f5227,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f873,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5225,plain,
spl0_468,
inference(avatar_split_clause,[],[f872,f5223]) ).
fof(f5223,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f872,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5221,plain,
spl0_467,
inference(avatar_split_clause,[],[f871,f5219]) ).
fof(f5219,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f871,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5217,plain,
spl0_466,
inference(avatar_split_clause,[],[f870,f5215]) ).
fof(f5215,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f870,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5213,plain,
spl0_465,
inference(avatar_split_clause,[],[f869,f5211]) ).
fof(f5211,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f869,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5209,plain,
spl0_464,
inference(avatar_split_clause,[],[f868,f5207]) ).
fof(f5207,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f868,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5205,plain,
spl0_463,
inference(avatar_split_clause,[],[f867,f5203]) ).
fof(f5203,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f867,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5201,plain,
spl0_462,
inference(avatar_split_clause,[],[f865,f5199]) ).
fof(f5199,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f865,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5197,plain,
spl0_461,
inference(avatar_split_clause,[],[f864,f5195]) ).
fof(f5195,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f864,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5193,plain,
spl0_460,
inference(avatar_split_clause,[],[f863,f5191]) ).
fof(f5191,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f863,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5189,plain,
spl0_459,
inference(avatar_split_clause,[],[f862,f5187]) ).
fof(f5187,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f862,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5185,plain,
spl0_458,
inference(avatar_split_clause,[],[f861,f5183]) ).
fof(f5183,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f861,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5181,plain,
spl0_457,
inference(avatar_split_clause,[],[f856,f5179]) ).
fof(f5179,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f856,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5177,plain,
spl0_456,
inference(avatar_split_clause,[],[f855,f5175]) ).
fof(f5175,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f855,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5173,plain,
spl0_455,
inference(avatar_split_clause,[],[f854,f5171]) ).
fof(f5171,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f854,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5169,plain,
spl0_454,
inference(avatar_split_clause,[],[f853,f5167]) ).
fof(f5167,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f853,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5165,plain,
spl0_453,
inference(avatar_split_clause,[],[f852,f5163]) ).
fof(f5163,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f852,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5161,plain,
spl0_452,
inference(avatar_split_clause,[],[f851,f5159]) ).
fof(f5159,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f851,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5157,plain,
spl0_451,
inference(avatar_split_clause,[],[f850,f5155]) ).
fof(f5155,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f850,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5153,plain,
spl0_450,
inference(avatar_split_clause,[],[f849,f5151]) ).
fof(f5151,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f849,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5149,plain,
spl0_449,
inference(avatar_split_clause,[],[f847,f5147]) ).
fof(f5147,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f847,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5145,plain,
spl0_448,
inference(avatar_split_clause,[],[f846,f5143]) ).
fof(f5143,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f846,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5141,plain,
spl0_447,
inference(avatar_split_clause,[],[f845,f5139]) ).
fof(f5139,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f845,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5137,plain,
spl0_446,
inference(avatar_split_clause,[],[f844,f5135]) ).
fof(f5135,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f844,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5133,plain,
spl0_445,
inference(avatar_split_clause,[],[f843,f5131]) ).
fof(f5131,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f843,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5129,plain,
spl0_444,
inference(avatar_split_clause,[],[f842,f5127]) ).
fof(f5127,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f842,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5125,plain,
spl0_443,
inference(avatar_split_clause,[],[f840,f5123]) ).
fof(f5123,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f840,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5121,plain,
spl0_442,
inference(avatar_split_clause,[],[f839,f5119]) ).
fof(f5119,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f839,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5117,plain,
spl0_441,
inference(avatar_split_clause,[],[f838,f5115]) ).
fof(f5115,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f838,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5113,plain,
spl0_440,
inference(avatar_split_clause,[],[f837,f5111]) ).
fof(f5111,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f837,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5109,plain,
spl0_439,
inference(avatar_split_clause,[],[f836,f5107]) ).
fof(f5107,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f836,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5105,plain,
spl0_438,
inference(avatar_split_clause,[],[f835,f5103]) ).
fof(f5103,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f835,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5101,plain,
spl0_437,
inference(avatar_split_clause,[],[f834,f5099]) ).
fof(f5099,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f834,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5097,plain,
spl0_436,
inference(avatar_split_clause,[],[f833,f5095]) ).
fof(f5095,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f833,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5093,plain,
spl0_435,
inference(avatar_split_clause,[],[f832,f5091]) ).
fof(f5091,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f832,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5089,plain,
spl0_434,
inference(avatar_split_clause,[],[f831,f5087]) ).
fof(f5087,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f831,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5085,plain,
spl0_433,
inference(avatar_split_clause,[],[f830,f5083]) ).
fof(f5083,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f830,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5081,plain,
spl0_432,
inference(avatar_split_clause,[],[f829,f5079]) ).
fof(f5079,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f829,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5077,plain,
spl0_431,
inference(avatar_split_clause,[],[f828,f5075]) ).
fof(f5075,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f828,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5073,plain,
spl0_430,
inference(avatar_split_clause,[],[f827,f5071]) ).
fof(f5071,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f827,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5069,plain,
spl0_429,
inference(avatar_split_clause,[],[f826,f5067]) ).
fof(f5067,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f826,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5065,plain,
spl0_428,
inference(avatar_split_clause,[],[f825,f5063]) ).
fof(f5063,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f825,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5061,plain,
spl0_427,
inference(avatar_split_clause,[],[f824,f5059]) ).
fof(f5059,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f824,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5057,plain,
spl0_426,
inference(avatar_split_clause,[],[f823,f5055]) ).
fof(f5055,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f823,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5053,plain,
spl0_425,
inference(avatar_split_clause,[],[f822,f5051]) ).
fof(f5051,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f822,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5049,plain,
spl0_424,
inference(avatar_split_clause,[],[f821,f5047]) ).
fof(f5047,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f821,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5045,plain,
spl0_423,
inference(avatar_split_clause,[],[f820,f5043]) ).
fof(f5043,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f820,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5041,plain,
spl0_422,
inference(avatar_split_clause,[],[f819,f5039]) ).
fof(f5039,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f819,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5037,plain,
spl0_421,
inference(avatar_split_clause,[],[f816,f5035]) ).
fof(f5035,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f816,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5033,plain,
spl0_420,
inference(avatar_split_clause,[],[f814,f5031]) ).
fof(f5031,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f814,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5029,plain,
spl0_419,
inference(avatar_split_clause,[],[f812,f5027]) ).
fof(f5027,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f812,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5025,plain,
spl0_418,
inference(avatar_split_clause,[],[f809,f5023]) ).
fof(f5023,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f809,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5021,plain,
spl0_417,
inference(avatar_split_clause,[],[f808,f5019]) ).
fof(f5019,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f808,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5017,plain,
spl0_416,
inference(avatar_split_clause,[],[f807,f5015]) ).
fof(f5015,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f807,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5013,plain,
spl0_415,
inference(avatar_split_clause,[],[f806,f5011]) ).
fof(f5011,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f806,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5009,plain,
spl0_414,
inference(avatar_split_clause,[],[f804,f5007]) ).
fof(f5007,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f804,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5005,plain,
spl0_413,
inference(avatar_split_clause,[],[f803,f5003]) ).
fof(f5003,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f803,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5001,plain,
spl0_412,
inference(avatar_split_clause,[],[f802,f4999]) ).
fof(f4999,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f802,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4997,plain,
spl0_411,
inference(avatar_split_clause,[],[f801,f4995]) ).
fof(f4995,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f801,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4993,plain,
spl0_410,
inference(avatar_split_clause,[],[f800,f4991]) ).
fof(f4991,plain,
( spl0_410
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f800,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4989,plain,
spl0_409,
inference(avatar_split_clause,[],[f799,f4987]) ).
fof(f4987,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f799,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4985,plain,
spl0_408,
inference(avatar_split_clause,[],[f798,f4983]) ).
fof(f4983,plain,
( spl0_408
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f798,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4981,plain,
spl0_407,
inference(avatar_split_clause,[],[f797,f4979]) ).
fof(f4979,plain,
( spl0_407
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f797,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4977,plain,
spl0_406,
inference(avatar_split_clause,[],[f796,f4975]) ).
fof(f4975,plain,
( spl0_406
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f796,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4973,plain,
spl0_405,
inference(avatar_split_clause,[],[f732,f4971]) ).
fof(f4971,plain,
( spl0_405
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f732,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4969,plain,
spl0_404,
inference(avatar_split_clause,[],[f729,f4967]) ).
fof(f4967,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f729,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4965,plain,
spl0_403,
inference(avatar_split_clause,[],[f728,f4963]) ).
fof(f4963,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f728,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4961,plain,
spl0_402,
inference(avatar_split_clause,[],[f727,f4959]) ).
fof(f4959,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f727,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4957,plain,
spl0_401,
inference(avatar_split_clause,[],[f726,f4955]) ).
fof(f4955,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f726,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4953,plain,
spl0_400,
inference(avatar_split_clause,[],[f725,f4951]) ).
fof(f4951,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f725,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4949,plain,
spl0_399,
inference(avatar_split_clause,[],[f724,f4947]) ).
fof(f4947,plain,
( spl0_399
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f724,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4945,plain,
spl0_398,
inference(avatar_split_clause,[],[f723,f4943]) ).
fof(f4943,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f723,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4941,plain,
spl0_397,
inference(avatar_split_clause,[],[f722,f4939]) ).
fof(f4939,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f722,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4937,plain,
spl0_396,
inference(avatar_split_clause,[],[f721,f4935]) ).
fof(f4935,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f721,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4933,plain,
spl0_395,
inference(avatar_split_clause,[],[f720,f4931]) ).
fof(f4931,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f720,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4929,plain,
spl0_394,
inference(avatar_split_clause,[],[f719,f4927]) ).
fof(f4927,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f719,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4925,plain,
spl0_393,
inference(avatar_split_clause,[],[f718,f4923]) ).
fof(f4923,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f718,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4921,plain,
spl0_392,
inference(avatar_split_clause,[],[f716,f4919]) ).
fof(f4919,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f716,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4917,plain,
spl0_391,
inference(avatar_split_clause,[],[f715,f4915]) ).
fof(f4915,plain,
( spl0_391
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f715,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4913,plain,
spl0_390,
inference(avatar_split_clause,[],[f714,f4911]) ).
fof(f4911,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f714,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4909,plain,
spl0_389,
inference(avatar_split_clause,[],[f713,f4907]) ).
fof(f4907,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f713,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4905,plain,
spl0_388,
inference(avatar_split_clause,[],[f712,f4903]) ).
fof(f4903,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f712,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4901,plain,
spl0_387,
inference(avatar_split_clause,[],[f711,f4899]) ).
fof(f4899,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f711,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4897,plain,
spl0_386,
inference(avatar_split_clause,[],[f710,f4895]) ).
fof(f4895,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f710,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4893,plain,
spl0_385,
inference(avatar_split_clause,[],[f709,f4891]) ).
fof(f4891,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f709,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4889,plain,
spl0_384,
inference(avatar_split_clause,[],[f706,f4887]) ).
fof(f4887,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f706,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4885,plain,
spl0_383,
inference(avatar_split_clause,[],[f705,f4883]) ).
fof(f4883,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f705,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4881,plain,
spl0_382,
inference(avatar_split_clause,[],[f704,f4879]) ).
fof(f4879,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f704,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4877,plain,
spl0_381,
inference(avatar_split_clause,[],[f703,f4875]) ).
fof(f4875,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f703,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4873,plain,
spl0_380,
inference(avatar_split_clause,[],[f702,f4871]) ).
fof(f4871,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f702,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4869,plain,
spl0_379,
inference(avatar_split_clause,[],[f701,f4867]) ).
fof(f4867,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f701,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4865,plain,
spl0_378,
inference(avatar_split_clause,[],[f700,f4863]) ).
fof(f4863,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f700,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4861,plain,
spl0_377,
inference(avatar_split_clause,[],[f698,f4859]) ).
fof(f4859,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f698,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4857,plain,
spl0_376,
inference(avatar_split_clause,[],[f697,f4855]) ).
fof(f4855,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f697,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4853,plain,
spl0_375,
inference(avatar_split_clause,[],[f696,f4851]) ).
fof(f4851,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f696,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4849,plain,
spl0_374,
inference(avatar_split_clause,[],[f695,f4847]) ).
fof(f4847,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f695,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4845,plain,
spl0_373,
inference(avatar_split_clause,[],[f694,f4843]) ).
fof(f4843,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f694,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4841,plain,
spl0_372,
inference(avatar_split_clause,[],[f693,f4839]) ).
fof(f4839,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f693,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4837,plain,
spl0_371,
inference(avatar_split_clause,[],[f692,f4835]) ).
fof(f4835,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f692,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4833,plain,
spl0_370,
inference(avatar_split_clause,[],[f691,f4831]) ).
fof(f4831,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f691,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4829,plain,
spl0_369,
inference(avatar_split_clause,[],[f688,f4827]) ).
fof(f4827,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f688,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4825,plain,
spl0_368,
inference(avatar_split_clause,[],[f686,f4823]) ).
fof(f4823,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f686,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4821,plain,
spl0_367,
inference(avatar_split_clause,[],[f685,f4819]) ).
fof(f4819,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f685,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4817,plain,
spl0_366,
inference(avatar_split_clause,[],[f683,f4815]) ).
fof(f4815,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f683,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4813,plain,
spl0_365,
inference(avatar_split_clause,[],[f680,f4811]) ).
fof(f4811,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f680,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4809,plain,
spl0_364,
inference(avatar_split_clause,[],[f679,f4807]) ).
fof(f4807,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f679,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4805,plain,
spl0_363,
inference(avatar_split_clause,[],[f678,f4803]) ).
fof(f4803,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f678,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4801,plain,
spl0_362,
inference(avatar_split_clause,[],[f677,f4799]) ).
fof(f4799,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f677,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4797,plain,
spl0_361,
inference(avatar_split_clause,[],[f676,f4795]) ).
fof(f4795,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f676,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4793,plain,
spl0_360,
inference(avatar_split_clause,[],[f675,f4791]) ).
fof(f4791,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f675,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4789,plain,
spl0_359,
inference(avatar_split_clause,[],[f674,f4787]) ).
fof(f4787,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f674,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4785,plain,
spl0_358,
inference(avatar_split_clause,[],[f673,f4783]) ).
fof(f4783,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f673,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4781,plain,
spl0_357,
inference(avatar_split_clause,[],[f672,f4779]) ).
fof(f4779,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f672,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4777,plain,
spl0_356,
inference(avatar_split_clause,[],[f671,f4775]) ).
fof(f4775,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f671,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4773,plain,
spl0_355,
inference(avatar_split_clause,[],[f670,f4771]) ).
fof(f4771,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f670,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4769,plain,
spl0_354,
inference(avatar_split_clause,[],[f668,f4767]) ).
fof(f4767,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f668,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4765,plain,
spl0_353,
inference(avatar_split_clause,[],[f666,f4763]) ).
fof(f4763,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f666,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4761,plain,
spl0_352,
inference(avatar_split_clause,[],[f663,f4759]) ).
fof(f4759,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f663,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4757,plain,
spl0_351,
inference(avatar_split_clause,[],[f661,f4755]) ).
fof(f4755,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f661,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4753,plain,
spl0_350,
inference(avatar_split_clause,[],[f659,f4751]) ).
fof(f4751,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f659,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4749,plain,
spl0_349,
inference(avatar_split_clause,[],[f656,f4747]) ).
fof(f4747,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f656,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4745,plain,
spl0_348,
inference(avatar_split_clause,[],[f655,f4743]) ).
fof(f4743,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f655,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4741,plain,
spl0_347,
inference(avatar_split_clause,[],[f654,f4739]) ).
fof(f4739,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f654,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4737,plain,
spl0_346,
inference(avatar_split_clause,[],[f653,f4735]) ).
fof(f4735,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f653,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4733,plain,
spl0_345,
inference(avatar_split_clause,[],[f651,f4731]) ).
fof(f4731,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f651,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4729,plain,
spl0_344,
inference(avatar_split_clause,[],[f650,f4727]) ).
fof(f4727,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f650,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4725,plain,
spl0_343,
inference(avatar_split_clause,[],[f649,f4723]) ).
fof(f4723,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f649,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4721,plain,
spl0_342,
inference(avatar_split_clause,[],[f648,f4719]) ).
fof(f4719,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f648,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4717,plain,
spl0_341,
inference(avatar_split_clause,[],[f647,f4715]) ).
fof(f4715,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f647,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4713,plain,
spl0_340,
inference(avatar_split_clause,[],[f646,f4711]) ).
fof(f4711,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f646,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4709,plain,
spl0_339,
inference(avatar_split_clause,[],[f645,f4707]) ).
fof(f4707,plain,
( spl0_339
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f645,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4705,plain,
spl0_338,
inference(avatar_split_clause,[],[f644,f4703]) ).
fof(f4703,plain,
( spl0_338
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f644,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4701,plain,
spl0_337,
inference(avatar_split_clause,[],[f643,f4699]) ).
fof(f4699,plain,
( spl0_337
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f643,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4697,plain,
spl0_336,
inference(avatar_split_clause,[],[f607,f4695]) ).
fof(f4695,plain,
( spl0_336
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f607,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4693,plain,
spl0_335,
inference(avatar_split_clause,[],[f606,f4691]) ).
fof(f4691,plain,
( spl0_335
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f606,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4689,plain,
spl0_334,
inference(avatar_split_clause,[],[f605,f4687]) ).
fof(f4687,plain,
( spl0_334
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f605,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4685,plain,
spl0_333,
inference(avatar_split_clause,[],[f604,f4683]) ).
fof(f4683,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f604,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4681,plain,
spl0_332,
inference(avatar_split_clause,[],[f603,f4679]) ).
fof(f4679,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f603,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4677,plain,
spl0_331,
inference(avatar_split_clause,[],[f601,f4675]) ).
fof(f4675,plain,
( spl0_331
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f601,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4673,plain,
spl0_330,
inference(avatar_split_clause,[],[f600,f4671]) ).
fof(f4671,plain,
( spl0_330
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f600,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4669,plain,
spl0_329,
inference(avatar_split_clause,[],[f599,f4667]) ).
fof(f4667,plain,
( spl0_329
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f599,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4665,plain,
spl0_328,
inference(avatar_split_clause,[],[f598,f4663]) ).
fof(f4663,plain,
( spl0_328
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f598,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4661,plain,
spl0_327,
inference(avatar_split_clause,[],[f597,f4659]) ).
fof(f4659,plain,
( spl0_327
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f597,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4657,plain,
spl0_326,
inference(avatar_split_clause,[],[f596,f4655]) ).
fof(f4655,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f596,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4653,plain,
spl0_325,
inference(avatar_split_clause,[],[f595,f4651]) ).
fof(f4651,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f595,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4649,plain,
spl0_324,
inference(avatar_split_clause,[],[f592,f4647]) ).
fof(f4647,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f592,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4645,plain,
spl0_323,
inference(avatar_split_clause,[],[f591,f4643]) ).
fof(f4643,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f591,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4641,plain,
spl0_322,
inference(avatar_split_clause,[],[f586,f4639]) ).
fof(f4639,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f586,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4637,plain,
spl0_321,
inference(avatar_split_clause,[],[f585,f4635]) ).
fof(f4635,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f585,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4633,plain,
spl0_320,
inference(avatar_split_clause,[],[f582,f4631]) ).
fof(f4631,plain,
( spl0_320
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f582,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4629,plain,
spl0_319,
inference(avatar_split_clause,[],[f581,f4627]) ).
fof(f4627,plain,
( spl0_319
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f581,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4625,plain,
spl0_318,
inference(avatar_split_clause,[],[f579,f4623]) ).
fof(f4623,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f579,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4621,plain,
spl0_317,
inference(avatar_split_clause,[],[f578,f4619]) ).
fof(f4619,plain,
( spl0_317
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f578,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4617,plain,
spl0_316,
inference(avatar_split_clause,[],[f577,f4615]) ).
fof(f4615,plain,
( spl0_316
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f577,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4613,plain,
spl0_315,
inference(avatar_split_clause,[],[f576,f4611]) ).
fof(f4611,plain,
( spl0_315
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f576,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4609,plain,
spl0_314,
inference(avatar_split_clause,[],[f575,f4607]) ).
fof(f4607,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f575,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4605,plain,
spl0_313,
inference(avatar_split_clause,[],[f574,f4603]) ).
fof(f4603,plain,
( spl0_313
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f574,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4601,plain,
spl0_312,
inference(avatar_split_clause,[],[f570,f4599]) ).
fof(f4599,plain,
( spl0_312
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f570,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4597,plain,
spl0_311,
inference(avatar_split_clause,[],[f568,f4595]) ).
fof(f4595,plain,
( spl0_311
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f568,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4593,plain,
spl0_310,
inference(avatar_split_clause,[],[f565,f4591]) ).
fof(f4591,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f565,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4589,plain,
spl0_309,
inference(avatar_split_clause,[],[f562,f4587]) ).
fof(f4587,plain,
( spl0_309
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f562,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4585,plain,
spl0_308,
inference(avatar_split_clause,[],[f561,f4583]) ).
fof(f4583,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f561,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4581,plain,
spl0_307,
inference(avatar_split_clause,[],[f559,f4579]) ).
fof(f4579,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f559,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4577,plain,
spl0_306,
inference(avatar_split_clause,[],[f558,f4575]) ).
fof(f4575,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f558,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4573,plain,
spl0_305,
inference(avatar_split_clause,[],[f557,f4571]) ).
fof(f4571,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f557,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4569,plain,
spl0_304,
inference(avatar_split_clause,[],[f554,f4567]) ).
fof(f4567,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f554,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4565,plain,
spl0_303,
inference(avatar_split_clause,[],[f553,f4563]) ).
fof(f4563,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f553,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4561,plain,
spl0_302,
inference(avatar_split_clause,[],[f551,f4559]) ).
fof(f4559,plain,
( spl0_302
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f551,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4557,plain,
spl0_301,
inference(avatar_split_clause,[],[f545,f4555]) ).
fof(f4555,plain,
( spl0_301
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f545,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4553,plain,
spl0_300,
inference(avatar_split_clause,[],[f544,f4551]) ).
fof(f4551,plain,
( spl0_300
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f544,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4549,plain,
spl0_299,
inference(avatar_split_clause,[],[f542,f4547]) ).
fof(f4547,plain,
( spl0_299
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f542,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4545,plain,
spl0_298,
inference(avatar_split_clause,[],[f541,f4543]) ).
fof(f4543,plain,
( spl0_298
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f541,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4541,plain,
spl0_297,
inference(avatar_split_clause,[],[f534,f4539]) ).
fof(f4539,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f534,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4537,plain,
spl0_296,
inference(avatar_split_clause,[],[f533,f4535]) ).
fof(f4535,plain,
( spl0_296
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f533,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4533,plain,
spl0_295,
inference(avatar_split_clause,[],[f531,f4531]) ).
fof(f4531,plain,
( spl0_295
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f531,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4529,plain,
spl0_294,
inference(avatar_split_clause,[],[f530,f4527]) ).
fof(f4527,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f530,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4525,plain,
spl0_293,
inference(avatar_split_clause,[],[f529,f4523]) ).
fof(f4523,plain,
( spl0_293
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f529,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4521,plain,
spl0_292,
inference(avatar_split_clause,[],[f527,f4519]) ).
fof(f4519,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f527,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4517,plain,
spl0_291,
inference(avatar_split_clause,[],[f526,f4515]) ).
fof(f4515,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f526,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4513,plain,
spl0_290,
inference(avatar_split_clause,[],[f525,f4511]) ).
fof(f4511,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f525,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4509,plain,
spl0_289,
inference(avatar_split_clause,[],[f524,f4507]) ).
fof(f4507,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f524,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4505,plain,
spl0_288,
inference(avatar_split_clause,[],[f523,f4503]) ).
fof(f4503,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f523,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4501,plain,
spl0_287,
inference(avatar_split_clause,[],[f522,f4499]) ).
fof(f4499,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f522,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4497,plain,
spl0_286,
inference(avatar_split_clause,[],[f521,f4495]) ).
fof(f4495,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f521,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4493,plain,
spl0_285,
inference(avatar_split_clause,[],[f520,f4491]) ).
fof(f4491,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f520,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4489,plain,
spl0_284,
inference(avatar_split_clause,[],[f519,f4487]) ).
fof(f4487,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f519,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4485,plain,
spl0_283,
inference(avatar_split_clause,[],[f518,f4483]) ).
fof(f4483,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f518,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4481,plain,
spl0_282,
inference(avatar_split_clause,[],[f515,f4479]) ).
fof(f4479,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f515,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4477,plain,
spl0_281,
inference(avatar_split_clause,[],[f513,f4475]) ).
fof(f4475,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f513,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4473,plain,
spl0_280,
inference(avatar_split_clause,[],[f511,f4471]) ).
fof(f4471,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f511,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4469,plain,
spl0_279,
inference(avatar_split_clause,[],[f508,f4467]) ).
fof(f4467,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f508,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4465,plain,
spl0_278,
inference(avatar_split_clause,[],[f507,f4463]) ).
fof(f4463,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f507,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4461,plain,
spl0_277,
inference(avatar_split_clause,[],[f506,f4459]) ).
fof(f4459,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f506,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4457,plain,
spl0_276,
inference(avatar_split_clause,[],[f503,f4455]) ).
fof(f4455,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f503,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4453,plain,
spl0_275,
inference(avatar_split_clause,[],[f500,f4451]) ).
fof(f4451,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f500,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4449,plain,
spl0_274,
inference(avatar_split_clause,[],[f499,f4447]) ).
fof(f4447,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f499,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4445,plain,
spl0_273,
inference(avatar_split_clause,[],[f497,f4443]) ).
fof(f4443,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f497,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4441,plain,
spl0_272,
inference(avatar_split_clause,[],[f496,f4439]) ).
fof(f4439,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f496,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4437,plain,
spl0_271,
inference(avatar_split_clause,[],[f495,f4435]) ).
fof(f4435,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f495,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4433,plain,
spl0_270,
inference(avatar_split_clause,[],[f494,f4431]) ).
fof(f4431,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f494,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4429,plain,
spl0_269,
inference(avatar_split_clause,[],[f493,f4427]) ).
fof(f4427,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f493,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4425,plain,
spl0_268,
inference(avatar_split_clause,[],[f491,f4423]) ).
fof(f4423,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f491,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4421,plain,
spl0_267,
inference(avatar_split_clause,[],[f488,f4419]) ).
fof(f4419,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f488,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4417,plain,
spl0_266,
inference(avatar_split_clause,[],[f487,f4415]) ).
fof(f4415,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f487,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4413,plain,
spl0_265,
inference(avatar_split_clause,[],[f483,f4411]) ).
fof(f4411,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f483,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4409,plain,
spl0_264,
inference(avatar_split_clause,[],[f481,f4407]) ).
fof(f4407,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f481,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4405,plain,
spl0_263,
inference(avatar_split_clause,[],[f473,f4403]) ).
fof(f4403,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f473,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4401,plain,
spl0_262,
inference(avatar_split_clause,[],[f472,f4399]) ).
fof(f4399,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f472,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4397,plain,
spl0_261,
inference(avatar_split_clause,[],[f471,f4395]) ).
fof(f4395,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f471,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4393,plain,
spl0_260,
inference(avatar_split_clause,[],[f470,f4391]) ).
fof(f4391,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f470,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4389,plain,
spl0_259,
inference(avatar_split_clause,[],[f469,f4387]) ).
fof(f4387,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f469,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4385,plain,
spl0_258,
inference(avatar_split_clause,[],[f468,f4383]) ).
fof(f4383,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f468,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4381,plain,
spl0_257,
inference(avatar_split_clause,[],[f467,f4379]) ).
fof(f4379,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4377,plain,
spl0_256,
inference(avatar_split_clause,[],[f466,f4375]) ).
fof(f4375,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f466,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4373,plain,
spl0_255,
inference(avatar_split_clause,[],[f465,f4371]) ).
fof(f4371,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f465,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4369,plain,
spl0_254,
inference(avatar_split_clause,[],[f464,f4367]) ).
fof(f4367,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f464,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4365,plain,
spl0_253,
inference(avatar_split_clause,[],[f463,f4363]) ).
fof(f4363,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f463,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4361,plain,
spl0_252,
inference(avatar_split_clause,[],[f462,f4359]) ).
fof(f4359,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f462,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4357,plain,
spl0_251,
inference(avatar_split_clause,[],[f461,f4355]) ).
fof(f4355,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f461,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4353,plain,
spl0_250,
inference(avatar_split_clause,[],[f460,f4351]) ).
fof(f4351,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f460,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4349,plain,
spl0_249,
inference(avatar_split_clause,[],[f459,f4347]) ).
fof(f4347,plain,
( spl0_249
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f459,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4345,plain,
spl0_248,
inference(avatar_split_clause,[],[f458,f4343]) ).
fof(f4343,plain,
( spl0_248
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f458,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4341,plain,
spl0_247,
inference(avatar_split_clause,[],[f457,f4339]) ).
fof(f4339,plain,
( spl0_247
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f457,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4337,plain,
spl0_246,
inference(avatar_split_clause,[],[f454,f4335]) ).
fof(f4335,plain,
( spl0_246
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4333,plain,
spl0_245,
inference(avatar_split_clause,[],[f453,f4331]) ).
fof(f4331,plain,
( spl0_245
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4329,plain,
spl0_244,
inference(avatar_split_clause,[],[f452,f4327]) ).
fof(f4327,plain,
( spl0_244
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4325,plain,
spl0_243,
inference(avatar_split_clause,[],[f451,f4323]) ).
fof(f4323,plain,
( spl0_243
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f451,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4321,plain,
spl0_242,
inference(avatar_split_clause,[],[f450,f4319]) ).
fof(f4319,plain,
( spl0_242
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f450,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4317,plain,
spl0_241,
inference(avatar_split_clause,[],[f449,f4315]) ).
fof(f4315,plain,
( spl0_241
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4313,plain,
spl0_240,
inference(avatar_split_clause,[],[f446,f4311]) ).
fof(f4311,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f446,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4309,plain,
spl0_239,
inference(avatar_split_clause,[],[f445,f4307]) ).
fof(f4307,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f445,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4305,plain,
spl0_238,
inference(avatar_split_clause,[],[f441,f4303]) ).
fof(f4303,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f441,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4301,plain,
spl0_237,
inference(avatar_split_clause,[],[f440,f4299]) ).
fof(f4299,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f440,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4297,plain,
spl0_236,
inference(avatar_split_clause,[],[f439,f4295]) ).
fof(f4295,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f439,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4293,plain,
spl0_235,
inference(avatar_split_clause,[],[f436,f4291]) ).
fof(f4291,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f436,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4289,plain,
spl0_234,
inference(avatar_split_clause,[],[f434,f4287]) ).
fof(f4287,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f434,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4285,plain,
spl0_233,
inference(avatar_split_clause,[],[f433,f4283]) ).
fof(f4283,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f433,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4281,plain,
spl0_232,
inference(avatar_split_clause,[],[f432,f4279]) ).
fof(f4279,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f432,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4277,plain,
spl0_231,
inference(avatar_split_clause,[],[f431,f4275]) ).
fof(f4275,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f431,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4273,plain,
spl0_230,
inference(avatar_split_clause,[],[f430,f4271]) ).
fof(f4271,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f430,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4269,plain,
spl0_229,
inference(avatar_split_clause,[],[f426,f4267]) ).
fof(f4267,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f426,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4265,plain,
spl0_228,
inference(avatar_split_clause,[],[f425,f4263]) ).
fof(f4263,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f425,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4261,plain,
spl0_227,
inference(avatar_split_clause,[],[f424,f4259]) ).
fof(f4259,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f424,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4257,plain,
spl0_226,
inference(avatar_split_clause,[],[f421,f4255]) ).
fof(f4255,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f421,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4253,plain,
spl0_225,
inference(avatar_split_clause,[],[f419,f4251]) ).
fof(f4251,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f419,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4249,plain,
spl0_224,
inference(avatar_split_clause,[],[f417,f4247]) ).
fof(f4247,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f417,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4245,plain,
spl0_223,
inference(avatar_split_clause,[],[f416,f4243]) ).
fof(f4243,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f416,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4241,plain,
spl0_222,
inference(avatar_split_clause,[],[f415,f4239]) ).
fof(f4239,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f415,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4237,plain,
spl0_221,
inference(avatar_split_clause,[],[f414,f4235]) ).
fof(f4235,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f414,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4233,plain,
spl0_220,
inference(avatar_split_clause,[],[f413,f4231]) ).
fof(f4231,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f413,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4229,plain,
spl0_219,
inference(avatar_split_clause,[],[f411,f4227]) ).
fof(f4227,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f411,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4225,plain,
spl0_218,
inference(avatar_split_clause,[],[f410,f4223]) ).
fof(f4223,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f410,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4221,plain,
spl0_217,
inference(avatar_split_clause,[],[f407,f4219]) ).
fof(f4219,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f407,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4217,plain,
spl0_216,
inference(avatar_split_clause,[],[f405,f4215]) ).
fof(f4215,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f405,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4213,plain,
spl0_215,
inference(avatar_split_clause,[],[f404,f4211]) ).
fof(f4211,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f404,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4209,plain,
spl0_214,
inference(avatar_split_clause,[],[f403,f4207]) ).
fof(f4207,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f403,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4205,plain,
spl0_213,
inference(avatar_split_clause,[],[f402,f4203]) ).
fof(f4203,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f402,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4201,plain,
spl0_212,
inference(avatar_split_clause,[],[f401,f4199]) ).
fof(f4199,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f401,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4197,plain,
spl0_211,
inference(avatar_split_clause,[],[f400,f4195]) ).
fof(f4195,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f400,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4193,plain,
spl0_210,
inference(avatar_split_clause,[],[f399,f4191]) ).
fof(f4191,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f399,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4189,plain,
spl0_209,
inference(avatar_split_clause,[],[f398,f4187]) ).
fof(f4187,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f398,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4185,plain,
spl0_208,
inference(avatar_split_clause,[],[f397,f4183]) ).
fof(f4183,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f397,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4181,plain,
spl0_207,
inference(avatar_split_clause,[],[f394,f4179]) ).
fof(f4179,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f394,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4177,plain,
spl0_206,
inference(avatar_split_clause,[],[f393,f4175]) ).
fof(f4175,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f393,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4173,plain,
spl0_205,
inference(avatar_split_clause,[],[f392,f4171]) ).
fof(f4171,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f392,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4169,plain,
spl0_204,
inference(avatar_split_clause,[],[f391,f4167]) ).
fof(f4167,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f391,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4165,plain,
spl0_203,
inference(avatar_split_clause,[],[f390,f4163]) ).
fof(f4163,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f390,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4161,plain,
spl0_202,
inference(avatar_split_clause,[],[f389,f4159]) ).
fof(f4159,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f389,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4157,plain,
spl0_201,
inference(avatar_split_clause,[],[f387,f4155]) ).
fof(f4155,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f387,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4153,plain,
spl0_200,
inference(avatar_split_clause,[],[f385,f4151]) ).
fof(f4151,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f385,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4149,plain,
spl0_199,
inference(avatar_split_clause,[],[f384,f4147]) ).
fof(f4147,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f384,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4145,plain,
spl0_198,
inference(avatar_split_clause,[],[f383,f4143]) ).
fof(f4143,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f383,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4141,plain,
spl0_197,
inference(avatar_split_clause,[],[f382,f4139]) ).
fof(f4139,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f382,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4137,plain,
spl0_196,
inference(avatar_split_clause,[],[f379,f4135]) ).
fof(f4135,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f379,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4133,plain,
spl0_195,
inference(avatar_split_clause,[],[f377,f4131]) ).
fof(f4131,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f377,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4129,plain,
spl0_194,
inference(avatar_split_clause,[],[f376,f4127]) ).
fof(f4127,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f376,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4125,plain,
spl0_193,
inference(avatar_split_clause,[],[f375,f4123]) ).
fof(f4123,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f375,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4121,plain,
spl0_192,
inference(avatar_split_clause,[],[f374,f4119]) ).
fof(f4119,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f374,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4117,plain,
spl0_191,
inference(avatar_split_clause,[],[f373,f4115]) ).
fof(f4115,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f373,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4113,plain,
spl0_190,
inference(avatar_split_clause,[],[f372,f4111]) ).
fof(f4111,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f372,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4109,plain,
spl0_189,
inference(avatar_split_clause,[],[f371,f4107]) ).
fof(f4107,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f371,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4105,plain,
spl0_188,
inference(avatar_split_clause,[],[f370,f4103]) ).
fof(f4103,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f370,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4101,plain,
spl0_187,
inference(avatar_split_clause,[],[f368,f4099]) ).
fof(f4099,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f368,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4097,plain,
spl0_186,
inference(avatar_split_clause,[],[f366,f4095]) ).
fof(f4095,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f366,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4093,plain,
spl0_185,
inference(avatar_split_clause,[],[f365,f4091]) ).
fof(f4091,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f365,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4089,plain,
spl0_184,
inference(avatar_split_clause,[],[f364,f4087]) ).
fof(f4087,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f364,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4085,plain,
spl0_183,
inference(avatar_split_clause,[],[f363,f4083]) ).
fof(f4083,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f363,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4081,plain,
spl0_182,
inference(avatar_split_clause,[],[f360,f4079]) ).
fof(f4079,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f360,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4077,plain,
spl0_181,
inference(avatar_split_clause,[],[f358,f4075]) ).
fof(f4075,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f358,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4073,plain,
spl0_180,
inference(avatar_split_clause,[],[f357,f4071]) ).
fof(f4071,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f357,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4069,plain,
spl0_179,
inference(avatar_split_clause,[],[f356,f4067]) ).
fof(f4067,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f356,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4065,plain,
spl0_178,
inference(avatar_split_clause,[],[f355,f4063]) ).
fof(f4063,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f355,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4061,plain,
spl0_177,
inference(avatar_split_clause,[],[f354,f4059]) ).
fof(f4059,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f354,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4057,plain,
spl0_176,
inference(avatar_split_clause,[],[f353,f4055]) ).
fof(f4055,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f353,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4053,plain,
spl0_175,
inference(avatar_split_clause,[],[f352,f4051]) ).
fof(f4051,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f352,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4049,plain,
spl0_174,
inference(avatar_split_clause,[],[f350,f4047]) ).
fof(f4047,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f350,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4045,plain,
spl0_173,
inference(avatar_split_clause,[],[f348,f4043]) ).
fof(f4043,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f348,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4041,plain,
spl0_172,
inference(avatar_split_clause,[],[f347,f4039]) ).
fof(f4039,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f347,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4037,plain,
spl0_171,
inference(avatar_split_clause,[],[f346,f4035]) ).
fof(f4035,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f346,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4033,plain,
spl0_170,
inference(avatar_split_clause,[],[f345,f4031]) ).
fof(f4031,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f345,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4029,plain,
spl0_169,
inference(avatar_split_clause,[],[f344,f4027]) ).
fof(f4027,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f344,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4025,plain,
spl0_168,
inference(avatar_split_clause,[],[f343,f4023]) ).
fof(f4023,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f343,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4021,plain,
spl0_167,
inference(avatar_split_clause,[],[f340,f4019]) ).
fof(f4019,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f340,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4017,plain,
spl0_166,
inference(avatar_split_clause,[],[f338,f4015]) ).
fof(f4015,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f338,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4013,plain,
spl0_165,
inference(avatar_split_clause,[],[f337,f4011]) ).
fof(f4011,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f337,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4009,plain,
spl0_164,
inference(avatar_split_clause,[],[f336,f4007]) ).
fof(f4007,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f336,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4005,plain,
spl0_163,
inference(avatar_split_clause,[],[f335,f4003]) ).
fof(f4003,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f335,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4001,plain,
spl0_162,
inference(avatar_split_clause,[],[f334,f3999]) ).
fof(f3999,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f334,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3997,plain,
spl0_161,
inference(avatar_split_clause,[],[f333,f3995]) ).
fof(f3995,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f333,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3993,plain,
spl0_160,
inference(avatar_split_clause,[],[f332,f3991]) ).
fof(f3991,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f332,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3989,plain,
spl0_159,
inference(avatar_split_clause,[],[f330,f3987]) ).
fof(f3987,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f330,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3985,plain,
spl0_158,
inference(avatar_split_clause,[],[f328,f3983]) ).
fof(f3983,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f328,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3981,plain,
spl0_157,
inference(avatar_split_clause,[],[f327,f3979]) ).
fof(f3979,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f327,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3977,plain,
spl0_156,
inference(avatar_split_clause,[],[f326,f3975]) ).
fof(f3975,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f326,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3973,plain,
spl0_155,
inference(avatar_split_clause,[],[f323,f3971]) ).
fof(f3971,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f323,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3969,plain,
spl0_154,
inference(avatar_split_clause,[],[f321,f3967]) ).
fof(f3967,plain,
( spl0_154
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f321,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3965,plain,
spl0_153,
inference(avatar_split_clause,[],[f320,f3963]) ).
fof(f3963,plain,
( spl0_153
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f320,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3961,plain,
spl0_152,
inference(avatar_split_clause,[],[f319,f3959]) ).
fof(f3959,plain,
( spl0_152
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f319,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3957,plain,
spl0_151,
inference(avatar_split_clause,[],[f318,f3955]) ).
fof(f3955,plain,
( spl0_151
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f318,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3953,plain,
spl0_150,
inference(avatar_split_clause,[],[f314,f3951]) ).
fof(f3951,plain,
( spl0_150
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f314,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3949,plain,
spl0_149,
inference(avatar_split_clause,[],[f307,f3947]) ).
fof(f3947,plain,
( spl0_149
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f307,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3945,plain,
spl0_148,
inference(avatar_split_clause,[],[f299,f3943]) ).
fof(f3943,plain,
( spl0_148
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f299,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3941,plain,
spl0_147,
inference(avatar_split_clause,[],[f298,f3939]) ).
fof(f3939,plain,
( spl0_147
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f298,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3937,plain,
spl0_146,
inference(avatar_split_clause,[],[f293,f3935]) ).
fof(f3935,plain,
( spl0_146
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f293,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3933,plain,
spl0_145,
inference(avatar_split_clause,[],[f291,f3931]) ).
fof(f3931,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f291,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3929,plain,
spl0_144,
inference(avatar_split_clause,[],[f289,f3927]) ).
fof(f3927,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f289,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3925,plain,
spl0_143,
inference(avatar_split_clause,[],[f288,f3923]) ).
fof(f3923,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f288,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3921,plain,
spl0_142,
inference(avatar_split_clause,[],[f285,f3919]) ).
fof(f3919,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f285,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3917,plain,
spl0_141,
inference(avatar_split_clause,[],[f283,f3915]) ).
fof(f3915,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f283,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3913,plain,
spl0_140,
inference(avatar_split_clause,[],[f282,f3911]) ).
fof(f3911,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f282,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3909,plain,
spl0_139,
inference(avatar_split_clause,[],[f281,f3907]) ).
fof(f3907,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f281,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3905,plain,
spl0_138,
inference(avatar_split_clause,[],[f280,f3903]) ).
fof(f3903,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f280,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3901,plain,
spl0_137,
inference(avatar_split_clause,[],[f279,f3899]) ).
fof(f3899,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f279,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3897,plain,
spl0_136,
inference(avatar_split_clause,[],[f278,f3895]) ).
fof(f3895,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f278,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3893,plain,
spl0_135,
inference(avatar_split_clause,[],[f277,f3891]) ).
fof(f3891,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f277,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3889,plain,
spl0_134,
inference(avatar_split_clause,[],[f276,f3887]) ).
fof(f3887,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f276,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3885,plain,
spl0_133,
inference(avatar_split_clause,[],[f275,f3883]) ).
fof(f3883,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f275,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3881,plain,
spl0_132,
inference(avatar_split_clause,[],[f274,f3879]) ).
fof(f3879,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f274,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3877,plain,
spl0_131,
inference(avatar_split_clause,[],[f272,f3875]) ).
fof(f3875,plain,
( spl0_131
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f272,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3873,plain,
spl0_130,
inference(avatar_split_clause,[],[f271,f3871]) ).
fof(f3871,plain,
( spl0_130
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f271,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3869,plain,
spl0_129,
inference(avatar_split_clause,[],[f270,f3867]) ).
fof(f3867,plain,
( spl0_129
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f270,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3865,plain,
spl0_128,
inference(avatar_split_clause,[],[f269,f3863]) ).
fof(f3863,plain,
( spl0_128
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f269,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3861,plain,
spl0_127,
inference(avatar_split_clause,[],[f268,f3859]) ).
fof(f3859,plain,
( spl0_127
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f268,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3857,plain,
spl0_126,
inference(avatar_split_clause,[],[f267,f3855]) ).
fof(f3855,plain,
( spl0_126
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f267,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3853,plain,
spl0_125,
inference(avatar_split_clause,[],[f266,f3851]) ).
fof(f3851,plain,
( spl0_125
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f266,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3849,plain,
spl0_124,
inference(avatar_split_clause,[],[f264,f3847]) ).
fof(f3847,plain,
( spl0_124
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f264,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3845,plain,
spl0_123,
inference(avatar_split_clause,[],[f263,f3843]) ).
fof(f3843,plain,
( spl0_123
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f263,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3841,plain,
spl0_122,
inference(avatar_split_clause,[],[f260,f3839]) ).
fof(f3839,plain,
( spl0_122
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f260,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3837,plain,
spl0_121,
inference(avatar_split_clause,[],[f259,f3835]) ).
fof(f3835,plain,
( spl0_121
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f259,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3833,plain,
spl0_120,
inference(avatar_split_clause,[],[f258,f3831]) ).
fof(f3831,plain,
( spl0_120
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f258,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3829,plain,
spl0_119,
inference(avatar_split_clause,[],[f257,f3827]) ).
fof(f3827,plain,
( spl0_119
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3825,plain,
spl0_118,
inference(avatar_split_clause,[],[f256,f3823]) ).
fof(f3823,plain,
( spl0_118
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3821,plain,
spl0_117,
inference(avatar_split_clause,[],[f255,f3819]) ).
fof(f3819,plain,
( spl0_117
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f255,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3817,plain,
spl0_116,
inference(avatar_split_clause,[],[f254,f3815]) ).
fof(f3815,plain,
( spl0_116
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f254,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3813,plain,
spl0_115,
inference(avatar_split_clause,[],[f253,f3811]) ).
fof(f3811,plain,
( spl0_115
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f253,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3809,plain,
spl0_114,
inference(avatar_split_clause,[],[f98,f3807]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3805,plain,
spl0_113,
inference(avatar_split_clause,[],[f66,f3803]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3801,plain,
spl0_112,
inference(avatar_split_clause,[],[f64,f3799]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3797,plain,
spl0_111,
inference(avatar_split_clause,[],[f40,f3795]) ).
fof(f3795,plain,
( spl0_111
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f40,axiom,
! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3793,plain,
spl0_110,
inference(avatar_split_clause,[],[f39,f3791]) ).
fof(f3791,plain,
( spl0_110
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f39,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3789,plain,
spl0_109,
inference(avatar_split_clause,[],[f23,f3787]) ).
fof(f3787,plain,
( spl0_109
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f23,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3785,plain,
~ spl0_108,
inference(avatar_split_clause,[],[f2733,f3782]) ).
fof(f3782,plain,
( spl0_108
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2733,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).
fof(f3780,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f2629,f3777]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3775,plain,
~ spl0_106,
inference(avatar_split_clause,[],[f2310,f3772]) ).
fof(f3772,plain,
( spl0_106
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3770,plain,
spl0_105,
inference(avatar_split_clause,[],[f2303,f3767]) ).
fof(f3767,plain,
( spl0_105
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3765,plain,
spl0_104,
inference(avatar_split_clause,[],[f2290,f3762]) ).
fof(f3762,plain,
( spl0_104
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3760,plain,
~ spl0_103,
inference(avatar_split_clause,[],[f2159,f3757]) ).
fof(f3757,plain,
( spl0_103
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2159,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3755,plain,
spl0_102,
inference(avatar_split_clause,[],[f1706,f3753]) ).
fof(f3753,plain,
( spl0_102
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1706,axiom,
! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3751,plain,
spl0_101,
inference(avatar_split_clause,[],[f1551,f3749]) ).
fof(f3749,plain,
( spl0_101
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1551,axiom,
! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3747,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f1370,f3744]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3742,plain,
~ spl0_99,
inference(avatar_split_clause,[],[f1250,f3739]) ).
fof(f3739,plain,
( spl0_99
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1250,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3737,plain,
spl0_98,
inference(avatar_split_clause,[],[f249,f3735]) ).
fof(f3735,plain,
( spl0_98
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3733,plain,
spl0_97,
inference(avatar_split_clause,[],[f248,f3731]) ).
fof(f3731,plain,
( spl0_97
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3729,plain,
spl0_96,
inference(avatar_split_clause,[],[f126,f3726]) ).
fof(f3726,plain,
( spl0_96
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f126,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3724,plain,
spl0_95,
inference(avatar_split_clause,[],[f124,f3721]) ).
fof(f3721,plain,
( spl0_95
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f124,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3719,plain,
spl0_94,
inference(avatar_split_clause,[],[f123,f3717]) ).
fof(f3717,plain,
( spl0_94
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f123,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3715,plain,
~ spl0_93,
inference(avatar_split_clause,[],[f2826,f3712]) ).
fof(f2826,axiom,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3710,plain,
spl0_92,
inference(avatar_split_clause,[],[f244,f3707]) ).
fof(f3707,plain,
( spl0_92
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3705,plain,
spl0_91,
inference(avatar_split_clause,[],[f243,f3702]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3700,plain,
spl0_90,
inference(avatar_split_clause,[],[f242,f3697]) ).
fof(f3697,plain,
( spl0_90
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3695,plain,
spl0_89,
inference(avatar_split_clause,[],[f241,f3692]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3690,plain,
spl0_88,
inference(avatar_split_clause,[],[f239,f3687]) ).
fof(f3687,plain,
( spl0_88
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3685,plain,
spl0_87,
inference(avatar_split_clause,[],[f238,f3682]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3680,plain,
spl0_86,
inference(avatar_split_clause,[],[f236,f3677]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3675,plain,
spl0_85,
inference(avatar_split_clause,[],[f235,f3672]) ).
fof(f3672,plain,
( spl0_85
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3670,plain,
spl0_84,
inference(avatar_split_clause,[],[f234,f3667]) ).
fof(f3667,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3665,plain,
spl0_83,
inference(avatar_split_clause,[],[f233,f3662]) ).
fof(f3662,plain,
( spl0_83
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3660,plain,
spl0_82,
inference(avatar_split_clause,[],[f232,f3657]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3655,plain,
spl0_81,
inference(avatar_split_clause,[],[f231,f3652]) ).
fof(f3652,plain,
( spl0_81
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3650,plain,
spl0_80,
inference(avatar_split_clause,[],[f230,f3647]) ).
fof(f3647,plain,
( spl0_80
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3645,plain,
spl0_79,
inference(avatar_split_clause,[],[f229,f3642]) ).
fof(f3642,plain,
( spl0_79
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3640,plain,
spl0_78,
inference(avatar_split_clause,[],[f228,f3637]) ).
fof(f3637,plain,
( spl0_78
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3635,plain,
spl0_77,
inference(avatar_split_clause,[],[f227,f3632]) ).
fof(f3632,plain,
( spl0_77
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3630,plain,
spl0_76,
inference(avatar_split_clause,[],[f226,f3627]) ).
fof(f3627,plain,
( spl0_76
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3625,plain,
spl0_75,
inference(avatar_split_clause,[],[f225,f3622]) ).
fof(f3622,plain,
( spl0_75
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3620,plain,
spl0_74,
inference(avatar_split_clause,[],[f224,f3617]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3615,plain,
spl0_73,
inference(avatar_split_clause,[],[f223,f3612]) ).
fof(f3612,plain,
( spl0_73
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3610,plain,
spl0_72,
inference(avatar_split_clause,[],[f222,f3607]) ).
fof(f3607,plain,
( spl0_72
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3605,plain,
spl0_71,
inference(avatar_split_clause,[],[f221,f3602]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3600,plain,
spl0_70,
inference(avatar_split_clause,[],[f220,f3597]) ).
fof(f3597,plain,
( spl0_70
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3595,plain,
spl0_69,
inference(avatar_split_clause,[],[f219,f3592]) ).
fof(f3592,plain,
( spl0_69
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3590,plain,
spl0_68,
inference(avatar_split_clause,[],[f218,f3587]) ).
fof(f3587,plain,
( spl0_68
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3585,plain,
spl0_67,
inference(avatar_split_clause,[],[f217,f3582]) ).
fof(f3582,plain,
( spl0_67
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3580,plain,
spl0_66,
inference(avatar_split_clause,[],[f216,f3577]) ).
fof(f3577,plain,
( spl0_66
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3575,plain,
spl0_65,
inference(avatar_split_clause,[],[f215,f3572]) ).
fof(f3572,plain,
( spl0_65
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3570,plain,
spl0_64,
inference(avatar_split_clause,[],[f214,f3567]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3565,plain,
spl0_63,
inference(avatar_split_clause,[],[f213,f3562]) ).
fof(f3562,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3560,plain,
spl0_62,
inference(avatar_split_clause,[],[f212,f3557]) ).
fof(f3557,plain,
( spl0_62
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3555,plain,
spl0_61,
inference(avatar_split_clause,[],[f211,f3552]) ).
fof(f3552,plain,
( spl0_61
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3550,plain,
spl0_60,
inference(avatar_split_clause,[],[f210,f3547]) ).
fof(f3547,plain,
( spl0_60
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3545,plain,
spl0_59,
inference(avatar_split_clause,[],[f209,f3542]) ).
fof(f3542,plain,
( spl0_59
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3540,plain,
spl0_58,
inference(avatar_split_clause,[],[f208,f3537]) ).
fof(f3537,plain,
( spl0_58
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3535,plain,
spl0_57,
inference(avatar_split_clause,[],[f203,f3532]) ).
fof(f3532,plain,
( spl0_57
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3530,plain,
spl0_56,
inference(avatar_split_clause,[],[f198,f3527]) ).
fof(f3527,plain,
( spl0_56
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3525,plain,
spl0_55,
inference(avatar_split_clause,[],[f195,f3522]) ).
fof(f3522,plain,
( spl0_55
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3520,plain,
spl0_54,
inference(avatar_split_clause,[],[f194,f3517]) ).
fof(f3517,plain,
( spl0_54
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3515,plain,
spl0_53,
inference(avatar_split_clause,[],[f189,f3512]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3510,plain,
spl0_52,
inference(avatar_split_clause,[],[f186,f3507]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3505,plain,
spl0_51,
inference(avatar_split_clause,[],[f184,f3502]) ).
fof(f3502,plain,
( spl0_51
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3500,plain,
spl0_50,
inference(avatar_split_clause,[],[f183,f3497]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3495,plain,
spl0_49,
inference(avatar_split_clause,[],[f182,f3492]) ).
fof(f3492,plain,
( spl0_49
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3490,plain,
spl0_48,
inference(avatar_split_clause,[],[f181,f3487]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3485,plain,
spl0_47,
inference(avatar_split_clause,[],[f180,f3482]) ).
fof(f3482,plain,
( spl0_47
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f180,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3480,plain,
spl0_46,
inference(avatar_split_clause,[],[f178,f3477]) ).
fof(f3477,plain,
( spl0_46
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3475,plain,
spl0_45,
inference(avatar_split_clause,[],[f177,f3472]) ).
fof(f3472,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3470,plain,
spl0_44,
inference(avatar_split_clause,[],[f176,f3467]) ).
fof(f3467,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3465,plain,
spl0_43,
inference(avatar_split_clause,[],[f175,f3462]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3460,plain,
spl0_42,
inference(avatar_split_clause,[],[f174,f3457]) ).
fof(f3457,plain,
( spl0_42
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3455,plain,
spl0_41,
inference(avatar_split_clause,[],[f173,f3452]) ).
fof(f3452,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3450,plain,
spl0_40,
inference(avatar_split_clause,[],[f172,f3447]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3445,plain,
spl0_39,
inference(avatar_split_clause,[],[f171,f3442]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3440,plain,
spl0_38,
inference(avatar_split_clause,[],[f170,f3437]) ).
fof(f3437,plain,
( spl0_38
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f170,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3435,plain,
spl0_37,
inference(avatar_split_clause,[],[f169,f3432]) ).
fof(f3432,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f169,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3430,plain,
spl0_36,
inference(avatar_split_clause,[],[f168,f3427]) ).
fof(f3427,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f168,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3425,plain,
spl0_35,
inference(avatar_split_clause,[],[f167,f3422]) ).
fof(f3422,plain,
( spl0_35
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f167,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3420,plain,
spl0_34,
inference(avatar_split_clause,[],[f166,f3417]) ).
fof(f3417,plain,
( spl0_34
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f166,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3415,plain,
spl0_33,
inference(avatar_split_clause,[],[f165,f3412]) ).
fof(f3412,plain,
( spl0_33
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f165,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3410,plain,
spl0_32,
inference(avatar_split_clause,[],[f164,f3407]) ).
fof(f3407,plain,
( spl0_32
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3405,plain,
spl0_31,
inference(avatar_split_clause,[],[f162,f3402]) ).
fof(f3402,plain,
( spl0_31
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3400,plain,
spl0_30,
inference(avatar_split_clause,[],[f161,f3397]) ).
fof(f3397,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3395,plain,
spl0_29,
inference(avatar_split_clause,[],[f160,f3392]) ).
fof(f3392,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3390,plain,
spl0_28,
inference(avatar_split_clause,[],[f159,f3387]) ).
fof(f3387,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3385,plain,
spl0_27,
inference(avatar_split_clause,[],[f158,f3382]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3380,plain,
spl0_26,
inference(avatar_split_clause,[],[f157,f3377]) ).
fof(f3377,plain,
( spl0_26
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3375,plain,
spl0_25,
inference(avatar_split_clause,[],[f156,f3372]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3370,plain,
spl0_24,
inference(avatar_split_clause,[],[f155,f3367]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3365,plain,
spl0_23,
inference(avatar_split_clause,[],[f154,f3362]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3360,plain,
spl0_22,
inference(avatar_split_clause,[],[f153,f3357]) ).
fof(f153,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3355,plain,
spl0_21,
inference(avatar_split_clause,[],[f151,f3352]) ).
fof(f151,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3350,plain,
spl0_20,
inference(avatar_split_clause,[],[f150,f3347]) ).
fof(f3347,plain,
( spl0_20
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3345,plain,
spl0_19,
inference(avatar_split_clause,[],[f149,f3342]) ).
fof(f3342,plain,
( spl0_19
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f149,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3340,plain,
spl0_18,
inference(avatar_split_clause,[],[f148,f3337]) ).
fof(f3337,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f148,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3335,plain,
spl0_17,
inference(avatar_split_clause,[],[f147,f3332]) ).
fof(f3332,plain,
( spl0_17
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3330,plain,
spl0_16,
inference(avatar_split_clause,[],[f146,f3327]) ).
fof(f3327,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3325,plain,
spl0_15,
inference(avatar_split_clause,[],[f145,f3322]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3320,plain,
spl0_14,
inference(avatar_split_clause,[],[f144,f3317]) ).
fof(f3317,plain,
( spl0_14
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f144,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3315,plain,
spl0_13,
inference(avatar_split_clause,[],[f143,f3312]) ).
fof(f3312,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3310,plain,
spl0_12,
inference(avatar_split_clause,[],[f142,f3307]) ).
fof(f3307,plain,
( spl0_12
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f142,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3305,plain,
spl0_11,
inference(avatar_split_clause,[],[f140,f3302]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3300,plain,
spl0_10,
inference(avatar_split_clause,[],[f139,f3297]) ).
fof(f3297,plain,
( spl0_10
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f139,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3295,plain,
spl0_9,
inference(avatar_split_clause,[],[f138,f3292]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3290,plain,
spl0_8,
inference(avatar_split_clause,[],[f137,f3287]) ).
fof(f3287,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3285,plain,
spl0_7,
inference(avatar_split_clause,[],[f136,f3282]) ).
fof(f3282,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3280,plain,
spl0_6,
inference(avatar_split_clause,[],[f135,f3277]) ).
fof(f3277,plain,
( spl0_6
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f135,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3275,plain,
spl0_5,
inference(avatar_split_clause,[],[f134,f3272]) ).
fof(f3272,plain,
( spl0_5
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3270,plain,
spl0_4,
inference(avatar_split_clause,[],[f133,f3267]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3265,plain,
spl0_3,
inference(avatar_split_clause,[],[f132,f3262]) ).
fof(f3262,plain,
( spl0_3
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3260,plain,
spl0_2,
inference(avatar_split_clause,[],[f131,f3257]) ).
fof(f3257,plain,
( spl0_2
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3255,plain,
spl0_1,
inference(avatar_split_clause,[],[f130,f3252]) ).
fof(f3252,plain,
( spl0_1
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWV243-1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 21:00:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (15252)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.43 % (15255)WARNING: value z3 for option sas not known
% 0.16/0.43 % (15257)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)
% 0.16/0.43 % (15259)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.43 % (15255)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)
% 0.16/0.43 % (15254)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.43 % (15256)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.43 % (15253)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.43 % (15258)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)
% 2.33/0.72 TRYING [1]
% 5.64/1.22 TRYING [2]
% 7.73/1.53 TRYING [1]
% 9.05/1.77 TRYING [1]
% 10.06/1.89 % (15257)First to succeed.
% 11.05/2.01 % (15257)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15252"
% 11.05/2.02 % (15257)Refutation found. Thanks to Tanya!
% 11.05/2.02 % SZS status Unsatisfiable for theBenchmark
% 11.05/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 11.48/2.09 % (15257)------------------------------
% 11.48/2.09 % (15257)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.48/2.09 % (15257)Termination reason: Refutation
% 11.48/2.09
% 11.48/2.09 % (15257)Memory used [KB]: 21619
% 11.48/2.09 % (15257)Time elapsed: 1.596 s
% 11.48/2.09 % (15257)Instructions burned: 2832 (million)
% 11.48/2.09 % (15252)Success in time 1.755 s
%------------------------------------------------------------------------------