TSTP Solution File: LAT278-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LAT278-1 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:26:46 EDT 2024
% Result : Unsatisfiable 10.23s 1.92s
% Output : Refutation 10.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4564
% Syntax : Number of formulae : 8525 (2769 unt; 0 def)
% Number of atoms : 19632 (3620 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 19446 (8339 ~;8590 |; 0 &)
% (2517 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2589 (2587 usr;2518 prp; 0-3 aty)
% Number of functors : 243 ( 243 usr; 49 con; 0-18 aty)
% Number of variables : 12225 (12225 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32675,plain,
$false,
inference(avatar_sat_refutation,[],[f3164,f3169,f3174,f3179,f3184,f3189,f3194,f3199,f3204,f3209,f3214,f3219,f3224,f3229,f3234,f3239,f3244,f3249,f3254,f3259,f3264,f3269,f3274,f3279,f3284,f3289,f3294,f3299,f3304,f3309,f3314,f3319,f3324,f3329,f3334,f3339,f3344,f3349,f3354,f3359,f3364,f3369,f3374,f3379,f3384,f3389,f3394,f3399,f3404,f3409,f3414,f3419,f3424,f3429,f3434,f3439,f3444,f3449,f3454,f3459,f3464,f3469,f3474,f3479,f3484,f3489,f3494,f3499,f3504,f3509,f3514,f3519,f3524,f3529,f3534,f3539,f3544,f3549,f3554,f3559,f3564,f3569,f3574,f3579,f3584,f3589,f3594,f3599,f3604,f3609,f3614,f3619,f3624,f3629,f3634,f3638,f3642,f3647,f3652,f3657,f3662,f3667,f3671,f3676,f3681,f3685,f3689,f3693,f3698,f3703,f3708,f3712,f3716,f3720,f3725,f3729,f3734,f3738,f3742,f3746,f3750,f3754,f3758,f3762,f3766,f3770,f3774,f3778,f3782,f3786,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4794,f4798,f4802,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5298,f5302,f5306,f5310,f5314,f5318,f5322,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5863,f5867,f5872,f5877,f5884,f5899,f6653,f6657,f6661,f6665,f6670,f6675,f6680,f6684,f6688,f6692,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6730,f6735,f6740,f6745,f6750,f6755,f6760,f6765,f6770,f6775,f6780,f6785,f6790,f6795,f6800,f6805,f6809,f6813,f6817,f6821,f6825,f6829,f6834,f6839,f6844,f6848,f6852,f6856,f6860,f6864,f6868,f6873,f6878,f6882,f6887,f6892,f6896,f6900,f6904,f6908,f6912,f6916,f6920,f6924,f6928,f6932,f6936,f6940,f6944,f6948,f6953,f6957,f6962,f6973,f6978,f6983,f6989,f6993,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7026,f7030,f7034,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7114,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7162,f7166,f7170,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7247,f7251,f7255,f7260,f7265,f7270,f7275,f7279,f7284,f7288,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7538,f7543,f7547,f7551,f7555,f7572,f7604,f7615,f7630,f7643,f7649,f7654,f7658,f7662,f7666,f7670,f7674,f7678,f7683,f7687,f7691,f7695,f7699,f7703,f7707,f7711,f7715,f7719,f7723,f7728,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7764,f7768,f7777,f7781,f7785,f7789,f7793,f7797,f7801,f7805,f7809,f7813,f7817,f7821,f7825,f7829,f7833,f7837,f7841,f7845,f7849,f7853,f7857,f7861,f7865,f7869,f7873,f7877,f7881,f7885,f7889,f7893,f7897,f7901,f7905,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f7943,f7947,f7951,f7955,f7959,f7963,f7967,f7971,f7975,f7979,f7983,f7988,f7992,f7996,f8011,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8157,f8161,f8165,f8169,f8173,f8177,f8181,f8185,f8189,f8193,f8198,f8202,f8206,f8210,f8214,f8218,f8222,f8226,f8230,f8234,f8238,f8242,f8246,f8250,f8254,f8258,f8262,f8266,f8270,f8274,f8278,f8283,f8287,f8291,f8295,f8299,f8303,f8307,f8311,f8315,f8319,f8323,f8327,f8331,f8335,f8339,f8343,f8347,f8351,f8355,f8359,f8363,f8368,f8372,f8376,f8380,f8384,f8388,f8392,f8396,f8400,f8404,f8408,f8412,f8416,f8420,f8424,f8428,f8432,f8436,f8440,f8444,f8448,f8499,f8553,f8586,f8622,f8666,f8670,f8674,f8678,f8682,f8686,f8690,f8694,f8698,f8702,f8706,f8710,f8714,f8718,f8722,f8726,f8731,f8735,f8739,f8743,f8747,f8751,f8755,f8759,f8763,f8767,f8771,f8775,f8779,f8783,f8788,f8792,f8796,f8800,f8804,f8808,f8812,f8816,f8820,f8824,f8828,f8832,f8836,f8840,f8844,f8848,f8852,f8856,f8860,f8864,f8868,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8905,f8909,f8913,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8950,f8954,f8959,f8966,f8970,f8974,f8978,f8982,f8990,f9049,f9089,f9128,f9165,f9180,f9205,f9209,f9213,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9245,f9250,f9254,f9258,f9262,f9266,f9270,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9306,f9310,f9314,f9318,f9322,f9326,f9330,f9334,f9338,f9342,f9346,f9350,f9354,f9358,f9362,f9366,f9370,f9374,f9378,f9382,f9386,f9390,f9394,f9398,f9402,f9406,f9410,f9414,f9418,f9422,f9426,f9430,f9434,f9438,f9442,f9446,f9450,f9454,f9458,f9462,f9466,f9470,f9474,f9478,f9482,f9486,f9490,f9494,f9499,f9507,f9511,f9515,f9519,f9523,f9527,f9531,f9557,f9569,f9589,f9646,f9693,f9751,f9857,f9915,f9919,f9923,f9927,f9931,f9936,f9940,f9944,f9948,f9952,f9956,f9960,f9964,f9968,f9972,f9976,f9981,f9985,f9989,f9993,f9997,f10001,f10005,f10009,f10013,f10017,f10022,f10032,f10036,f10040,f10044,f10048,f10052,f10056,f10060,f10064,f10074,f10078,f10082,f10086,f10090,f10094,f10098,f10102,f10106,f10110,f10120,f10124,f10128,f10132,f10136,f10140,f10144,f10148,f10152,f10156,f10160,f10164,f10168,f10172,f10176,f10180,f10184,f10188,f10192,f10196,f10200,f10204,f10208,f10212,f10216,f10220,f10224,f10228,f10232,f10236,f10240,f10248,f10252,f10256,f10260,f10264,f10268,f10272,f10276,f10280,f10284,f10288,f10292,f10296,f10300,f10304,f10308,f10312,f10316,f10320,f10324,f10328,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10365,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10401,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10581,f10640,f10826,f11288,f11318,f11322,f11326,f11330,f11335,f11339,f11343,f11347,f11351,f11355,f11359,f11363,f11367,f11371,f11375,f11379,f11383,f11387,f11391,f11395,f11399,f11403,f11407,f11411,f11415,f11419,f11423,f11427,f11431,f11435,f11439,f11443,f11447,f11451,f11455,f11459,f11463,f11467,f11471,f11475,f11479,f11483,f11487,f11491,f11495,f11499,f11510,f11514,f11518,f11522,f11526,f11530,f11534,f11538,f11542,f11546,f11559,f11563,f11567,f11571,f11575,f11579,f11583,f11587,f11591,f11595,f11614,f11618,f11622,f11626,f11630,f11634,f11638,f11642,f11646,f11650,f11654,f11658,f11662,f11666,f11670,f11674,f11678,f11682,f11686,f11690,f11694,f11699,f11706,f11710,f11714,f11718,f11723,f11731,f11736,f11740,f11745,f11777,f11781,f11785,f11789,f11793,f11797,f11801,f12705,f12811,f12862,f12866,f12870,f12874,f12878,f12882,f12886,f12890,f12894,f12898,f12902,f12906,f12910,f12914,f12918,f12922,f12926,f12930,f12934,f12938,f12942,f12946,f12950,f12954,f12958,f12968,f12972,f12976,f12980,f12984,f12988,f12992,f12996,f13000,f13004,f13013,f13017,f13021,f13025,f13029,f13033,f13037,f13041,f13045,f13049,f13057,f13061,f13065,f13069,f13073,f13077,f13081,f13085,f13089,f13093,f13097,f13101,f13105,f13109,f13113,f13117,f13121,f13125,f13129,f13133,f13137,f13145,f13149,f13153,f13157,f13161,f13165,f13170,f13179,f13183,f13192,f13196,f13275,f13807,f13940,f14077,f14149,f14153,f14157,f14161,f14166,f14170,f14174,f14178,f14182,f14186,f14190,f14194,f14198,f14202,f14221,f14225,f14229,f14233,f14237,f14241,f14245,f14249,f14253,f14257,f14264,f14268,f14272,f14276,f14280,f14284,f14288,f14292,f14296,f14300,f14304,f14308,f14312,f14316,f14320,f14324,f14328,f14332,f14336,f14340,f14344,f14349,f14353,f14357,f14361,f14365,f14369,f14373,f14377,f14381,f14385,f14389,f14393,f14397,f14401,f14406,f14430,f14435,f14453,f14458,f14463,f14483,f14487,f14491,f14495,f14499,f14503,f14507,f14511,f14515,f14520,f14524,f14528,f14911,f15185,f15531,f15535,f15539,f15543,f15547,f15551,f15555,f15559,f15563,f15567,f15571,f15575,f15593,f15597,f15601,f15605,f15609,f15613,f15617,f15621,f15625,f15629,f15633,f15638,f15642,f15646,f15650,f15654,f15658,f15662,f15666,f15670,f15674,f15678,f15682,f15686,f15690,f15694,f15698,f15702,f15706,f15710,f15714,f15718,f15722,f15726,f15730,f15734,f15738,f15742,f15746,f15750,f15754,f15758,f15762,f15766,f15770,f15774,f15778,f15782,f15786,f15790,f15794,f15798,f15803,f15807,f15835,f15840,f15898,f15903,f15998,f16003,f16106,f16110,f16115,f16145,f16150,f16167,f16172,f16180,f16185,f16193,f16199,f16205,f16209,f16213,f16219,f16225,f16229,f16234,f16238,f16242,f16246,f16252,f16285,f16289,f16303,f16307,f16449,f16569,f16743,f16849,f17173,f17363,f17435,f17439,f17443,f17447,f17451,f17455,f17459,f17463,f17467,f17471,f17475,f17479,f17483,f17487,f17491,f17495,f17500,f17504,f17508,f17512,f17516,f17520,f17524,f17528,f17532,f17536,f17540,f17545,f17549,f17553,f17557,f17561,f17565,f17569,f17573,f17577,f17581,f17585,f17593,f17597,f17601,f17605,f17609,f17613,f17617,f17621,f17625,f17629,f17633,f17637,f17641,f17645,f17649,f17653,f17657,f17661,f17665,f17671,f17697,f17701,f17707,f17792,f17797,f17820,f17824,f17828,f17833,f17837,f17842,f17847,f17852,f17857,f17862,f17866,f17870,f17874,f17878,f17883,f17905,f17909,f17913,f17918,f17923,f17928,f17935,f17941,f17946,f17952,f17957,f17970,f17974,f17979,f17988,f17992,f17996,f18000,f18004,f18014,f18403,f18875,f18890,f18894,f18898,f18902,f18906,f18910,f18914,f18920,f18926,f18931,f18935,f18939,f18943,f18947,f18951,f18955,f18959,f18963,f18967,f18975,f18979,f18983,f18987,f18991,f18995,f18999,f19003,f19007,f19011,f19015,f19019,f19023,f19027,f19033,f19356,f19360,f19578,f19741,f20030,f20034,f20038,f20043,f20047,f20051,f20056,f20060,f20064,f20068,f20083,f20087,f20091,f20095,f20099,f20103,f20107,f20111,f20175,f20207,f20574,f20578,f20583,f20587,f20591,f20595,f20599,f20603,f20607,f20611,f20615,f20619,f20694,f20698,f20702,f20706,f20710,f20714,f20719,f20724,f20730,f20752,f20756,f20761,f20774,f20778,f20782,f20787,f20808,f20813,f20871,f20875,f20879,f20884,f21245,f21249,f21359,f21363,f21367,f21371,f21375,f21379,f21383,f21387,f21391,f21397,f21401,f21405,f21409,f21413,f21417,f21421,f21425,f21429,f21433,f21439,f21443,f21447,f21451,f21455,f21459,f21463,f21467,f21471,f21475,f21485,f21489,f21493,f21497,f21501,f21505,f21509,f21513,f21517,f21521,f21526,f21530,f21534,f21538,f21542,f21546,f21550,f21554,f21558,f21562,f21566,f21571,f21575,f21579,f21583,f21587,f21591,f21595,f21599,f21603,f21607,f21614,f21637,f21644,f21667,f21671,f21675,f21679,f21685,f21750,f21754,f21758,f21762,f21766,f21770,f21774,f21778,f21783,f21810,f21816,f22085,f22089,f22706,f22710,f22714,f22718,f22722,f22726,f22730,f22734,f22738,f22742,f22746,f22750,f22754,f22758,f22762,f22766,f22770,f22774,f22778,f22782,f22786,f22790,f22794,f22798,f22802,f22806,f22810,f22814,f22818,f22822,f22826,f22862,f23262,f23541,f23545,f23552,f23556,f23560,f23564,f23568,f23572,f23576,f23580,f23584,f23588,f23592,f23596,f23600,f23604,f23608,f23612,f23616,f23620,f23624,f23629,f23654,f23658,f23663,f23713,f23717,f23721,f23726,f23814,f24446,f24460,f24464,f24468,f24472,f24476,f24481,f24486,f24490,f24494,f24498,f24510,f24514,f24518,f24522,f24528,f24534,f24616,f24620,f24624,f24629,f24634,f24644,f24648,f24705,f24709,f24713,f25081,f25129,f25133,f25137,f25142,f25146,f25150,f25280,f25284,f25288,f25311,f25315,f25319,f25323,f25327,f25331,f25335,f25339,f25343,f25347,f25351,f25355,f25359,f25730,f25734,f25738,f25742,f25746,f25750,f25755,f25895,f25899,f25916,f25920,f25924,f25928,f25932,f25936,f25940,f25944,f25948,f25952,f25957,f25961,f25965,f25969,f25973,f25977,f25981,f25985,f25989,f25993,f25997,f26001,f26005,f26009,f26013,f26017,f26023,f26031,f26037,f26045,f26051,f26055,f26071,f26077,f26126,f26132,f26145,f26150,f26155,f26532,f26864,f26925,f26929,f26953,f26958,f26962,f26966,f26970,f26974,f26979,f27068,f27072,f27076,f27080,f27084,f27088,f27092,f27409,f27413,f27488,f27492,f27501,f27505,f27509,f27513,f27517,f27523,f27545,f27694,f27698,f27702,f27706,f27858,f27863,f27868,f27873,f27878,f27882,f27886,f27890,f27916,f27920,f27924,f27989,f27993,f27997,f28001,f28005,f28009,f28013,f28074,f28166,f28171,f28175,f28204,f28208,f28212,f28216,f28220,f28224,f28229,f28234,f28239,f28306,f28331,f28335,f28339,f28343,f28376,f28380,f28384,f28388,f28394,f28422,f28457,f28464,f28555,f28561,f28580,f28619,f28625,f28643,f28680,f28684,f28724,f28728,f28732,f28736,f28889,f28896,f28940,f28944,f28989,f29010,f29033,f29037,f29079,f29103,f29107,f29120,f29124,f29137,f29141,f29145,f29149,f29153,f29157,f29162,f29167,f29171,f29175,f29179,f29183,f29187,f29191,f29195,f29199,f29203,f29219,f29226,f29236,f29244,f29314,f29318,f29328,f29332,f29336,f29340,f29344,f29348,f29352,f29356,f29360,f29365,f29370,f29374,f29378,f29382,f29386,f29390,f29396,f29400,f29406,f29410,f29415,f29420,f29463,f29470,f29474,f29478,f29482,f29483,f29517,f29521,f29525,f29529,f29533,f29537,f29589,f29629,f29685,f29844,f30256,f30417,f30421,f30425,f30432,f30436,f30440,f30444,f30448,f30453,f30457,f30461,f30465,f30469,f30473,f30477,f30481,f30485,f30489,f30493,f30497,f30501,f30506,f30511,f30518,f30522,f30526,f30531,f30537,f30556,f30561,f30565,f30569,f30573,f30577,f30581,f30593,f30597,f30601,f30605,f30610,f30614,f30618,f30622,f30626,f30630,f30634,f30645,f30650,f30654,f30659,f30664,f30668,f30672,f30676,f30680,f30684,f30688,f30692,f30696,f30719,f30749,f30754,f30759,f30763,f30768,f30772,f30776,f30780,f30784,f30789,f30793,f30797,f30802,f30808,f30813,f30817,f30821,f30825,f30829,f30833,f30837,f30841,f30845,f30850,f30854,f30858,f30862,f30866,f30870,f30875,f30879,f30883,f30901,f30905,f30909,f30913,f30917,f31078,f31082,f31237,f31242,f31305,f31601,f32014,f32202,f32206,f32210,f32214,f32218,f32222,f32226,f32230,f32234,f32239,f32253,f32258,f32274,f32278,f32282,f32286,f32290,f32294,f32298,f32302,f32307,f32311,f32315,f32319,f32323,f32327,f32331,f32336,f32341,f32346,f32350,f32354,f32363,f32367,f32371,f32375,f32379,f32383,f32387,f32391,f32395,f32399,f32403,f32408,f32412,f32416,f32420,f32425,f32430,f32435,f32439,f32443,f32448,f32453,f32457,f32461,f32465,f32470,f32475,f32481,f32486,f32492,f32497,f32502,f32506,f32510,f32514,f32518,f32577,f32606,f32611,f32615,f32619,f32624,f32628,f32632,f32636,f32640,f32644,f32648,f32652,f32656,f32660,f32665,f32669,f32673,f32674]) ).
fof(f32674,plain,
( ~ spl0_797
| spl0_1
| ~ spl0_796
| ~ spl0_798
| ~ spl0_1680 ),
inference(avatar_split_clause,[],[f17284,f15788,f7267,f7257,f3161,f7262]) ).
fof(f7262,plain,
( spl0_797
<=> c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f3161,plain,
( spl0_1
<=> c_Relation_Orefl(v_A,v_r,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f7257,plain,
( spl0_796
<=> v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f7267,plain,
( spl0_798
<=> v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f15788,plain,
( spl0_1680
<=> ! [X93,X3] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Orefl(c_Tarski_Opotype_Opset(X93,X3,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f17284,plain,
( c_Relation_Orefl(v_A,v_r,t_a)
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ spl0_796
| ~ spl0_798
| ~ spl0_1680 ),
inference(forward_demodulation,[],[f17280,f7269]) ).
fof(f7269,plain,
( v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7267]) ).
fof(f17280,plain,
( c_Relation_Orefl(v_A,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ spl0_796
| ~ spl0_1680 ),
inference(superposition,[],[f15789,f7259]) ).
fof(f7259,plain,
( v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7257]) ).
fof(f15789,plain,
( ! [X3,X93] :
( c_Relation_Orefl(c_Tarski_Opotype_Opset(X93,X3,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3)
| ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)) )
| ~ spl0_1680 ),
inference(avatar_component_clause,[],[f15788]) ).
fof(f32673,plain,
( spl0_2517
| ~ spl0_1666
| ~ spl0_1667 ),
inference(avatar_split_clause,[],[f17040,f15736,f15732,f32671]) ).
fof(f32671,plain,
( spl0_2517
<=> ! [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_2517])]) ).
fof(f15732,plain,
( spl0_1666
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f15736,plain,
( spl0_1667
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f17040,plain,
( ! [X2,X0,X1] :
( c_less(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X2,X2,X1) )
| ~ spl0_1666
| ~ spl0_1667 ),
inference(duplicate_literal_removal,[],[f17020]) ).
fof(f17020,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_1666
| ~ spl0_1667 ),
inference(resolution,[],[f15737,f15733]) ).
fof(f15733,plain,
( ! [X3,X26,X16,X15] :
( c_less(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3)
| ~ c_less(X15,X16,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
| ~ spl0_1666 ),
inference(avatar_component_clause,[],[f15732]) ).
fof(f15737,plain,
( ! [X3,X26,X16,X15] :
( ~ c_less(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3)
| c_less(X15,X16,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
| ~ spl0_1667 ),
inference(avatar_component_clause,[],[f15736]) ).
fof(f32669,plain,
( spl0_2516
| ~ spl0_1661
| ~ spl0_1663 ),
inference(avatar_split_clause,[],[f16911,f15720,f15712,f32667]) ).
fof(f32667,plain,
( spl0_2516
<=> ! [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_2516])]) ).
fof(f15712,plain,
( spl0_1661
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f15720,plain,
( spl0_1663
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f16911,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X2,X1) )
| ~ spl0_1661
| ~ spl0_1663 ),
inference(duplicate_literal_removal,[],[f16887]) ).
fof(f16887,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_1661
| ~ spl0_1663 ),
inference(resolution,[],[f15721,f15713]) ).
fof(f15713,plain,
( ! [X3,X26,X16,X15] :
( c_lessequals(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3)
| ~ c_lessequals(X15,X16,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
| ~ spl0_1661 ),
inference(avatar_component_clause,[],[f15712]) ).
fof(f15721,plain,
( ! [X3,X26,X16,X15] :
( ~ c_lessequals(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3)
| c_lessequals(X15,X16,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
| ~ spl0_1663 ),
inference(avatar_component_clause,[],[f15720]) ).
fof(f32665,plain,
( spl0_2515
| ~ spl0_1160
| ~ spl0_1640 ),
inference(avatar_split_clause,[],[f16600,f15627,f9320,f32663]) ).
fof(f32663,plain,
( spl0_2515
<=> ! [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_2515])]) ).
fof(f9320,plain,
( spl0_1160
<=> ! [X41,X8,X3] : c_List_Olast(c_append(X41,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f15627,plain,
( spl0_1640
<=> ! [X13,X41,X11] : c_List_Orev(c_List_Olist_OCons(X11,X41,X13),X13) = c_append(c_List_Orev(X41,X13),c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f16600,plain,
( ! [X2,X0,X1] : c_List_Olast(c_List_Orev(c_List_Olist_OCons(X2,X0,X1),X1),X1) = X2
| ~ spl0_1160
| ~ spl0_1640 ),
inference(superposition,[],[f9321,f15628]) ).
fof(f15628,plain,
( ! [X41,X11,X13] : c_List_Orev(c_List_Olist_OCons(X11,X41,X13),X13) = c_append(c_List_Orev(X41,X13),c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13)
| ~ spl0_1640 ),
inference(avatar_component_clause,[],[f15627]) ).
fof(f9321,plain,
( ! [X41,X3,X8] : c_List_Olast(c_append(X41,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) = X8
| ~ spl0_1160 ),
inference(avatar_component_clause,[],[f9320]) ).
fof(f32660,plain,
( spl0_2514
| ~ spl0_821
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16120,f16113,f7363,f32658]) ).
fof(f32658,plain,
( spl0_2514
<=> ! [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_2514])]) ).
fof(f7363,plain,
( spl0_821
<=> ! [X11,X3,X42] : c_List_Oop_Amem(X11,c_List_Olist_OCons(X11,X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f16113,plain,
( spl0_1694
<=> ! [X13,X11,X10] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_plus(c_1,X10,tc_nat),X11,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f16120,plain,
( ! [X2,X0,X1] : c_List_Oop_Amem(X0,c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_821
| ~ spl0_1694 ),
inference(superposition,[],[f7364,f16114]) ).
fof(f16114,plain,
( ! [X10,X11,X13] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_plus(c_1,X10,tc_nat),X11,X13)
| ~ spl0_1694 ),
inference(avatar_component_clause,[],[f16113]) ).
fof(f7364,plain,
( ! [X3,X11,X42] : c_List_Oop_Amem(X11,c_List_Olist_OCons(X11,X42,X3),X3)
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7363]) ).
fof(f32656,plain,
( spl0_2513
| ~ spl0_856
| ~ spl0_1690 ),
inference(avatar_split_clause,[],[f16047,f16001,f7503,f32654]) ).
fof(f32654,plain,
( spl0_2513
<=> ! [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_2513])]) ).
fof(f7503,plain,
( spl0_856
<=> ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f16001,plain,
( spl0_1690
<=> ! [X25,X10] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_plus(c_1,X25,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f16047,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X1,c_plus(X1,c_times(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_856
| ~ spl0_1690 ),
inference(superposition,[],[f7504,f16002]) ).
fof(f16002,plain,
( ! [X10,X25] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_plus(c_1,X25,tc_nat),X10,tc_nat)
| ~ spl0_1690 ),
inference(avatar_component_clause,[],[f16001]) ).
fof(f7504,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_nat),tc_nat)
| ~ spl0_856 ),
inference(avatar_component_clause,[],[f7503]) ).
fof(f32652,plain,
( spl0_2512
| ~ spl0_830
| ~ spl0_1690 ),
inference(avatar_split_clause,[],[f16016,f16001,f7399,f32650]) ).
fof(f32650,plain,
( spl0_2512
<=> ! [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_2512])]) ).
fof(f7399,plain,
( spl0_830
<=> ! [X52,X24] : ~ c_less(c_plus(X24,X52,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f16016,plain,
( ! [X0,X1] : ~ c_less(c_times(c_plus(c_1,X1,tc_nat),X0,tc_nat),X0,tc_nat)
| ~ spl0_830
| ~ spl0_1690 ),
inference(superposition,[],[f7400,f16002]) ).
fof(f7400,plain,
( ! [X52,X24] : ~ c_less(c_plus(X24,X52,tc_nat),X24,tc_nat)
| ~ spl0_830 ),
inference(avatar_component_clause,[],[f7399]) ).
fof(f32648,plain,
( spl0_2511
| ~ spl0_855
| ~ spl0_1688 ),
inference(avatar_split_clause,[],[f15943,f15901,f7499,f32646]) ).
fof(f32646,plain,
( spl0_2511
<=> ! [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_2511])]) ).
fof(f7499,plain,
( spl0_855
<=> ! [X25,X9] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f15901,plain,
( spl0_1688
<=> ! [X25,X10] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f15943,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_plus(X0,c_times(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_855
| ~ spl0_1688 ),
inference(superposition,[],[f7500,f15902]) ).
fof(f15902,plain,
( ! [X10,X25] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_1688 ),
inference(avatar_component_clause,[],[f15901]) ).
fof(f7500,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_nat),tc_nat)
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f7499]) ).
fof(f32644,plain,
( spl0_2510
| ~ spl0_830
| ~ spl0_1688 ),
inference(avatar_split_clause,[],[f15913,f15901,f7399,f32642]) ).
fof(f32642,plain,
( spl0_2510
<=> ! [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_2510])]) ).
fof(f15913,plain,
( ! [X0,X1] : ~ c_less(c_times(X0,c_plus(c_1,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_830
| ~ spl0_1688 ),
inference(superposition,[],[f7400,f15902]) ).
fof(f32640,plain,
( spl0_2509
| ~ spl0_855
| ~ spl0_1686 ),
inference(avatar_split_clause,[],[f15846,f15838,f7499,f32638]) ).
fof(f32638,plain,
( spl0_2509
<=> ! [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_2509])]) ).
fof(f15838,plain,
( spl0_1686
<=> ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f15846,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_Nat_Opower(X0,c_plus(c_1,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_855
| ~ spl0_1686 ),
inference(superposition,[],[f7500,f15839]) ).
fof(f15839,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_1686 ),
inference(avatar_component_clause,[],[f15838]) ).
fof(f32636,plain,
( spl0_2508
| ~ spl0_857
| ~ spl0_1683 ),
inference(avatar_split_clause,[],[f15813,f15801,f7507,f32634]) ).
fof(f32634,plain,
( spl0_2508
<=> ! [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_2508])]) ).
fof(f7507,plain,
( spl0_857
<=> ! [X25,X9] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f15801,plain,
( spl0_1683
<=> ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f15813,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_857
| ~ spl0_1683 ),
inference(superposition,[],[f7508,f15802]) ).
fof(f15802,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_IntDef_Oint)
| ~ spl0_1683 ),
inference(avatar_component_clause,[],[f15801]) ).
fof(f7508,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7507]) ).
fof(f32632,plain,
( spl0_2507
| ~ spl0_831
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f15431,f14489,f7403,f32630]) ).
fof(f32630,plain,
( spl0_2507
<=> ! [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_2507])]) ).
fof(f7403,plain,
( spl0_831
<=> ! [X52,X24] : ~ c_less(c_plus(X52,X24,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f14489,plain,
( spl0_1607
<=> ! [X57,X3,X15] : c_Nat_Osize(c_List_Olist_OCons(X15,X57,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X57,tc_List_Olist(X3)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f15431,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_831
| ~ spl0_1607 ),
inference(superposition,[],[f7404,f14490]) ).
fof(f14490,plain,
( ! [X3,X57,X15] : c_Nat_Osize(c_List_Olist_OCons(X15,X57,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X57,tc_List_Olist(X3)),c_1,tc_nat)
| ~ spl0_1607 ),
inference(avatar_component_clause,[],[f14489]) ).
fof(f7404,plain,
( ! [X52,X24] : ~ c_less(c_plus(X52,X24,tc_nat),X24,tc_nat)
| ~ spl0_831 ),
inference(avatar_component_clause,[],[f7403]) ).
fof(f32628,plain,
( spl0_2506
| ~ spl0_853
| ~ spl0_1591 ),
inference(avatar_split_clause,[],[f15217,f14371,f7491,f32626]) ).
fof(f32626,plain,
( spl0_2506
<=> ! [X0,X3,X2,X1] : c_in(X0,c_union(X1,c_insert(X0,X2,X3),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f7491,plain,
( spl0_853
<=> ! [X11,X27,X3] : c_in(X11,c_insert(X11,X27,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f14371,plain,
( spl0_1591
<=> ! [X3,X31,X27,X15] : c_union(X27,c_insert(X15,X31,X3),X3) = c_insert(X15,c_union(X27,X31,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f15217,plain,
( ! [X2,X3,X0,X1] : c_in(X0,c_union(X1,c_insert(X0,X2,X3),X3),X3)
| ~ spl0_853
| ~ spl0_1591 ),
inference(superposition,[],[f7492,f14372]) ).
fof(f14372,plain,
( ! [X31,X3,X27,X15] : c_union(X27,c_insert(X15,X31,X3),X3) = c_insert(X15,c_union(X27,X31,X3),X3)
| ~ spl0_1591 ),
inference(avatar_component_clause,[],[f14371]) ).
fof(f7492,plain,
( ! [X3,X11,X27] : c_in(X11,c_insert(X11,X27,X3),X3)
| ~ spl0_853 ),
inference(avatar_component_clause,[],[f7491]) ).
fof(f32624,plain,
( spl0_2505
| ~ spl0_791
| ~ spl0_1557 ),
inference(avatar_split_clause,[],[f14888,f14231,f7237,f32622]) ).
fof(f32622,plain,
( spl0_2505
<=> ! [X0,X1] : c_List_Oset(X0,X1) = c_List_Oset(c_append(X0,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f7237,plain,
( spl0_791
<=> ! [X8,X3] : c_union(X8,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f14231,plain,
( spl0_1557
<=> ! [X41,X3,X42] : c_List_Oset(c_append(X41,X42,X3),X3) = c_union(c_List_Oset(X41,X3),c_List_Oset(X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f14888,plain,
( ! [X0,X1] : c_List_Oset(X0,X1) = c_List_Oset(c_append(X0,X0,X1),X1)
| ~ spl0_791
| ~ spl0_1557 ),
inference(superposition,[],[f14232,f7238]) ).
fof(f7238,plain,
( ! [X3,X8] : c_union(X8,X8,X3) = X8
| ~ spl0_791 ),
inference(avatar_component_clause,[],[f7237]) ).
fof(f14232,plain,
( ! [X41,X3,X42] : c_List_Oset(c_append(X41,X42,X3),X3) = c_union(c_List_Oset(X41,X3),c_List_Oset(X42,X3),X3)
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f14231]) ).
fof(f32619,plain,
( spl0_2504
| ~ spl0_821
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f14806,f14219,f7363,f32617]) ).
fof(f32617,plain,
( spl0_2504
<=> ! [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_2504])]) ).
fof(f14219,plain,
( spl0_1554
<=> ! [X41,X11,X42,X13] : c_append(c_List_Olist_OCons(X11,X41,X13),X42,X13) = c_List_Olist_OCons(X11,c_append(X41,X42,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f14806,plain,
( ! [X2,X3,X0,X1] : c_List_Oop_Amem(X0,c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_821
| ~ spl0_1554 ),
inference(superposition,[],[f7364,f14220]) ).
fof(f14220,plain,
( ! [X41,X11,X42,X13] : c_append(c_List_Olist_OCons(X11,X41,X13),X42,X13) = c_List_Olist_OCons(X11,c_append(X41,X42,X13),X13)
| ~ spl0_1554 ),
inference(avatar_component_clause,[],[f14219]) ).
fof(f32615,plain,
( spl0_2503
| ~ spl0_864
| ~ spl0_1526 ),
inference(avatar_split_clause,[],[f14071,f13151,f7535,f32613]) ).
fof(f32613,plain,
( spl0_2503
<=> ! [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_2503])]) ).
fof(f7535,plain,
( spl0_864
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f13151,plain,
( spl0_1526
<=> ! [X25,X10] :
( X10 = X25
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f14071,plain,
( ! [X0] :
( c_1 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_864
| ~ spl0_1526 ),
inference(superposition,[],[f13152,f7537]) ).
fof(f7537,plain,
( c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_864 ),
inference(avatar_component_clause,[],[f7535]) ).
fof(f13152,plain,
( ! [X10,X25] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)
| X10 = X25 )
| ~ spl0_1526 ),
inference(avatar_component_clause,[],[f13151]) ).
fof(f32611,plain,
( spl0_2502
| ~ spl0_696
| ~ spl0_866
| ~ spl0_1037
| ~ spl0_1493 ),
inference(avatar_split_clause,[],[f13664,f13015,f8426,f7545,f6836,f32609]) ).
fof(f32609,plain,
( spl0_2502
<=> ! [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_2502])]) ).
fof(f6836,plain,
( spl0_696
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f7545,plain,
( spl0_866
<=> ! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f8426,plain,
( spl0_1037
<=> ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f13015,plain,
( spl0_1493
<=> ! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,c_Numeral_Obin__succ(X35)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f13664,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_696
| ~ spl0_866
| ~ spl0_1037
| ~ spl0_1493 ),
inference(forward_demodulation,[],[f13656,f8645]) ).
fof(f8645,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_866
| ~ spl0_1037 ),
inference(superposition,[],[f8427,f7546]) ).
fof(f7546,plain,
( ! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin)
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f7545]) ).
fof(f8427,plain,
( ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1037 ),
inference(avatar_component_clause,[],[f8426]) ).
fof(f13656,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_696
| ~ spl0_1493 ),
inference(superposition,[],[f13016,f6838]) ).
fof(f6838,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_696 ),
inference(avatar_component_clause,[],[f6836]) ).
fof(f13016,plain,
( ! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,c_Numeral_Obin__succ(X35)),c_Numeral_Obit_OB0)
| ~ spl0_1493 ),
inference(avatar_component_clause,[],[f13015]) ).
fof(f32606,plain,
( spl0_2501
| ~ spl0_790
| ~ spl0_1425 ),
inference(avatar_split_clause,[],[f12653,f11644,f7233,f32604]) ).
fof(f32604,plain,
( spl0_2501
<=> ! [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_2501])]) ).
fof(f7233,plain,
( spl0_790
<=> ! [X27,X3] : c_UNIV = c_union(X27,c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f11644,plain,
( spl0_1425
<=> ! [X31,X27,X80,X3] :
( c_lessequals(X27,X80,tc_set(X3))
| ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f12653,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_UNIV,X2,tc_set(X1))
| c_lessequals(X0,X2,tc_set(X1)) )
| ~ spl0_790
| ~ spl0_1425 ),
inference(superposition,[],[f11645,f7234]) ).
fof(f7234,plain,
( ! [X3,X27] : c_UNIV = c_union(X27,c_UNIV,X3)
| ~ spl0_790 ),
inference(avatar_component_clause,[],[f7233]) ).
fof(f11645,plain,
( ! [X31,X3,X80,X27] :
( ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3))
| c_lessequals(X27,X80,tc_set(X3)) )
| ~ spl0_1425 ),
inference(avatar_component_clause,[],[f11644]) ).
fof(f32577,plain,
( ~ spl0_92
| spl0_2500
| ~ spl0_770
| ~ spl0_1400 ),
inference(avatar_split_clause,[],[f12394,f11520,f7152,f32575,f3616]) ).
fof(f3616,plain,
( spl0_92
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f32575,plain,
( spl0_2500
<=> ! [X0,X1] :
( ~ c_lessequals(X1,c_0,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f7152,plain,
( spl0_770
<=> ! [X10] : c_0 = c_Orderings_Omin(X10,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f11520,plain,
( spl0_1400
<=> ! [X37,X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X8,X17)
| ~ c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f12394,plain,
( ! [X0,X1] :
( ~ c_lessequals(X1,c_0,tc_nat)
| c_lessequals(X1,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_770
| ~ spl0_1400 ),
inference(superposition,[],[f11521,f7153]) ).
fof(f7153,plain,
( ! [X10] : c_0 = c_Orderings_Omin(X10,c_0,tc_nat)
| ~ spl0_770 ),
inference(avatar_component_clause,[],[f7152]) ).
fof(f11521,plain,
( ! [X11,X8,X37,X17] :
( ~ c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17)
| c_lessequals(X11,X8,X17)
| ~ class_Orderings_Olinorder(X17) )
| ~ spl0_1400 ),
inference(avatar_component_clause,[],[f11520]) ).
fof(f32518,plain,
( ~ spl0_92
| spl0_2499
| ~ spl0_767
| ~ spl0_1396 ),
inference(avatar_split_clause,[],[f12356,f11497,f7140,f32516,f3616]) ).
fof(f32516,plain,
( spl0_2499
<=> ! [X0,X1] :
( ~ c_less(X0,X1,tc_nat)
| c_less(c_0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f7140,plain,
( spl0_767
<=> ! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f11497,plain,
( spl0_1396
<=> ! [X37,X11,X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X11,X37,X3)
| ~ c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f12356,plain,
( ! [X0,X1] :
( ~ c_less(X0,X1,tc_nat)
| c_less(c_0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_767
| ~ spl0_1396 ),
inference(superposition,[],[f11498,f7141]) ).
fof(f7141,plain,
( ! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8
| ~ spl0_767 ),
inference(avatar_component_clause,[],[f7140]) ).
fof(f11498,plain,
( ! [X3,X11,X8,X37] :
( ~ c_less(c_Orderings_Omax(X11,X8,X3),X37,X3)
| c_less(X11,X37,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_1396 ),
inference(avatar_component_clause,[],[f11497]) ).
fof(f32514,plain,
( spl0_2498
| ~ spl0_698
| ~ spl0_775
| ~ spl0_1381 ),
inference(avatar_split_clause,[],[f12165,f11437,f7172,f6846,f32512]) ).
fof(f32512,plain,
( spl0_2498
<=> ! [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_2498])]) ).
fof(f6846,plain,
( spl0_698
<=> ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f7172,plain,
( spl0_775
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f11437,plain,
( spl0_1381
<=> ! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f12165,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_698
| ~ spl0_775
| ~ spl0_1381 ),
inference(forward_demodulation,[],[f12158,f6847]) ).
fof(f6847,plain,
( ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8
| ~ spl0_698 ),
inference(avatar_component_clause,[],[f6846]) ).
fof(f12158,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_775
| ~ spl0_1381 ),
inference(superposition,[],[f11438,f7174]) ).
fof(f7174,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_775 ),
inference(avatar_component_clause,[],[f7172]) ).
fof(f11438,plain,
( ! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),c_Numeral_Obit_OB1)
| ~ spl0_1381 ),
inference(avatar_component_clause,[],[f11437]) ).
fof(f32510,plain,
( spl0_2497
| ~ spl0_699
| ~ spl0_775
| ~ spl0_1380 ),
inference(avatar_split_clause,[],[f12156,f11433,f7172,f6850,f32508]) ).
fof(f32508,plain,
( spl0_2497
<=> ! [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_2497])]) ).
fof(f6850,plain,
( spl0_699
<=> ! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f11433,plain,
( spl0_1380
<=> ! [X36,X8,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),c_Numeral_OBit(X35,X8)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f12156,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_699
| ~ spl0_775
| ~ spl0_1380 ),
inference(forward_demodulation,[],[f12148,f6851]) ).
fof(f6851,plain,
( ! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8
| ~ spl0_699 ),
inference(avatar_component_clause,[],[f6850]) ).
fof(f12148,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_775
| ~ spl0_1380 ),
inference(superposition,[],[f11434,f7174]) ).
fof(f11434,plain,
( ! [X36,X8,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),c_Numeral_OBit(X35,X8)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),X8)
| ~ spl0_1380 ),
inference(avatar_component_clause,[],[f11433]) ).
fof(f32506,plain,
( spl0_2496
| ~ spl0_1023
| ~ spl0_2424 ),
inference(avatar_split_clause,[],[f32111,f30915,f8370,f32504]) ).
fof(f32504,plain,
( spl0_2496
<=> ! [X0,X1] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f8370,plain,
( spl0_1023
<=> ! [X27,X3] :
( c_emptyset = X27
| c_in(c_Main_Oall__not__in__conv__1(X27,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f30915,plain,
( spl0_2424
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f32111,plain,
( ! [X0,X1] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X1)
| ~ spl0_1023
| ~ spl0_2424 ),
inference(resolution,[],[f30916,f8371]) ).
fof(f8371,plain,
( ! [X3,X27] :
( c_in(c_Main_Oall__not__in__conv__1(X27,X3),X27,X3)
| c_emptyset = X27 )
| ~ spl0_1023 ),
inference(avatar_component_clause,[],[f8370]) ).
fof(f30916,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
| ~ spl0_2424 ),
inference(avatar_component_clause,[],[f30915]) ).
fof(f32502,plain,
( spl0_2495
| ~ spl0_751
| ~ spl0_1364 ),
inference(avatar_split_clause,[],[f11906,f11369,f7076,f32500]) ).
fof(f32500,plain,
( spl0_2495
<=> ! [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_2495])]) ).
fof(f7076,plain,
( spl0_751
<=> ! [X8,X3] : c_List_Odrop(c_0,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f11369,plain,
( spl0_1364
<=> ! [X41,X3,X10] :
( c_List_Olist_ONil != c_List_Odrop(X10,X41,X3)
| c_lessequals(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f11906,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_lessequals(c_Nat_Osize(X0,tc_List_Olist(X1)),c_0,tc_nat) )
| ~ spl0_751
| ~ spl0_1364 ),
inference(superposition,[],[f11370,f7077]) ).
fof(f7077,plain,
( ! [X3,X8] : c_List_Odrop(c_0,X8,X3) = X8
| ~ spl0_751 ),
inference(avatar_component_clause,[],[f7076]) ).
fof(f11370,plain,
( ! [X41,X10,X3] :
( c_List_Olist_ONil != c_List_Odrop(X10,X41,X3)
| c_lessequals(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) )
| ~ spl0_1364 ),
inference(avatar_component_clause,[],[f11369]) ).
fof(f32497,plain,
( spl0_2494
| ~ spl0_790
| ~ spl0_1357 ),
inference(avatar_split_clause,[],[f11859,f11341,f7233,f32495]) ).
fof(f32495,plain,
( spl0_2494
<=> ! [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_2494])]) ).
fof(f11341,plain,
( spl0_1357
<=> ! [X34,X3,X33] :
( c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f11859,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_790
| ~ spl0_1357 ),
inference(superposition,[],[f11342,f7234]) ).
fof(f11342,plain,
( ! [X3,X34,X33] :
( ~ c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3))
| c_in(X33,c_Finite__Set_OFinites,tc_set(X3)) )
| ~ spl0_1357 ),
inference(avatar_component_clause,[],[f11341]) ).
fof(f32492,plain,
( spl0_2493
| ~ spl0_88
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11309,f10435,f3596,f32489]) ).
fof(f32489,plain,
( spl0_2493
<=> 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_2493])]) ).
fof(f3596,plain,
( spl0_88
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f10435,plain,
( spl0_1345
<=> ! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f11309,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_88
| ~ spl0_1345 ),
inference(resolution,[],[f10436,f3598]) ).
fof(f3598,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f3596]) ).
fof(f10436,plain,
( ! [X3] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X3) )
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f10435]) ).
fof(f32486,plain,
( spl0_2492
| ~ spl0_54
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11308,f10435,f3426,f32483]) ).
fof(f32483,plain,
( spl0_2492
<=> 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_2492])]) ).
fof(f3426,plain,
( spl0_54
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f11308,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_54
| ~ spl0_1345 ),
inference(resolution,[],[f10436,f3428]) ).
fof(f3428,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3426]) ).
fof(f32481,plain,
( spl0_2491
| ~ spl0_53
| ~ spl0_1344 ),
inference(avatar_split_clause,[],[f11307,f10431,f3421,f32478]) ).
fof(f32478,plain,
( spl0_2491
<=> 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_2491])]) ).
fof(f3421,plain,
( spl0_53
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f10431,plain,
( spl0_1344
<=> ! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f11307,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_53
| ~ spl0_1344 ),
inference(resolution,[],[f10432,f3423]) ).
fof(f3423,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f3421]) ).
fof(f10432,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X3) )
| ~ spl0_1344 ),
inference(avatar_component_clause,[],[f10431]) ).
fof(f32475,plain,
( spl0_2490
| ~ spl0_706
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f11300,f10427,f6880,f32473]) ).
fof(f32473,plain,
( spl0_2490
<=> ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_UNIV = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f6880,plain,
( spl0_706
<=> ! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f10427,plain,
( spl0_1343
<=> ! [X27,X3,X31] :
( c_UNIV = X31
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f11300,plain,
( ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_UNIV = X1 )
| ~ spl0_706
| ~ spl0_1343 ),
inference(superposition,[],[f10428,f6881]) ).
fof(f6881,plain,
( ! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3)
| ~ spl0_706 ),
inference(avatar_component_clause,[],[f6880]) ).
fof(f10428,plain,
( ! [X31,X3,X27] :
( c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_UNIV = X31 )
| ~ spl0_1343 ),
inference(avatar_component_clause,[],[f10427]) ).
fof(f32470,plain,
( spl0_2489
| ~ spl0_2095
| ~ spl0_2488 ),
inference(avatar_split_clause,[],[f32466,f32463,f25139,f32468]) ).
fof(f32468,plain,
( spl0_2489
<=> ! [X0,X1] : c_IntDef_ONats != c_Relation_OImage(c_emptyset,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f25139,plain,
( spl0_2095
<=> c_UNIV = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f32463,plain,
( spl0_2488
<=> ! [X0,X1] : c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f32466,plain,
( ! [X0,X1] : c_IntDef_ONats != c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_2095
| ~ spl0_2488 ),
inference(forward_demodulation,[],[f32464,f25141]) ).
fof(f25141,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_2095 ),
inference(avatar_component_clause,[],[f25139]) ).
fof(f32464,plain,
( ! [X0,X1] : c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_2488 ),
inference(avatar_component_clause,[],[f32463]) ).
fof(f32465,plain,
( spl0_102
| spl0_2488
| ~ spl0_706
| ~ spl0_1342 ),
inference(avatar_split_clause,[],[f11293,f10423,f6880,f32463,f3664]) ).
fof(f3664,plain,
( spl0_102
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f10423,plain,
( spl0_1342
<=> ! [X27,X3,X31] :
( c_UNIV = X27
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f11293,plain,
( ! [X0,X1] :
( c_UNIV != c_Relation_OImage(c_emptyset,X1,X0,X0)
| c_emptyset = c_UNIV )
| ~ spl0_706
| ~ spl0_1342 ),
inference(superposition,[],[f10424,f6881]) ).
fof(f10424,plain,
( ! [X31,X3,X27] :
( c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_UNIV = X27 )
| ~ spl0_1342 ),
inference(avatar_component_clause,[],[f10423]) ).
fof(f32461,plain,
( spl0_2487
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340 ),
inference(avatar_split_clause,[],[f11235,f10415,f10092,f6703,f3695,f32459]) ).
fof(f32459,plain,
( spl0_2487
<=> ! [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_2487])]) ).
fof(f3695,plain,
( spl0_109
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f6703,plain,
( spl0_667
<=> ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f10092,plain,
( spl0_1261
<=> ! [X25,X10] : c_IntDef_Oint(c_plus(X25,X10,tc_nat)) = c_plus(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f10415,plain,
( spl0_1340
<=> ! [X25] : c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f11235,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340 ),
inference(forward_demodulation,[],[f11234,f6704]) ).
fof(f6704,plain,
( ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f6703]) ).
fof(f11234,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_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340 ),
inference(forward_demodulation,[],[f11196,f10671]) ).
fof(f10671,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_109
| ~ spl0_1261 ),
inference(superposition,[],[f10093,f3697]) ).
fof(f3697,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f3695]) ).
fof(f10093,plain,
( ! [X10,X25] : c_IntDef_Oint(c_plus(X25,X10,tc_nat)) = c_plus(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ spl0_1261 ),
inference(avatar_component_clause,[],[f10092]) ).
fof(f11196,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_667
| ~ spl0_1340 ),
inference(superposition,[],[f6704,f10416]) ).
fof(f10416,plain,
( ! [X25] : c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat))
| ~ spl0_1340 ),
inference(avatar_component_clause,[],[f10415]) ).
fof(f32457,plain,
( spl0_2486
| ~ spl0_773
| ~ spl0_2419 ),
inference(avatar_split_clause,[],[f32031,f30881,f7164,f32455]) ).
fof(f32455,plain,
( spl0_2486
<=> ! [X0] : c_0 != c_plus(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f7164,plain,
( spl0_773
<=> ! [X8] : c_plus(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f30881,plain,
( spl0_2419
<=> ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f32031,plain,
( ! [X0] : c_0 != c_plus(c_1,X0,tc_nat)
| ~ spl0_773
| ~ spl0_2419 ),
inference(superposition,[],[f30882,f7165]) ).
fof(f7165,plain,
( ! [X8] : c_plus(c_0,X8,tc_nat) = X8
| ~ spl0_773 ),
inference(avatar_component_clause,[],[f7164]) ).
fof(f30882,plain,
( ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat)
| ~ spl0_2419 ),
inference(avatar_component_clause,[],[f30881]) ).
fof(f32453,plain,
( spl0_2485
| ~ spl0_938
| ~ spl0_1326 ),
inference(avatar_split_clause,[],[f11094,f10359,f7907,f32450]) ).
fof(f32450,plain,
( spl0_2485
<=> 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_2485])]) ).
fof(f7907,plain,
( spl0_938
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f10359,plain,
( spl0_1326
<=> ! [X11,X27,X3] : c_insert(X11,X27,X3) = c_insert(X11,c_insert(X11,X27,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f11094,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_938
| ~ spl0_1326 ),
inference(superposition,[],[f10360,f7909]) ).
fof(f7909,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f7907]) ).
fof(f10360,plain,
( ! [X3,X11,X27] : c_insert(X11,X27,X3) = c_insert(X11,c_insert(X11,X27,X3),X3)
| ~ spl0_1326 ),
inference(avatar_component_clause,[],[f10359]) ).
fof(f32448,plain,
( spl0_2484
| ~ spl0_786
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f11009,f10318,f7217,f32446]) ).
fof(f32446,plain,
( spl0_2484
<=> ! [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_2484])]) ).
fof(f7217,plain,
( spl0_786
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f10318,plain,
( spl0_1316
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f11009,plain,
( ! [X0] :
( c_emptyset = c_minus(c_0,c_1,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) )
| ~ spl0_786
| ~ spl0_1316 ),
inference(resolution,[],[f10319,f7218]) ).
fof(f7218,plain,
( ! [X3] :
( c_lessequals(c_0,c_1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) )
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f7217]) ).
fof(f10319,plain,
( ! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) )
| ~ spl0_1316 ),
inference(avatar_component_clause,[],[f10318]) ).
fof(f32443,plain,
( ~ spl0_92
| spl0_2483
| ~ spl0_708
| ~ spl0_1311 ),
inference(avatar_split_clause,[],[f10984,f10298,f6889,f32441,f3616]) ).
fof(f32441,plain,
( spl0_2483
<=> ! [X0] :
( c_emptyset != c_SetInterval_OlessThan(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f6889,plain,
( spl0_708
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f10298,plain,
( spl0_1311
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OlessThan(X11,X3) != c_SetInterval_OlessThan(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f10984,plain,
( ! [X0] :
( c_emptyset != c_SetInterval_OlessThan(X0,tc_nat)
| c_0 = X0
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_708
| ~ spl0_1311 ),
inference(superposition,[],[f10299,f6891]) ).
fof(f6891,plain,
( c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat)
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f6889]) ).
fof(f10299,plain,
( ! [X3,X11,X8] :
( c_SetInterval_OlessThan(X11,X3) != c_SetInterval_OlessThan(X8,X3)
| X8 = X11
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_1311 ),
inference(avatar_component_clause,[],[f10298]) ).
fof(f32439,plain,
( spl0_2482
| ~ spl0_719
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10958,f10282,f6934,f32437]) ).
fof(f32437,plain,
( spl0_2482
<=> ! [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_2482])]) ).
fof(f6934,plain,
( spl0_719
<=> ! [X27,X3] : c_lessequals(c_emptyset,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f10282,plain,
( spl0_1307
<=> ! [X9,X3,X74] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X74,X9,X3)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X74,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f10958,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,c_emptyset,tc_set(X0)) )
| ~ spl0_719
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f6935]) ).
fof(f6935,plain,
( ! [X3,X27] : c_lessequals(c_emptyset,X27,tc_set(X3))
| ~ spl0_719 ),
inference(avatar_component_clause,[],[f6934]) ).
fof(f10283,plain,
( ! [X3,X9,X74] :
( ~ c_lessequals(X74,X9,X3)
| ~ class_Orderings_Oorder(X3)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X74,X3) )
| ~ spl0_1307 ),
inference(avatar_component_clause,[],[f10282]) ).
fof(f32435,plain,
( spl0_2481
| ~ spl0_786
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10948,f10282,f7217,f32433]) ).
fof(f32433,plain,
( spl0_2481
<=> ! [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_2481])]) ).
fof(f10948,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_786
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f7218]) ).
fof(f32430,plain,
( spl0_2480
| ~ spl0_715
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10941,f10282,f6918,f32428]) ).
fof(f32428,plain,
( spl0_2480
<=> ! [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_2480])]) ).
fof(f6918,plain,
( spl0_715
<=> ! [X27,X3] : c_lessequals(X27,c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f10941,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_UNIV,X1,tc_set(X0)) )
| ~ spl0_715
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f6919]) ).
fof(f6919,plain,
( ! [X3,X27] : c_lessequals(X27,c_UNIV,tc_set(X3))
| ~ spl0_715 ),
inference(avatar_component_clause,[],[f6918]) ).
fof(f32425,plain,
( spl0_2479
| ~ spl0_2095
| ~ spl0_2478 ),
inference(avatar_split_clause,[],[f32421,f32418,f25139,f32423]) ).
fof(f32423,plain,
( spl0_2479
<=> ! [X0] :
( c_IntDef_ONats != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f32418,plain,
( spl0_2478
<=> ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f32421,plain,
( ! [X0] :
( c_IntDef_ONats != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 )
| ~ spl0_2095
| ~ spl0_2478 ),
inference(forward_demodulation,[],[f32419,f25141]) ).
fof(f32419,plain,
( ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0 )
| ~ spl0_2478 ),
inference(avatar_component_clause,[],[f32418]) ).
fof(f32420,plain,
( ~ spl0_92
| spl0_2478
| ~ spl0_707
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f10920,f10250,f6884,f32418,f3616]) ).
fof(f6884,plain,
( spl0_707
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f10250,plain,
( spl0_1299
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatLeast(X11,X3) != c_SetInterval_OatLeast(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f10920,plain,
( ! [X0] :
( c_UNIV != c_SetInterval_OatLeast(X0,tc_nat)
| c_0 = X0
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_707
| ~ spl0_1299 ),
inference(superposition,[],[f10251,f6886]) ).
fof(f6886,plain,
( c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat)
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f6884]) ).
fof(f10251,plain,
( ! [X3,X11,X8] :
( c_SetInterval_OatLeast(X11,X3) != c_SetInterval_OatLeast(X8,X3)
| X8 = X11
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_1299 ),
inference(avatar_component_clause,[],[f10250]) ).
fof(f32416,plain,
( spl0_2477
| ~ spl0_764
| ~ spl0_2419 ),
inference(avatar_split_clause,[],[f32029,f30881,f7128,f32414]) ).
fof(f32414,plain,
( spl0_2477
<=> ! [X0] : c_0 != c_plus(X0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f7128,plain,
( spl0_764
<=> ! [X8] : c_plus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f32029,plain,
( ! [X0] : c_0 != c_plus(X0,c_1,tc_nat)
| ~ spl0_764
| ~ spl0_2419 ),
inference(superposition,[],[f30882,f7129]) ).
fof(f7129,plain,
( ! [X8] : c_plus(X8,c_0,tc_nat) = X8
| ~ spl0_764 ),
inference(avatar_component_clause,[],[f7128]) ).
fof(f32412,plain,
( spl0_2476
| ~ spl0_719
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10907,f10238,f6934,f32410]) ).
fof(f32410,plain,
( spl0_2476
<=> ! [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_2476])]) ).
fof(f10238,plain,
( spl0_1296
<=> ! [X25,X3,X10] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f10907,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,c_emptyset,tc_set(X0)) )
| ~ spl0_719
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f6935]) ).
fof(f10239,plain,
( ! [X3,X10,X25] :
( ~ c_lessequals(X10,X25,X3)
| ~ class_Orderings_Oorder(X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) )
| ~ spl0_1296 ),
inference(avatar_component_clause,[],[f10238]) ).
fof(f32408,plain,
( spl0_2475
| ~ spl0_786
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10897,f10238,f7217,f32406]) ).
fof(f32406,plain,
( spl0_2475
<=> ! [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_2475])]) ).
fof(f10897,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_786
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f7218]) ).
fof(f32403,plain,
( spl0_2474
| ~ spl0_715
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10890,f10238,f6918,f32401]) ).
fof(f32401,plain,
( spl0_2474
<=> ! [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_2474])]) ).
fof(f10890,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(X0))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_UNIV,X1,tc_set(X0)) )
| ~ spl0_715
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f6919]) ).
fof(f32399,plain,
( spl0_2473
| ~ spl0_785
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10868,f10234,f7213,f32397]) ).
fof(f32397,plain,
( spl0_2473
<=> ! [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_2473])]) ).
fof(f7213,plain,
( spl0_785
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f10234,plain,
( spl0_1295
<=> ! [X25,X3,X10] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastAtMost(X25,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f10868,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_785
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f7214]) ).
fof(f7214,plain,
( ! [X3] :
( c_less(c_0,c_1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) )
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7213]) ).
fof(f10235,plain,
( ! [X3,X10,X25] :
( ~ c_less(X10,X25,X3)
| ~ class_Orderings_Oorder(X3)
| c_emptyset = c_SetInterval_OatLeastAtMost(X25,X10,X3) )
| ~ spl0_1295 ),
inference(avatar_component_clause,[],[f10234]) ).
fof(f32395,plain,
( spl0_2472
| ~ spl0_92
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10857,f10230,f3616,f32393]) ).
fof(f32393,plain,
( spl0_2472
<=> ! [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_2472])]) ).
fof(f10230,plain,
( spl0_1294
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatLeast(X9,X3) = c_uminus(c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f10857,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,tc_nat) = c_uminus(c_SetInterval_OlessThan(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_92
| ~ spl0_1294 ),
inference(resolution,[],[f10231,f3618]) ).
fof(f3618,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f3616]) ).
fof(f10231,plain,
( ! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatLeast(X9,X3) = c_uminus(c_SetInterval_OlessThan(X9,X3),tc_set(X3)) )
| ~ spl0_1294 ),
inference(avatar_component_clause,[],[f10230]) ).
fof(f32391,plain,
( spl0_2471
| ~ spl0_28
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10856,f10230,f3296,f32389]) ).
fof(f32389,plain,
( spl0_2471
<=> ! [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_2471])]) ).
fof(f3296,plain,
( spl0_28
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f10856,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OlessThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint))
| ~ spl0_28
| ~ spl0_1294 ),
inference(resolution,[],[f10231,f3298]) ).
fof(f3298,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3296]) ).
fof(f32387,plain,
( spl0_2470
| ~ spl0_92
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f10855,f10226,f3616,f32385]) ).
fof(f32385,plain,
( spl0_2470
<=> ! [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_2470])]) ).
fof(f10226,plain,
( spl0_1293
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatMost(X9,X3) = c_uminus(c_SetInterval_OgreaterThan(X9,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f10855,plain,
( ! [X0] : c_SetInterval_OatMost(X0,tc_nat) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_92
| ~ spl0_1293 ),
inference(resolution,[],[f10227,f3618]) ).
fof(f10227,plain,
( ! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatMost(X9,X3) = c_uminus(c_SetInterval_OgreaterThan(X9,X3),tc_set(X3)) )
| ~ spl0_1293 ),
inference(avatar_component_clause,[],[f10226]) ).
fof(f32383,plain,
( spl0_2469
| ~ spl0_28
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f10854,f10226,f3296,f32381]) ).
fof(f32381,plain,
( spl0_2469
<=> ! [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_2469])]) ).
fof(f10854,plain,
( ! [X0] : c_SetInterval_OatMost(X0,tc_IntDef_Oint) = c_uminus(c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint))
| ~ spl0_28
| ~ spl0_1293 ),
inference(resolution,[],[f10227,f3298]) ).
fof(f32379,plain,
( spl0_2468
| ~ spl0_92
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10853,f10222,f3616,f32377]) ).
fof(f32377,plain,
( spl0_2468
<=> ! [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_2468])]) ).
fof(f10222,plain,
( spl0_1292
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatMost(X9,X3),tc_set(X3)) = c_SetInterval_OgreaterThan(X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f10853,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(X0,tc_nat)
| ~ spl0_92
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f3618]) ).
fof(f10223,plain,
( ! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatMost(X9,X3),tc_set(X3)) = c_SetInterval_OgreaterThan(X9,X3) )
| ~ spl0_1292 ),
inference(avatar_component_clause,[],[f10222]) ).
fof(f32375,plain,
( spl0_2467
| ~ spl0_28
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10852,f10222,f3296,f32373]) ).
fof(f32373,plain,
( spl0_2467
<=> ! [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_2467])]) ).
fof(f10852,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(X0,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f3298]) ).
fof(f32371,plain,
( spl0_2466
| ~ spl0_764
| ~ spl0_2412 ),
inference(avatar_split_clause,[],[f31732,f30852,f7128,f32369]) ).
fof(f32369,plain,
( spl0_2466
<=> ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_1,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).
fof(f30852,plain,
( spl0_2412
<=> ! [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_2412])]) ).
fof(f31732,plain,
( ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_1,X0,X1),X1)
| ~ spl0_764
| ~ spl0_2412 ),
inference(superposition,[],[f30853,f7129]) ).
fof(f30853,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_2412 ),
inference(avatar_component_clause,[],[f30852]) ).
fof(f32367,plain,
( spl0_2465
| ~ spl0_92
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10851,f10218,f3616,f32365]) ).
fof(f32365,plain,
( spl0_2465
<=> ! [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_2465])]) ).
fof(f10218,plain,
( spl0_1291
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatLeast(X9,X3),tc_set(X3)) = c_SetInterval_OlessThan(X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f10851,plain,
( ! [X0] : c_SetInterval_OlessThan(X0,tc_nat) = c_uminus(c_SetInterval_OatLeast(X0,tc_nat),tc_set(tc_nat))
| ~ spl0_92
| ~ spl0_1291 ),
inference(resolution,[],[f10219,f3618]) ).
fof(f10219,plain,
( ! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatLeast(X9,X3),tc_set(X3)) = c_SetInterval_OlessThan(X9,X3) )
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f10218]) ).
fof(f32363,plain,
( spl0_2464
| ~ spl0_28
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10850,f10218,f3296,f32361]) ).
fof(f32361,plain,
( spl0_2464
<=> ! [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_2464])]) ).
fof(f10850,plain,
( ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(X0,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_1291 ),
inference(resolution,[],[f10219,f3298]) ).
fof(f32354,plain,
( ~ spl0_40
| spl0_2463
| ~ spl0_109
| ~ spl0_1204
| ~ spl0_1261
| ~ spl0_1268 ),
inference(avatar_split_clause,[],[f10716,f10126,f10092,f9497,f3695,f32352,f3356]) ).
fof(f3356,plain,
( spl0_40
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f32352,plain,
( spl0_2463
<=> ! [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_2463])]) ).
fof(f9497,plain,
( spl0_1204
<=> ! [X10] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f10126,plain,
( spl0_1268
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f10716,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_109
| ~ spl0_1204
| ~ spl0_1261
| ~ spl0_1268 ),
inference(forward_demodulation,[],[f10703,f10671]) ).
fof(f10703,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_1204
| ~ spl0_1268 ),
inference(resolution,[],[f10127,f9498]) ).
fof(f9498,plain,
( ! [X10] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1204 ),
inference(avatar_component_clause,[],[f9497]) ).
fof(f10127,plain,
( ! [X3,X15] :
( c_lessequals(c_0,c_uminus(X15,X3),X3)
| ~ c_lessequals(X15,c_0,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) )
| ~ spl0_1268 ),
inference(avatar_component_clause,[],[f10126]) ).
fof(f32350,plain,
( spl0_2462
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1266 ),
inference(avatar_split_clause,[],[f10694,f10118,f8297,f3421,f32348]) ).
fof(f32348,plain,
( spl0_2462
<=> ! [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_2462])]) ).
fof(f8297,plain,
( spl0_1005
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f10118,plain,
( spl0_1266
<=> ! [X37,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(X37,X3) = c_times(X37,c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f10694,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1266 ),
inference(forward_demodulation,[],[f10693,f8587]) ).
fof(f8587,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1005 ),
inference(resolution,[],[f8298,f3423]) ).
fof(f8298,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) )
| ~ spl0_1005 ),
inference(avatar_component_clause,[],[f8297]) ).
fof(f10693,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_53
| ~ spl0_1266 ),
inference(resolution,[],[f10119,f3423]) ).
fof(f10119,plain,
( ! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(X37,X3) = c_times(X37,c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) )
| ~ spl0_1266 ),
inference(avatar_component_clause,[],[f10118]) ).
fof(f32346,plain,
( spl0_2461
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1265 ),
inference(avatar_split_clause,[],[f10692,f10108,f8297,f3421,f32344]) ).
fof(f32344,plain,
( spl0_2461
<=> ! [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_2461])]) ).
fof(f10108,plain,
( spl0_1265
<=> ! [X37,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X37,X3) = c_uminus(X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f10692,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_times(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1265 ),
inference(forward_demodulation,[],[f10691,f8587]) ).
fof(f10691,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_53
| ~ spl0_1265 ),
inference(resolution,[],[f10109,f3423]) ).
fof(f10109,plain,
( ! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X37,X3) = c_uminus(X37,X3) )
| ~ spl0_1265 ),
inference(avatar_component_clause,[],[f10108]) ).
fof(f32341,plain,
( spl0_2460
| ~ spl0_110
| ~ spl0_1207 ),
inference(avatar_split_clause,[],[f9901,f9513,f3700,f32339]) ).
fof(f32339,plain,
( spl0_2460
<=> ! [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_2460])]) ).
fof(f3700,plain,
( spl0_110
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f9513,plain,
( spl0_1207
<=> ! [X25,X10] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f9901,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_110
| ~ spl0_1207 ),
inference(superposition,[],[f9514,f3702]) ).
fof(f3702,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f3700]) ).
fof(f9514,plain,
( ! [X10,X25] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint)
| ~ spl0_1207 ),
inference(avatar_component_clause,[],[f9513]) ).
fof(f32336,plain,
( spl0_2459
| ~ spl0_109
| ~ spl0_1207 ),
inference(avatar_split_clause,[],[f9900,f9513,f3695,f32334]) ).
fof(f32334,plain,
( spl0_2459
<=> ! [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_2459])]) ).
fof(f9900,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_109
| ~ spl0_1207 ),
inference(superposition,[],[f9514,f3697]) ).
fof(f32331,plain,
( spl0_2458
| ~ spl0_109
| ~ spl0_1207 ),
inference(avatar_split_clause,[],[f9898,f9513,f3695,f32329]) ).
fof(f32329,plain,
( spl0_2458
<=> ! [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_2458])]) ).
fof(f9898,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_109
| ~ spl0_1207 ),
inference(superposition,[],[f9514,f3697]) ).
fof(f32327,plain,
( spl0_2457
| ~ spl0_775
| ~ spl0_1178 ),
inference(avatar_split_clause,[],[f9723,f9392,f7172,f32325]) ).
fof(f32325,plain,
( spl0_2457
<=> ! [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_2457])]) ).
fof(f9392,plain,
( spl0_1178
<=> ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f9723,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_775
| ~ spl0_1178 ),
inference(superposition,[],[f9393,f7174]) ).
fof(f9393,plain,
( ! [X3,X35] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_1178 ),
inference(avatar_component_clause,[],[f9392]) ).
fof(f32323,plain,
( spl0_2456
| ~ spl0_764
| ~ spl0_2411 ),
inference(avatar_split_clause,[],[f31730,f30848,f7128,f32321]) ).
fof(f32321,plain,
( spl0_2456
<=> ! [X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).
fof(f30848,plain,
( spl0_2411
<=> ! [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_2411])]) ).
fof(f31730,plain,
( ! [X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_764
| ~ spl0_2411 ),
inference(superposition,[],[f30849,f7129]) ).
fof(f30849,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2)
| ~ spl0_2411 ),
inference(avatar_component_clause,[],[f30848]) ).
fof(f32319,plain,
( spl0_2455
| ~ spl0_832
| ~ spl0_1174 ),
inference(avatar_split_clause,[],[f9700,f9376,f7407,f32317]) ).
fof(f32317,plain,
( spl0_2455
<=> ! [X0,X1] :
( c_less(X0,X1,tc_nat)
| c_0 = c_minus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).
fof(f7407,plain,
( spl0_832
<=> ! [X10] :
( c_0 = X10
| c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f9376,plain,
( spl0_1174
<=> ! [X25,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f9700,plain,
( ! [X0,X1] :
( c_less(X0,X1,tc_nat)
| c_0 = c_minus(X1,X0,tc_nat) )
| ~ spl0_832
| ~ spl0_1174 ),
inference(resolution,[],[f9377,f7408]) ).
fof(f7408,plain,
( ! [X10] :
( c_less(c_0,X10,tc_nat)
| c_0 = X10 )
| ~ spl0_832 ),
inference(avatar_component_clause,[],[f7407]) ).
fof(f9377,plain,
( ! [X10,X25] :
( ~ c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat)
| c_less(X25,X10,tc_nat) )
| ~ spl0_1174 ),
inference(avatar_component_clause,[],[f9376]) ).
fof(f32315,plain,
( spl0_2454
| ~ spl0_832
| ~ spl0_1173 ),
inference(avatar_split_clause,[],[f9697,f9372,f7407,f32313]) ).
fof(f32313,plain,
( spl0_2454
<=> ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).
fof(f9372,plain,
( spl0_1173
<=> ! [X25,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f9697,plain,
( ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X1,X0,tc_nat) )
| ~ spl0_832
| ~ spl0_1173 ),
inference(resolution,[],[f9373,f7408]) ).
fof(f9373,plain,
( ! [X10,X25] :
( ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat)
| c_less(c_0,X10,tc_nat) )
| ~ spl0_1173 ),
inference(avatar_component_clause,[],[f9372]) ).
fof(f32311,plain,
( spl0_2453
| ~ spl0_832
| ~ spl0_1172 ),
inference(avatar_split_clause,[],[f9694,f9368,f7407,f32309]) ).
fof(f32309,plain,
( spl0_2453
<=> ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).
fof(f9368,plain,
( spl0_1172
<=> ! [X25,X10] :
( c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f9694,plain,
( ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_times(X0,X1,tc_nat) )
| ~ spl0_832
| ~ spl0_1172 ),
inference(resolution,[],[f9369,f7408]) ).
fof(f9369,plain,
( ! [X10,X25] :
( ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat)
| c_less(c_0,X25,tc_nat) )
| ~ spl0_1172 ),
inference(avatar_component_clause,[],[f9368]) ).
fof(f32307,plain,
( spl0_2452
| ~ spl0_832
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9623,f9308,f7407,f32305]) ).
fof(f32305,plain,
( spl0_2452
<=> ! [X0] :
( c_0 = c_List_Ohd(c_List_Oupt(c_0,X0),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).
fof(f9308,plain,
( spl0_1157
<=> ! [X52,X8] :
( ~ c_less(X8,X52,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X52),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f9623,plain,
( ! [X0] :
( c_0 = c_List_Ohd(c_List_Oupt(c_0,X0),tc_nat)
| c_0 = X0 )
| ~ spl0_832
| ~ spl0_1157 ),
inference(resolution,[],[f9309,f7408]) ).
fof(f9309,plain,
( ! [X8,X52] :
( ~ c_less(X8,X52,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X52),tc_nat) = X8 )
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9308]) ).
fof(f32302,plain,
( spl0_2451
| ~ spl0_974
| ~ spl0_1127 ),
inference(avatar_split_clause,[],[f9198,f9087,f8171,f32300]) ).
fof(f32300,plain,
( spl0_2451
<=> ! [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_2451])]) ).
fof(f8171,plain,
( spl0_974
<=> ! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f9087,plain,
( spl0_1127
<=> ! [X15] : c_uminus(X15,tc_IntDef_Oint) = c_div(X15,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f9198,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_974
| ~ spl0_1127 ),
inference(superposition,[],[f9088,f8172]) ).
fof(f8172,plain,
( ! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint)
| ~ spl0_974 ),
inference(avatar_component_clause,[],[f8171]) ).
fof(f9088,plain,
( ! [X15] : c_uminus(X15,tc_IntDef_Oint) = c_div(X15,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9087]) ).
fof(f32298,plain,
( spl0_2450
| ~ spl0_1019
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9187,f8939,f8353,f32296]) ).
fof(f32296,plain,
( spl0_2450
<=> ! [X0,X1] :
( ~ c_in(X1,c_Pow(c_emptyset,X0),tc_set(X0))
| c_emptyset = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).
fof(f8353,plain,
( spl0_1019
<=> ! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f8939,plain,
( spl0_1115
<=> ! [X16,X3,X15] :
( X15 = X16
| ~ c_in(X16,c_insert(X15,c_emptyset,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f9187,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_Pow(c_emptyset,X0),tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_1019
| ~ spl0_1115 ),
inference(superposition,[],[f8940,f8354]) ).
fof(f8354,plain,
( ! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3))
| ~ spl0_1019 ),
inference(avatar_component_clause,[],[f8353]) ).
fof(f8940,plain,
( ! [X3,X16,X15] :
( ~ c_in(X16,c_insert(X15,c_emptyset,X3),X3)
| X15 = X16 )
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f8939]) ).
fof(f32294,plain,
( spl0_2449
| ~ spl0_994
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9186,f8939,f8252,f32292]) ).
fof(f32292,plain,
( spl0_2449
<=> ! [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_2449])]) ).
fof(f8252,plain,
( spl0_994
<=> ! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f9186,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| c_List_Olist_ONil = X1 )
| ~ spl0_994
| ~ spl0_1115 ),
inference(superposition,[],[f8940,f8253]) ).
fof(f8253,plain,
( ! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13))
| ~ spl0_994 ),
inference(avatar_component_clause,[],[f8252]) ).
fof(f32290,plain,
( spl0_2448
| ~ spl0_822
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f9107,f8818,f7367,f32288]) ).
fof(f32288,plain,
( spl0_2448
<=> ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f7367,plain,
( spl0_822
<=> ! [X8,X3] : c_List_Orev(c_List_Orev(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f8818,plain,
( spl0_1085
<=> ! [X41,X3,X42] :
( X41 = X42
| c_List_Orev(X41,X3) != c_List_Orev(X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f9107,plain,
( ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 )
| ~ spl0_822
| ~ spl0_1085 ),
inference(superposition,[],[f8819,f7368]) ).
fof(f7368,plain,
( ! [X3,X8] : c_List_Orev(c_List_Orev(X8,X3),X3) = X8
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7367]) ).
fof(f8819,plain,
( ! [X41,X3,X42] :
( c_List_Orev(X41,X3) != c_List_Orev(X42,X3)
| X41 = X42 )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f8818]) ).
fof(f32286,plain,
( spl0_2447
| ~ spl0_993
| ~ spl0_1083 ),
inference(avatar_split_clause,[],[f9105,f8810,f8248,f32284]) ).
fof(f32284,plain,
( spl0_2447
<=> ! [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_2447])]) ).
fof(f8248,plain,
( spl0_993
<=> ! [X11,X8,X3] : c_Nat_Osize(c_List_Oreplicate(X8,X11,X3),tc_List_Olist(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f8810,plain,
( spl0_1083
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_less(c_0,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f9105,plain,
( ! [X2,X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_993
| ~ spl0_1083 ),
inference(superposition,[],[f8811,f8249]) ).
fof(f8249,plain,
( ! [X3,X11,X8] : c_Nat_Osize(c_List_Oreplicate(X8,X11,X3),tc_List_Olist(X3)) = X8
| ~ spl0_993 ),
inference(avatar_component_clause,[],[f8248]) ).
fof(f8811,plain,
( ! [X41,X3] :
( c_less(c_0,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Olist_ONil = X41 )
| ~ spl0_1083 ),
inference(avatar_component_clause,[],[f8810]) ).
fof(f32282,plain,
( spl0_2446
| ~ spl0_667
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9078,f8765,f6703,f32280]) ).
fof(f32280,plain,
( spl0_2446
<=> ! [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_2446])]) ).
fof(f8765,plain,
( spl0_1072
<=> ! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f9078,plain,
( ! [X0,X1] :
( ~ c_less(c_IntDef_Onat(X1),X0,tc_nat)
| c_less(X1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_667
| ~ spl0_1072 ),
inference(superposition,[],[f8766,f6704]) ).
fof(f8766,plain,
( ! [X37,X35] :
( ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat)
| c_less(X35,X37,tc_IntDef_Oint) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f8765]) ).
fof(f32278,plain,
( spl0_2445
| ~ spl0_794
| ~ spl0_2376 ),
inference(avatar_split_clause,[],[f31362,f30652,f7249,f32276]) ).
fof(f32276,plain,
( spl0_2445
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f7249,plain,
( spl0_794
<=> ! [X27,X3,X15] : c_emptyset != c_insert(X15,X27,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f30652,plain,
( spl0_2376
<=> ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f31362,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_794
| ~ spl0_2376 ),
inference(superposition,[],[f7250,f30653]) ).
fof(f30653,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_2376 ),
inference(avatar_component_clause,[],[f30652]) ).
fof(f7250,plain,
( ! [X3,X27,X15] : c_emptyset != c_insert(X15,X27,X3)
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f7249]) ).
fof(f32274,plain,
( spl0_2444
| ~ spl0_667
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9073,f8765,f6703,f32272]) ).
fof(f32272,plain,
( spl0_2444
<=> ! [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_2444])]) ).
fof(f9073,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_IntDef_Oint(X0),X1,tc_IntDef_Oint) )
| ~ spl0_667
| ~ spl0_1072 ),
inference(superposition,[],[f8766,f6704]) ).
fof(f32258,plain,
( spl0_2443
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2442 ),
inference(avatar_split_clause,[],[f32254,f32251,f10415,f10092,f6703,f3695,f32256]) ).
fof(f32256,plain,
( spl0_2443
<=> ! [X0] : c_Divides_Oop_Amod(X0,c_plus(c_1,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f32251,plain,
( spl0_2442
<=> ! [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_2442])]) ).
fof(f32254,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_plus(c_1,X0,tc_nat),tc_nat) = X0
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2442 ),
inference(forward_demodulation,[],[f32252,f11235]) ).
fof(f32252,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_2442 ),
inference(avatar_component_clause,[],[f32251]) ).
fof(f32253,plain,
( spl0_2442
| ~ spl0_955
| ~ spl0_1059 ),
inference(avatar_split_clause,[],[f9019,f8712,f7977,f32251]) ).
fof(f7977,plain,
( spl0_955
<=> ! [X10] : c_less(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f8712,plain,
( spl0_1059
<=> ! [X8,X10] :
( ~ c_less(X8,X10,tc_nat)
| c_Divides_Oop_Amod(X8,X10,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f9019,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_955
| ~ spl0_1059 ),
inference(resolution,[],[f8713,f7978]) ).
fof(f7978,plain,
( ! [X10] : c_less(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_955 ),
inference(avatar_component_clause,[],[f7977]) ).
fof(f8713,plain,
( ! [X10,X8] :
( ~ c_less(X8,X10,tc_nat)
| c_Divides_Oop_Amod(X8,X10,tc_nat) = X8 )
| ~ spl0_1059 ),
inference(avatar_component_clause,[],[f8712]) ).
fof(f32239,plain,
( spl0_2441
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2440 ),
inference(avatar_split_clause,[],[f32235,f32232,f10415,f10092,f6703,f3695,f32237]) ).
fof(f32237,plain,
( spl0_2441
<=> ! [X0] : c_0 = c_div(X0,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).
fof(f32232,plain,
( spl0_2440
<=> ! [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_2440])]) ).
fof(f32235,plain,
( ! [X0] : c_0 = c_div(X0,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2440 ),
inference(forward_demodulation,[],[f32233,f11235]) ).
fof(f32233,plain,
( ! [X0] : c_0 = c_div(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_2440 ),
inference(avatar_component_clause,[],[f32232]) ).
fof(f32234,plain,
( spl0_2440
| ~ spl0_955
| ~ spl0_1057 ),
inference(avatar_split_clause,[],[f9006,f8704,f7977,f32232]) ).
fof(f8704,plain,
( spl0_1057
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_0 = c_div(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f9006,plain,
( ! [X0] : c_0 = c_div(X0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_955
| ~ spl0_1057 ),
inference(resolution,[],[f8705,f7978]) ).
fof(f8705,plain,
( ! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_0 = c_div(X25,X10,tc_nat) )
| ~ spl0_1057 ),
inference(avatar_component_clause,[],[f8704]) ).
fof(f32230,plain,
( spl0_2439
| ~ spl0_805
| ~ spl0_1048 ),
inference(avatar_split_clause,[],[f8992,f8668,f7299,f32228]) ).
fof(f32228,plain,
( spl0_2439
<=> ! [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_2439])]) ).
fof(f7299,plain,
( spl0_805
<=> ! [X8,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f8668,plain,
( spl0_1048
<=> ! [X11,X3] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X11,X3),X3) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f8992,plain,
( ! [X0,X1] :
( c_Main_Onot__Some__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_805
| ~ spl0_1048 ),
inference(superposition,[],[f7300,f8669]) ).
fof(f8669,plain,
( ! [X3,X11] :
( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X11,X3),X3) = X11
| c_Datatype_Ooption_ONone = X11 )
| ~ spl0_1048 ),
inference(avatar_component_clause,[],[f8668]) ).
fof(f7300,plain,
( ! [X3,X8] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X3),X3) = X8
| ~ spl0_805 ),
inference(avatar_component_clause,[],[f7299]) ).
fof(f32226,plain,
( spl0_2438
| ~ spl0_805
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f8984,f8664,f7299,f32224]) ).
fof(f32224,plain,
( spl0_2438
<=> ! [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_2438])]) ).
fof(f8664,plain,
( spl0_1047
<=> ! [X11,X3] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X11,X3),X3) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f8984,plain,
( ! [X0,X1] :
( c_Main_Onot__None__eq__1(X0,X1) = c_Datatype_Othe(X0,X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_805
| ~ spl0_1047 ),
inference(superposition,[],[f7300,f8665]) ).
fof(f8665,plain,
( ! [X3,X11] :
( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X11,X3),X3) = X11
| c_Datatype_Ooption_ONone = X11 )
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f8664]) ).
fof(f32222,plain,
( spl0_2437
| ~ spl0_908
| ~ spl0_1008 ),
inference(avatar_split_clause,[],[f8592,f8309,f7787,f32220]) ).
fof(f32220,plain,
( spl0_2437
<=> ! [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_2437])]) ).
fof(f7787,plain,
( spl0_908
<=> ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f8309,plain,
( spl0_1008
<=> ! [X35] : c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f8592,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_908
| ~ spl0_1008 ),
inference(superposition,[],[f7788,f8310]) ).
fof(f8310,plain,
( ! [X35] : c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X35),c_Numeral_Obit_OB0)
| ~ spl0_1008 ),
inference(avatar_component_clause,[],[f8309]) ).
fof(f7788,plain,
( ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0))
| ~ spl0_908 ),
inference(avatar_component_clause,[],[f7787]) ).
fof(f32218,plain,
( spl0_2436
| ~ spl0_794
| ~ spl0_2375 ),
inference(avatar_split_clause,[],[f31317,f30648,f7249,f32216]) ).
fof(f32216,plain,
( spl0_2436
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f30648,plain,
( spl0_2375
<=> ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f31317,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_794
| ~ spl0_2375 ),
inference(superposition,[],[f7250,f30649]) ).
fof(f30649,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_2375 ),
inference(avatar_component_clause,[],[f30648]) ).
fof(f32214,plain,
( spl0_2435
| ~ spl0_900
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f8564,f8276,f7754,f32212]) ).
fof(f32212,plain,
( spl0_2435
<=> ! [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_2435])]) ).
fof(f7754,plain,
( spl0_900
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_emptyset != c_List_Oset(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f8276,plain,
( spl0_1000
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate1(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f8564,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orotate1(X0,X1) )
| ~ spl0_900
| ~ spl0_1000 ),
inference(superposition,[],[f7755,f8277]) ).
fof(f8277,plain,
( ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate1(X41,X3),X3)
| ~ spl0_1000 ),
inference(avatar_component_clause,[],[f8276]) ).
fof(f7755,plain,
( ! [X41,X3] :
( c_emptyset != c_List_Oset(X41,X3)
| c_List_Olist_ONil = X41 )
| ~ spl0_900 ),
inference(avatar_component_clause,[],[f7754]) ).
fof(f32210,plain,
( spl0_2434
| ~ spl0_900
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f8562,f8272,f7754,f32208]) ).
fof(f32208,plain,
( spl0_2434
<=> ! [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_2434])]) ).
fof(f8272,plain,
( spl0_999
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orev(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f8562,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_900
| ~ spl0_999 ),
inference(superposition,[],[f7755,f8273]) ).
fof(f8273,plain,
( ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orev(X41,X3),X3)
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f8272]) ).
fof(f32206,plain,
( spl0_2433
| ~ spl0_900
| ~ spl0_998 ),
inference(avatar_split_clause,[],[f8559,f8268,f7754,f32204]) ).
fof(f32204,plain,
( spl0_2433
<=> ! [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_2433])]) ).
fof(f8268,plain,
( spl0_998
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Oremdups(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f8559,plain,
( ! [X0,X1] :
( c_emptyset != c_List_Oset(X0,X1)
| c_List_Olist_ONil = c_List_Oremdups(X0,X1) )
| ~ spl0_900
| ~ spl0_998 ),
inference(superposition,[],[f7755,f8269]) ).
fof(f8269,plain,
( ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Oremdups(X41,X3),X3)
| ~ spl0_998 ),
inference(avatar_component_clause,[],[f8268]) ).
fof(f32202,plain,
( spl0_2432
| ~ spl0_968
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f8484,f8150,f8146,f32200]) ).
fof(f32200,plain,
( spl0_2432
<=> ! [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_2432])]) ).
fof(f8146,plain,
( spl0_968
<=> ! [X37] :
( ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X37)) = X37 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f8150,plain,
( spl0_969
<=> ! [X37] :
( c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f8484,plain,
( ! [X0] :
( c_0 = c_IntDef_Oint(c_IntDef_Onat(X0))
| c_IntDef_Oint(c_IntDef_Onat(X0)) = X0 )
| ~ spl0_968
| ~ spl0_969 ),
inference(resolution,[],[f8151,f8147]) ).
fof(f8147,plain,
( ! [X37] :
( ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X37)) = X37 )
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8146]) ).
fof(f8151,plain,
( ! [X37] :
( c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X37)) )
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f8150]) ).
fof(f32014,plain,
( spl0_2431
| ~ spl0_2095
| ~ spl0_2416 ),
inference(avatar_split_clause,[],[f30871,f30868,f25139,f32012]) ).
fof(f32012,plain,
( spl0_2431
<=> ! [X0,X1] : c_IntDef_ONats = c_union(c_uminus(X0,tc_set(X1)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f30868,plain,
( spl0_2416
<=> ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f30871,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_2095
| ~ spl0_2416 ),
inference(forward_demodulation,[],[f30869,f25141]) ).
fof(f30869,plain,
( ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_2416 ),
inference(avatar_component_clause,[],[f30868]) ).
fof(f31601,plain,
( spl0_2430
| ~ spl0_2095
| ~ spl0_2396 ),
inference(avatar_split_clause,[],[f30785,f30782,f25139,f31599]) ).
fof(f31599,plain,
( spl0_2430
<=> ! [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_2430])]) ).
fof(f30782,plain,
( spl0_2396
<=> ! [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_2396])]) ).
fof(f30785,plain,
( ! [X0] :
( c_IntDef_ONats = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_2095
| ~ spl0_2396 ),
inference(forward_demodulation,[],[f30783,f25141]) ).
fof(f30783,plain,
( ! [X0] :
( c_UNIV = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_2396 ),
inference(avatar_component_clause,[],[f30782]) ).
fof(f31305,plain,
( spl0_2429
| ~ spl0_109
| ~ spl0_2387 ),
inference(avatar_split_clause,[],[f30720,f30717,f3695,f31302]) ).
fof(f31302,plain,
( spl0_2429
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).
fof(f30717,plain,
( spl0_2387
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).
fof(f30720,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_2387 ),
inference(superposition,[],[f30718,f3697]) ).
fof(f30718,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ spl0_2387 ),
inference(avatar_component_clause,[],[f30717]) ).
fof(f31242,plain,
( spl0_2428
| ~ spl0_109
| ~ spl0_2386 ),
inference(avatar_split_clause,[],[f30697,f30694,f3695,f31239]) ).
fof(f31239,plain,
( spl0_2428
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).
fof(f30694,plain,
( spl0_2386
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).
fof(f30697,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_2386 ),
inference(superposition,[],[f30695,f3697]) ).
fof(f30695,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ spl0_2386 ),
inference(avatar_component_clause,[],[f30694]) ).
fof(f31237,plain,
( ~ spl0_2427
| ~ spl0_10
| ~ spl0_1142
| ~ spl0_1752
| spl0_2352 ),
inference(avatar_split_clause,[],[f30532,f30528,f17547,f9248,f3206,f31234]) ).
fof(f31234,plain,
( spl0_2427
<=> 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_2427])]) ).
fof(f3206,plain,
( spl0_10
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f9248,plain,
( spl0_1142
<=> ! [X37,X35] : c_plus(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X37,X35,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f17547,plain,
( spl0_1752
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_plus(X15,X16,X3),X3) = c_plus(c_uminus(X15,X3),c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f30528,plain,
( spl0_2352
<=> 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_2352])]) ).
fof(f30532,plain,
( ~ c_lessequals(c_0,c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_1142
| ~ spl0_1752
| spl0_2352 ),
inference(forward_demodulation,[],[f30530,f18256]) ).
fof(f18256,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_10
| ~ spl0_1142
| ~ spl0_1752 ),
inference(forward_demodulation,[],[f18255,f9249]) ).
fof(f9249,plain,
( ! [X37,X35] : c_plus(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X37,X35,tc_IntDef_Oint)
| ~ spl0_1142 ),
inference(avatar_component_clause,[],[f9248]) ).
fof(f18255,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_10
| ~ spl0_1752 ),
inference(resolution,[],[f17548,f3208]) ).
fof(f3208,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f3206]) ).
fof(f17548,plain,
( ! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_plus(X15,X16,X3),X3) = c_plus(c_uminus(X15,X3),c_uminus(X16,X3),X3) )
| ~ spl0_1752 ),
inference(avatar_component_clause,[],[f17547]) ).
fof(f30530,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_2352 ),
inference(avatar_component_clause,[],[f30528]) ).
fof(f31082,plain,
( spl0_2426
| ~ spl0_12
| ~ spl0_1576
| ~ spl0_2347 ),
inference(avatar_split_clause,[],[f30507,f30504,f14310,f3216,f31080]) ).
fof(f31080,plain,
( spl0_2426
<=> ! [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_2426])]) ).
fof(f3216,plain,
( spl0_12
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f14310,plain,
( spl0_1576
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_uminus(c_times(X15,X16,X3),X3) = c_times(X15,c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f30504,plain,
( spl0_2347
<=> ! [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_2347])]) ).
fof(f30507,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_12
| ~ spl0_1576
| ~ spl0_2347 ),
inference(forward_demodulation,[],[f30505,f15071]) ).
fof(f15071,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_12
| ~ spl0_1576 ),
inference(resolution,[],[f14311,f3218]) ).
fof(f3218,plain,
( class_Ring__and__Field_Oring(tc_IntDef_Oint)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f3216]) ).
fof(f14311,plain,
( ! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_uminus(c_times(X15,X16,X3),X3) = c_times(X15,c_uminus(X16,X3),X3) )
| ~ spl0_1576 ),
inference(avatar_component_clause,[],[f14310]) ).
fof(f30505,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2347 ),
inference(avatar_component_clause,[],[f30504]) ).
fof(f31078,plain,
( spl0_2425
| ~ spl0_12
| ~ spl0_1575
| ~ spl0_2346 ),
inference(avatar_split_clause,[],[f30502,f30499,f14306,f3216,f31076]) ).
fof(f31076,plain,
( spl0_2425
<=> ! [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_2425])]) ).
fof(f14306,plain,
( spl0_1575
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_times(c_uminus(X15,X3),X16,X3) = c_uminus(c_times(X15,X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f30499,plain,
( spl0_2346
<=> ! [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_2346])]) ).
fof(f30502,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_uminus(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_12
| ~ spl0_1575
| ~ spl0_2346 ),
inference(forward_demodulation,[],[f30500,f15070]) ).
fof(f15070,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_12
| ~ spl0_1575 ),
inference(resolution,[],[f14307,f3218]) ).
fof(f14307,plain,
( ! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_times(c_uminus(X15,X3),X16,X3) = c_uminus(c_times(X15,X16,X3),X3) )
| ~ spl0_1575 ),
inference(avatar_component_clause,[],[f14306]) ).
fof(f30500,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2346 ),
inference(avatar_component_clause,[],[f30499]) ).
fof(f30917,plain,
( spl0_2424
| ~ spl0_118
| ~ spl0_2118 ),
inference(avatar_split_clause,[],[f25850,f25744,f3736,f30915]) ).
fof(f3736,plain,
( spl0_118
<=> ! [X3,X26] : ~ c_in(X26,c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f25744,plain,
( spl0_2118
<=> ! [X17,X20,X3,X83] :
( ~ c_in(X83,c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_OconverseE__1(X20,X83,X17,X3),c_Main_OconverseE__2(X20,X83,X17,X3),X17,X3),X20,tc_prod(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f25850,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
| ~ spl0_118
| ~ spl0_2118 ),
inference(resolution,[],[f25745,f3737]) ).
fof(f3737,plain,
( ! [X3,X26] : ~ c_in(X26,c_emptyset,X3)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3736]) ).
fof(f25745,plain,
( ! [X3,X83,X17,X20] :
( c_in(c_Pair(c_Main_OconverseE__1(X20,X83,X17,X3),c_Main_OconverseE__2(X20,X83,X17,X3),X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(X83,c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17)) )
| ~ spl0_2118 ),
inference(avatar_component_clause,[],[f25744]) ).
fof(f30913,plain,
( spl0_2423
| ~ spl0_764
| ~ spl0_769
| ~ spl0_1982 ),
inference(avatar_split_clause,[],[f21658,f21642,f7148,f7128,f30911]) ).
fof(f30911,plain,
( spl0_2423
<=> ! [X0] : c_1 = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).
fof(f7148,plain,
( spl0_769
<=> ! [X10] : c_0 = c_Orderings_Omin(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f21642,plain,
( spl0_1982
<=> ! [X25,X10] : c_plus(c_1,c_Orderings_Omin(X25,X10,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f21658,plain,
( ! [X0] : c_1 = c_Orderings_Omin(c_1,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_764
| ~ spl0_769
| ~ spl0_1982 ),
inference(forward_demodulation,[],[f21657,f7129]) ).
fof(f21657,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_764
| ~ spl0_769
| ~ spl0_1982 ),
inference(forward_demodulation,[],[f21645,f7149]) ).
fof(f7149,plain,
( ! [X10] : c_0 = c_Orderings_Omin(c_0,X10,tc_nat)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f7148]) ).
fof(f21645,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_764
| ~ spl0_1982 ),
inference(superposition,[],[f21643,f7129]) ).
fof(f21643,plain,
( ! [X10,X25] : c_plus(c_1,c_Orderings_Omin(X25,X10,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_1982 ),
inference(avatar_component_clause,[],[f21642]) ).
fof(f30909,plain,
( spl0_2422
| ~ spl0_993
| ~ spl0_1798
| ~ spl0_1799 ),
inference(avatar_split_clause,[],[f18703,f17868,f17864,f8248,f30907]) ).
fof(f30907,plain,
( spl0_2422
<=> ! [X0,X3] : c_Orderings_Omin(X0,X3,tc_nat) = c_Orderings_Omin(X3,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).
fof(f17864,plain,
( spl0_1798
<=> ! [X41,X3,X10] : c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) = c_Nat_Osize(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f17868,plain,
( spl0_1799
<=> ! [X24,X11,X9,X3] : c_List_Oreplicate(c_Orderings_Omin(X24,X9,tc_nat),X11,X3) = c_List_Osublist(c_List_Oreplicate(X9,X11,X3),c_SetInterval_OlessThan(X24,tc_nat),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f18703,plain,
( ! [X3,X0] : c_Orderings_Omin(X0,X3,tc_nat) = c_Orderings_Omin(X3,X0,tc_nat)
| ~ spl0_993
| ~ spl0_1798
| ~ spl0_1799 ),
inference(forward_demodulation,[],[f18702,f8249]) ).
fof(f18702,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_993
| ~ spl0_1798
| ~ spl0_1799 ),
inference(forward_demodulation,[],[f18693,f8249]) ).
fof(f18693,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_1798
| ~ spl0_1799 ),
inference(superposition,[],[f17865,f17869]) ).
fof(f17869,plain,
( ! [X3,X11,X9,X24] : c_List_Oreplicate(c_Orderings_Omin(X24,X9,tc_nat),X11,X3) = c_List_Osublist(c_List_Oreplicate(X9,X11,X3),c_SetInterval_OlessThan(X24,tc_nat),X3)
| ~ spl0_1799 ),
inference(avatar_component_clause,[],[f17868]) ).
fof(f17865,plain,
( ! [X41,X3,X10] : c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) = c_Nat_Osize(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),tc_List_Olist(X3))
| ~ spl0_1798 ),
inference(avatar_component_clause,[],[f17864]) ).
fof(f30905,plain,
( spl0_2421
| ~ spl0_710
| ~ spl0_1034
| ~ spl0_1797 ),
inference(avatar_split_clause,[],[f18665,f17860,f8414,f6898,f30903]) ).
fof(f30903,plain,
( spl0_2421
<=> ! [X0,X1] : c_Inter(c_insert(X1,c_emptyset,tc_set(X0)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).
fof(f6898,plain,
( spl0_710
<=> ! [X3] : c_UNIV = c_Inter(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f8414,plain,
( spl0_1034
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(X8,X3),c_UNIV,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f17860,plain,
( spl0_1797
<=> ! [X15,X3,X31] : c_Inter(c_insert(X15,X31,tc_set(X3)),X3) = c_Relation_OImage(c_Relation_Odiag(X15,X3),c_Inter(X31,X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f18665,plain,
( ! [X0,X1] : c_Inter(c_insert(X1,c_emptyset,tc_set(X0)),X0) = X1
| ~ spl0_710
| ~ spl0_1034
| ~ spl0_1797 ),
inference(forward_demodulation,[],[f18643,f8415]) ).
fof(f8415,plain,
( ! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X3),c_UNIV,X3,X3) = X8
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f8414]) ).
fof(f18643,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_710
| ~ spl0_1797 ),
inference(superposition,[],[f17861,f6899]) ).
fof(f6899,plain,
( ! [X3] : c_UNIV = c_Inter(c_emptyset,X3)
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f6898]) ).
fof(f17861,plain,
( ! [X31,X3,X15] : c_Inter(c_insert(X15,X31,tc_set(X3)),X3) = c_Relation_OImage(c_Relation_Odiag(X15,X3),c_Inter(X31,X3),X3,X3)
| ~ spl0_1797 ),
inference(avatar_component_clause,[],[f17860]) ).
fof(f30901,plain,
( spl0_2420
| ~ spl0_706
| ~ spl0_867
| ~ spl0_1797 ),
inference(avatar_split_clause,[],[f18662,f17860,f7549,f6880,f30899]) ).
fof(f30899,plain,
( spl0_2420
<=> ! [X0,X1] : c_emptyset = c_Inter(c_insert(c_emptyset,X1,tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).
fof(f7549,plain,
( spl0_867
<=> ! [X3,X31] : c_emptyset = c_Relation_OImage(c_emptyset,X31,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f18662,plain,
( ! [X0,X1] : c_emptyset = c_Inter(c_insert(c_emptyset,X1,tc_set(X0)),X0)
| ~ spl0_706
| ~ spl0_867
| ~ spl0_1797 ),
inference(forward_demodulation,[],[f18641,f7550]) ).
fof(f7550,plain,
( ! [X31,X3] : c_emptyset = c_Relation_OImage(c_emptyset,X31,X3,X3)
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7549]) ).
fof(f18641,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_706
| ~ spl0_1797 ),
inference(superposition,[],[f17861,f6881]) ).
fof(f30883,plain,
( spl0_2419
| ~ spl0_863
| ~ spl0_1787 ),
inference(avatar_split_clause,[],[f17804,f17795,f7531,f30881]) ).
fof(f7531,plain,
( spl0_863
<=> ! [X25] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f17795,plain,
( spl0_1787
<=> ! [X25,X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f17804,plain,
( ! [X0,X1] : c_0 != c_plus(X0,c_plus(c_1,X1,tc_nat),tc_nat)
| ~ spl0_863
| ~ spl0_1787 ),
inference(superposition,[],[f7532,f17796]) ).
fof(f17796,plain,
( ! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_1787 ),
inference(avatar_component_clause,[],[f17795]) ).
fof(f7532,plain,
( ! [X25] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat)
| ~ spl0_863 ),
inference(avatar_component_clause,[],[f7531]) ).
fof(f30879,plain,
( spl0_2418
| ~ spl0_1430
| ~ spl0_1679 ),
inference(avatar_split_clause,[],[f17276,f15784,f11664,f30877]) ).
fof(f30877,plain,
( spl0_2418
<=> ! [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_2418])]) ).
fof(f11664,plain,
( spl0_1430
<=> ! [X20,X3,X15] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| ~ c_in(c_Pair(X15,X15,X3,X3),X20,tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f15784,plain,
( spl0_1679
<=> ! [X27,X3,X15] :
( ~ c_in(X15,X27,X3)
| c_in(c_Pair(X15,X15,X3,X3),c_Relation_Odiag(X27,X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f17276,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_Wellfounded__Recursion_Owf(c_Relation_Odiag(X1,X2),X2) )
| ~ spl0_1430
| ~ spl0_1679 ),
inference(resolution,[],[f15785,f11665]) ).
fof(f11665,plain,
( ! [X3,X15,X20] :
( ~ c_in(c_Pair(X15,X15,X3,X3),X20,tc_prod(X3,X3))
| ~ c_Wellfounded__Recursion_Owf(X20,X3) )
| ~ spl0_1430 ),
inference(avatar_component_clause,[],[f11664]) ).
fof(f15785,plain,
( ! [X3,X27,X15] :
( c_in(c_Pair(X15,X15,X3,X3),c_Relation_Odiag(X27,X3),tc_prod(X3,X3))
| ~ c_in(X15,X27,X3) )
| ~ spl0_1679 ),
inference(avatar_component_clause,[],[f15784]) ).
fof(f30875,plain,
( spl0_2417
| ~ spl0_1521
| ~ spl0_1678 ),
inference(avatar_split_clause,[],[f17275,f15780,f13127,f30873]) ).
fof(f30873,plain,
( spl0_2417
<=> ! [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_2417])]) ).
fof(f13127,plain,
( spl0_1521
<=> ! [X41,X27,X3] :
( ~ c_in(c_Main_Oin__listsI__1(X27,X41,X3),X27,X3)
| c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f15780,plain,
( spl0_1678
<=> ! [X41,X27,X3] :
( c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_Main_Oin__listsI__1(X27,X41,X3),c_List_Oset(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f17275,plain,
( ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
| ~ spl0_1521
| ~ spl0_1678 ),
inference(duplicate_literal_removal,[],[f17264]) ).
fof(f17264,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_1521
| ~ spl0_1678 ),
inference(resolution,[],[f15781,f13128]) ).
fof(f13128,plain,
( ! [X41,X3,X27] :
( ~ c_in(c_Main_Oin__listsI__1(X27,X41,X3),X27,X3)
| c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) )
| ~ spl0_1521 ),
inference(avatar_component_clause,[],[f13127]) ).
fof(f15781,plain,
( ! [X41,X3,X27] :
( c_in(c_Main_Oin__listsI__1(X27,X41,X3),c_List_Oset(X41,X3),X3)
| c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) )
| ~ spl0_1678 ),
inference(avatar_component_clause,[],[f15780]) ).
fof(f30870,plain,
( spl0_2416
| ~ spl0_788
| ~ spl0_849
| ~ spl0_1671 ),
inference(avatar_split_clause,[],[f17167,f15752,f7475,f7225,f30868]) ).
fof(f7225,plain,
( spl0_788
<=> ! [X3] : c_UNIV = c_uminus(c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f7475,plain,
( spl0_849
<=> ! [X27,X3] : c_emptyset = c_minus(X27,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f15752,plain,
( spl0_1671
<=> ! [X27,X3,X31] : c_uminus(c_minus(X27,X31,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X27,tc_set(X3)),X31,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f17167,plain,
( ! [X0,X1] : c_UNIV = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_788
| ~ spl0_849
| ~ spl0_1671 ),
inference(forward_demodulation,[],[f17128,f7226]) ).
fof(f7226,plain,
( ! [X3] : c_UNIV = c_uminus(c_emptyset,tc_set(X3))
| ~ spl0_788 ),
inference(avatar_component_clause,[],[f7225]) ).
fof(f17128,plain,
( ! [X0,X1] : c_uminus(c_emptyset,tc_set(X1)) = c_union(c_uminus(X0,tc_set(X1)),X0,X1)
| ~ spl0_849
| ~ spl0_1671 ),
inference(superposition,[],[f15753,f7476]) ).
fof(f7476,plain,
( ! [X3,X27] : c_emptyset = c_minus(X27,X27,tc_set(X3))
| ~ spl0_849 ),
inference(avatar_component_clause,[],[f7475]) ).
fof(f15753,plain,
( ! [X31,X3,X27] : c_uminus(c_minus(X27,X31,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X27,tc_set(X3)),X31,X3)
| ~ spl0_1671 ),
inference(avatar_component_clause,[],[f15752]) ).
fof(f30866,plain,
( spl0_2415
| ~ spl0_751
| ~ spl0_764
| ~ spl0_1696 ),
inference(avatar_split_clause,[],[f16162,f16148,f7128,f7076,f30864]) ).
fof(f30864,plain,
( spl0_2415
<=> ! [X2,X0,X1] : c_List_Odrop(c_1,c_List_Olist_OCons(X2,X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).
fof(f16148,plain,
( spl0_1696
<=> ! [X41,X10,X11,X3] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_plus(c_1,X10,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f16162,plain,
( ! [X2,X0,X1] : c_List_Odrop(c_1,c_List_Olist_OCons(X2,X0,X1),X1) = X0
| ~ spl0_751
| ~ spl0_764
| ~ spl0_1696 ),
inference(forward_demodulation,[],[f16151,f7077]) ).
fof(f16151,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_764
| ~ spl0_1696 ),
inference(superposition,[],[f16149,f7129]) ).
fof(f16149,plain,
( ! [X41,X10,X3,X11] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_plus(c_1,X10,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3)
| ~ spl0_1696 ),
inference(avatar_component_clause,[],[f16148]) ).
fof(f30862,plain,
( spl0_2414
| ~ spl0_993
| ~ spl0_1607
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16141,f16113,f14489,f8248,f30860]) ).
fof(f30860,plain,
( spl0_2414
<=> ! [X1] : c_plus(c_1,X1,tc_nat) = c_plus(X1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f16141,plain,
( ! [X1] : c_plus(c_1,X1,tc_nat) = c_plus(X1,c_1,tc_nat)
| ~ spl0_993
| ~ spl0_1607
| ~ spl0_1694 ),
inference(forward_demodulation,[],[f16140,f8249]) ).
fof(f16140,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_993
| ~ spl0_1607
| ~ spl0_1694 ),
inference(forward_demodulation,[],[f16136,f8249]) ).
fof(f16136,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_1607
| ~ spl0_1694 ),
inference(superposition,[],[f14490,f16114]) ).
fof(f30858,plain,
( spl0_2413
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16139,f16113,f7128,f7108,f30856]) ).
fof(f30856,plain,
( spl0_2413
<=> ! [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_2413])]) ).
fof(f7108,plain,
( spl0_759
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X11,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f16139,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694 ),
inference(forward_demodulation,[],[f16116,f7129]) ).
fof(f16116,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_759
| ~ spl0_1694 ),
inference(superposition,[],[f16114,f7109]) ).
fof(f7109,plain,
( ! [X11,X13] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X11,X13)
| ~ spl0_759 ),
inference(avatar_component_clause,[],[f7108]) ).
fof(f30854,plain,
( spl0_2412
| ~ spl0_757
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16119,f16113,f7100,f30852]) ).
fof(f7100,plain,
( spl0_757
<=> ! [X13,X41,X11] : ~ c_List_Onull(c_List_Olist_OCons(X11,X41,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f16119,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),X2)
| ~ spl0_757
| ~ spl0_1694 ),
inference(superposition,[],[f7101,f16114]) ).
fof(f7101,plain,
( ! [X41,X11,X13] : ~ c_List_Onull(c_List_Olist_OCons(X11,X41,X13),X13)
| ~ spl0_757 ),
inference(avatar_component_clause,[],[f7100]) ).
fof(f30850,plain,
( spl0_2411
| ~ spl0_754
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16117,f16113,f7088,f30848]) ).
fof(f7088,plain,
( spl0_754
<=> ! [X56,X3,X14] : c_List_Olist_ONil != c_List_Olist_OCons(X14,X56,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f16117,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2)
| ~ spl0_754
| ~ spl0_1694 ),
inference(superposition,[],[f7089,f16114]) ).
fof(f7089,plain,
( ! [X3,X56,X14] : c_List_Olist_ONil != c_List_Olist_OCons(X14,X56,X3)
| ~ spl0_754 ),
inference(avatar_component_clause,[],[f7088]) ).
fof(f30845,plain,
( spl0_2410
| ~ spl0_752
| ~ spl0_773
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f15461,f14489,f7164,f7080,f30843]) ).
fof(f30843,plain,
( spl0_2410
<=> ! [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_2410])]) ).
fof(f7080,plain,
( spl0_752
<=> ! [X3] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f15461,plain,
( ! [X0,X1] : c_1 = c_Nat_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_752
| ~ spl0_773
| ~ spl0_1607 ),
inference(forward_demodulation,[],[f15406,f7165]) ).
fof(f15406,plain,
( ! [X0,X1] : c_Nat_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),tc_List_Olist(X0)) = c_plus(c_0,c_1,tc_nat)
| ~ spl0_752
| ~ spl0_1607 ),
inference(superposition,[],[f14490,f7081]) ).
fof(f7081,plain,
( ! [X3] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3))
| ~ spl0_752 ),
inference(avatar_component_clause,[],[f7080]) ).
fof(f30841,plain,
( spl0_2409
| ~ spl0_858
| ~ spl0_2317 ),
inference(avatar_split_clause,[],[f30325,f29523,f7511,f30839]) ).
fof(f30839,plain,
( spl0_2409
<=> ! [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_2409])]) ).
fof(f7511,plain,
( spl0_858
<=> ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f29523,plain,
( spl0_2317
<=> ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).
fof(f30325,plain,
( ! [X0] : c_Divides_Oop_Advd(c_Main_Ozmod__eq__0D__dest__1(X0,X0),X0,tc_IntDef_Oint)
| ~ spl0_858
| ~ spl0_2317 ),
inference(superposition,[],[f7512,f29524]) ).
fof(f29524,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_2317 ),
inference(avatar_component_clause,[],[f29523]) ).
fof(f7512,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7511]) ).
fof(f30837,plain,
( spl0_2408
| ~ spl0_794
| ~ spl0_1591 ),
inference(avatar_split_clause,[],[f15216,f14371,f7249,f30835]) ).
fof(f30835,plain,
( spl0_2408
<=> ! [X2,X0,X1,X3] : c_emptyset != c_union(X1,c_insert(X0,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).
fof(f15216,plain,
( ! [X2,X3,X0,X1] : c_emptyset != c_union(X1,c_insert(X0,X2,X3),X3)
| ~ spl0_794
| ~ spl0_1591 ),
inference(superposition,[],[f7250,f14372]) ).
fof(f30833,plain,
( spl0_2407
| ~ spl0_765
| ~ spl0_766
| ~ spl0_1564 ),
inference(avatar_split_clause,[],[f14983,f14262,f7136,f7132,f30831]) ).
fof(f30831,plain,
( spl0_2407
<=> ! [X0,X1] : c_0 = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).
fof(f7132,plain,
( spl0_765
<=> ! [X10] : c_0 = c_minus(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f7136,plain,
( spl0_766
<=> ! [X25] : c_0 = c_minus(X25,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f14262,plain,
( spl0_1564
<=> ! [X24,X9,X52] : c_minus(c_minus(X24,X52,tc_nat),X9,tc_nat) = c_minus(X24,c_plus(X52,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f14983,plain,
( ! [X0,X1] : c_0 = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat)
| ~ spl0_765
| ~ spl0_766
| ~ spl0_1564 ),
inference(forward_demodulation,[],[f14958,f7133]) ).
fof(f7133,plain,
( ! [X10] : c_0 = c_minus(c_0,X10,tc_nat)
| ~ spl0_765 ),
inference(avatar_component_clause,[],[f7132]) ).
fof(f14958,plain,
( ! [X0,X1] : c_minus(c_0,X1,tc_nat) = c_minus(X0,c_plus(X0,X1,tc_nat),tc_nat)
| ~ spl0_766
| ~ spl0_1564 ),
inference(superposition,[],[f14263,f7137]) ).
fof(f7137,plain,
( ! [X25] : c_0 = c_minus(X25,X25,tc_nat)
| ~ spl0_766 ),
inference(avatar_component_clause,[],[f7136]) ).
fof(f14263,plain,
( ! [X9,X52,X24] : c_minus(c_minus(X24,X52,tc_nat),X9,tc_nat) = c_minus(X24,c_plus(X52,X9,tc_nat),tc_nat)
| ~ spl0_1564 ),
inference(avatar_component_clause,[],[f14262]) ).
fof(f30829,plain,
( spl0_2406
| ~ spl0_736
| ~ spl0_1556 ),
inference(avatar_split_clause,[],[f14874,f14227,f7015,f30827]) ).
fof(f30827,plain,
( spl0_2406
<=> ! [X0,X1] : c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).
fof(f7015,plain,
( spl0_736
<=> ! [X10] : c_0 = c_Divides_Oop_Amod(X10,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f14227,plain,
( spl0_1556
<=> ! [X8,X3,X10] :
( c_List_Orotate(X10,X8,X3) = X8
| c_0 != c_Divides_Oop_Amod(X10,c_Nat_Osize(X8,tc_List_Olist(X3)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f14874,plain,
( ! [X0,X1] : c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0
| ~ spl0_736
| ~ spl0_1556 ),
inference(trivial_inequality_removal,[],[f14862]) ).
fof(f14862,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_Nat_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 )
| ~ spl0_736
| ~ spl0_1556 ),
inference(superposition,[],[f14228,f7016]) ).
fof(f7016,plain,
( ! [X10] : c_0 = c_Divides_Oop_Amod(X10,X10,tc_nat)
| ~ spl0_736 ),
inference(avatar_component_clause,[],[f7015]) ).
fof(f14228,plain,
( ! [X3,X10,X8] :
( c_0 != c_Divides_Oop_Amod(X10,c_Nat_Osize(X8,tc_List_Olist(X3)),tc_nat)
| c_List_Orotate(X10,X8,X3) = X8 )
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f14227]) ).
fof(f30825,plain,
( spl0_2405
| ~ spl0_757
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f14805,f14219,f7100,f30823]) ).
fof(f30823,plain,
( spl0_2405
<=> ! [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_2405])]) ).
fof(f14805,plain,
( ! [X2,X3,X0,X1] : ~ c_List_Onull(c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_757
| ~ spl0_1554 ),
inference(superposition,[],[f7101,f14220]) ).
fof(f30821,plain,
( spl0_2404
| ~ spl0_754
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f14803,f14219,f7088,f30819]) ).
fof(f30819,plain,
( spl0_2404
<=> ! [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_2404])]) ).
fof(f14803,plain,
( ! [X2,X3,X0,X1] : c_List_Olist_ONil != c_append(c_List_Olist_OCons(X0,X1,X3),X2,X3)
| ~ spl0_754
| ~ spl0_1554 ),
inference(superposition,[],[f7089,f14220]) ).
fof(f30817,plain,
( spl0_2403
| ~ spl0_827
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f14444,f14433,f7387,f30815]) ).
fof(f30815,plain,
( spl0_2403
<=> ! [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_2403])]) ).
fof(f7387,plain,
( spl0_827
<=> ! [X25,X10] : c_lessequals(c_minus(X25,X10,tc_nat),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f14433,plain,
( spl0_1601
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_plus(c_1,X74,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f14444,plain,
( ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X1,X0,tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_827
| ~ spl0_1601 ),
inference(superposition,[],[f7388,f14434]) ).
fof(f14434,plain,
( ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_plus(c_1,X74,tc_nat),tc_nat)
| ~ spl0_1601 ),
inference(avatar_component_clause,[],[f14433]) ).
fof(f7388,plain,
( ! [X10,X25] : c_lessequals(c_minus(X25,X10,tc_nat),X25,tc_nat)
| ~ spl0_827 ),
inference(avatar_component_clause,[],[f7387]) ).
fof(f30813,plain,
( spl0_2402
| ~ spl0_981
| ~ spl0_1525 ),
inference(avatar_split_clause,[],[f14054,f13147,f8200,f30811]) ).
fof(f30811,plain,
( spl0_2402
<=> ! [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_2402])]) ).
fof(f8200,plain,
( spl0_981
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olist_ONil != c_append(X41,X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f13147,plain,
( spl0_1525
<=> ! [X8,X3,X10] : c_append(c_List_Osublist(X8,c_SetInterval_OlessThan(X10,tc_nat),X3),c_List_Odrop(X10,X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f14054,plain,
( ! [X2,X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Odrop(X1,X0,X2) )
| ~ spl0_981
| ~ spl0_1525 ),
inference(superposition,[],[f8201,f13148]) ).
fof(f13148,plain,
( ! [X3,X10,X8] : c_append(c_List_Osublist(X8,c_SetInterval_OlessThan(X10,tc_nat),X3),c_List_Odrop(X10,X8,X3),X3) = X8
| ~ spl0_1525 ),
inference(avatar_component_clause,[],[f13147]) ).
fof(f8201,plain,
( ! [X41,X3,X42] :
( c_List_Olist_ONil != c_append(X41,X42,X3)
| c_List_Olist_ONil = X42 )
| ~ spl0_981 ),
inference(avatar_component_clause,[],[f8200]) ).
fof(f30808,plain,
( spl0_2401
| ~ spl0_696
| ~ spl0_799
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f12823,f11783,f7272,f6836,f30805]) ).
fof(f30805,plain,
( spl0_2401
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).
fof(f7272,plain,
( spl0_799
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f11783,plain,
( spl0_1450
<=> ! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f12823,plain,
( c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)),c_Numeral_Obit_OB1)
| ~ spl0_696
| ~ spl0_799
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12822,f7274]) ).
fof(f7274,plain,
( c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7272]) ).
fof(f12822,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)),c_Numeral_Obit_OB1)
| ~ spl0_696
| ~ spl0_799
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12813,f6838]) ).
fof(f12813,plain,
( c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)),c_Numeral_Obit_OB1)
| ~ spl0_799
| ~ spl0_1450 ),
inference(superposition,[],[f11784,f7274]) ).
fof(f11784,plain,
( ! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),c_Numeral_Obit_OB1)
| ~ spl0_1450 ),
inference(avatar_component_clause,[],[f11783]) ).
fof(f30802,plain,
( ~ spl0_2400
| spl0_653
| ~ spl0_799
| ~ spl0_1236
| ~ spl0_1449 ),
inference(avatar_split_clause,[],[f12807,f11779,f9978,f7272,f5881,f30799]) ).
fof(f30799,plain,
( spl0_2400
<=> c_less(c_0,c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).
fof(f5881,plain,
( spl0_653
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f9978,plain,
( spl0_1236
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f11779,plain,
( spl0_1449
<=> ! [X36] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X36),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f12807,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_799
| ~ spl0_1236
| ~ spl0_1449 ),
inference(forward_demodulation,[],[f12804,f9980]) ).
fof(f9980,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1236 ),
inference(avatar_component_clause,[],[f9978]) ).
fof(f12804,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_799
| ~ spl0_1449 ),
inference(superposition,[],[f11780,f7274]) ).
fof(f11780,plain,
( ! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat) )
| ~ spl0_1449 ),
inference(avatar_component_clause,[],[f11779]) ).
fof(f30797,plain,
( spl0_2399
| ~ spl0_1104
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f12530,f11573,f8894,f30795]) ).
fof(f30795,plain,
( spl0_2399
<=> ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).
fof(f8894,plain,
( spl0_1104
<=> ! [X17,X3,X16,X8] : c_fst(c_Pair(X8,X16,X3,X17),X3,X17) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f11573,plain,
( spl0_1411
<=> ! [X37,X17,X3] : c_Pair(c_Main_Osurj__pair__1(X37,X3,X17),c_Main_Osurj__pair__2(X37,X3,X17),X3,X17) = X37 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f12530,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1104
| ~ spl0_1411 ),
inference(superposition,[],[f8895,f11574]) ).
fof(f11574,plain,
( ! [X3,X37,X17] : c_Pair(c_Main_Osurj__pair__1(X37,X3,X17),c_Main_Osurj__pair__2(X37,X3,X17),X3,X17) = X37
| ~ spl0_1411 ),
inference(avatar_component_clause,[],[f11573]) ).
fof(f8895,plain,
( ! [X3,X8,X16,X17] : c_fst(c_Pair(X8,X16,X3,X17),X3,X17) = X8
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f8894]) ).
fof(f30793,plain,
( spl0_2398
| ~ spl0_856
| ~ spl0_2314 ),
inference(avatar_split_clause,[],[f30175,f29480,f7503,f30791]) ).
fof(f30791,plain,
( spl0_2398
<=> ! [X0] : c_Divides_Oop_Advd(c_Main_Omod__eq__0D__dest__1(X0,X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).
fof(f29480,plain,
( spl0_2314
<=> ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).
fof(f30175,plain,
( ! [X0] : c_Divides_Oop_Advd(c_Main_Omod__eq__0D__dest__1(X0,X0),X0,tc_nat)
| ~ spl0_856
| ~ spl0_2314 ),
inference(superposition,[],[f7504,f29481]) ).
fof(f29481,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_2314 ),
inference(avatar_component_clause,[],[f29480]) ).
fof(f30789,plain,
( spl0_2397
| ~ spl0_1105
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f12529,f11573,f8898,f30787]) ).
fof(f30787,plain,
( spl0_2397
<=> ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).
fof(f8898,plain,
( spl0_1105
<=> ! [X17,X8,X3,X15] : c_snd(c_Pair(X15,X8,X17,X3),X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f12529,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1105
| ~ spl0_1411 ),
inference(superposition,[],[f8899,f11574]) ).
fof(f8899,plain,
( ! [X3,X8,X17,X15] : c_snd(c_Pair(X15,X8,X17,X3),X17,X3) = X8
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f8898]) ).
fof(f30784,plain,
( spl0_2396
| ~ spl0_719
| ~ spl0_788
| ~ spl0_1382 ),
inference(avatar_split_clause,[],[f12193,f11441,f7225,f6934,f30782]) ).
fof(f11441,plain,
( spl0_1382
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_uminus(X15,X3) = c_HOL_Oabs(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f12193,plain,
( ! [X0] :
( c_UNIV = c_HOL_Oabs(c_emptyset,tc_set(X0))
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0)) )
| ~ spl0_719
| ~ spl0_788
| ~ spl0_1382 ),
inference(forward_demodulation,[],[f12179,f7226]) ).
fof(f12179,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_719
| ~ spl0_1382 ),
inference(resolution,[],[f11442,f6935]) ).
fof(f11442,plain,
( ! [X3,X15] :
( ~ c_lessequals(X15,c_0,X3)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_uminus(X15,X3) = c_HOL_Oabs(X15,X3) )
| ~ spl0_1382 ),
inference(avatar_component_clause,[],[f11441]) ).
fof(f30780,plain,
( spl0_2395
| ~ spl0_853
| ~ spl0_1374 ),
inference(avatar_split_clause,[],[f12001,f11409,f7491,f30778]) ).
fof(f30778,plain,
( spl0_2395
<=> ! [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_2395])]) ).
fof(f11409,plain,
( spl0_1374
<=> ! [X13,X41,X11] : c_List_Oset(c_List_Olist_OCons(X11,X41,X13),X13) = c_insert(X11,c_List_Oset(X41,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f12001,plain,
( ! [X2,X0,X1] : c_in(X0,c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2),X2)
| ~ spl0_853
| ~ spl0_1374 ),
inference(superposition,[],[f7492,f11410]) ).
fof(f11410,plain,
( ! [X41,X11,X13] : c_List_Oset(c_List_Olist_OCons(X11,X41,X13),X13) = c_insert(X11,c_List_Oset(X41,X13),X13)
| ~ spl0_1374 ),
inference(avatar_component_clause,[],[f11409]) ).
fof(f30776,plain,
( spl0_2394
| ~ spl0_115
| ~ spl0_1372 ),
inference(avatar_split_clause,[],[f11971,f11401,f3722,f30774]) ).
fof(f30774,plain,
( spl0_2394
<=> ! [X0,X1] : c_List_Onth(c_List_Oreplicate(c_1,X0,X1),c_0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f3722,plain,
( spl0_115
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f11401,plain,
( spl0_1372
<=> ! [X24,X10,X3,X8] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(c_List_Oreplicate(X10,X8,X3),X24,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f11971,plain,
( ! [X0,X1] : c_List_Onth(c_List_Oreplicate(c_1,X0,X1),c_0,X1) = X0
| ~ spl0_115
| ~ spl0_1372 ),
inference(resolution,[],[f11402,f3724]) ).
fof(f3724,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f3722]) ).
fof(f11402,plain,
( ! [X3,X10,X8,X24] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(c_List_Oreplicate(X10,X8,X3),X24,X3) = X8 )
| ~ spl0_1372 ),
inference(avatar_component_clause,[],[f11401]) ).
fof(f30772,plain,
( spl0_2393
| ~ spl0_821
| ~ spl0_1367 ),
inference(avatar_split_clause,[],[f11937,f11381,f7363,f30770]) ).
fof(f30770,plain,
( spl0_2393
<=> ! [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_2393])]) ).
fof(f11381,plain,
( spl0_1367
<=> ! [X8,X3] :
( c_List_Olist_ONil = X8
| c_List_Olist_OCons(c_List_Ohd(X8,X3),c_List_Otl(X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f11937,plain,
( ! [X0,X1] :
( c_List_Oop_Amem(c_List_Ohd(X0,X1),X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_821
| ~ spl0_1367 ),
inference(superposition,[],[f7364,f11382]) ).
fof(f11382,plain,
( ! [X3,X8] :
( c_List_Olist_OCons(c_List_Ohd(X8,X3),c_List_Otl(X8,X3),X3) = X8
| c_List_Olist_ONil = X8 )
| ~ spl0_1367 ),
inference(avatar_component_clause,[],[f11381]) ).
fof(f30768,plain,
( spl0_2392
| ~ spl0_72
| ~ spl0_764
| ~ spl0_1192
| ~ spl0_1443 ),
inference(avatar_split_clause,[],[f11727,f11721,f9448,f7128,f3516,f30765]) ).
fof(f30765,plain,
( spl0_2392
<=> c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) = c_SetInterval_OatLeastAtMost(c_0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).
fof(f3516,plain,
( spl0_72
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f9448,plain,
( spl0_1192
<=> ! [X3,X15] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_OatLeastAtMost(X15,X15,X3) = c_insert(X15,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f11721,plain,
( spl0_1443
<=> ! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_plus(c_1,X25,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f11727,plain,
( c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) = c_SetInterval_OatLeastAtMost(c_0,c_0,tc_nat)
| ~ spl0_72
| ~ spl0_764
| ~ spl0_1192
| ~ spl0_1443 ),
inference(forward_demodulation,[],[f11724,f9848]) ).
fof(f9848,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_72
| ~ spl0_1192 ),
inference(resolution,[],[f9449,f3518]) ).
fof(f3518,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f3516]) ).
fof(f9449,plain,
( ! [X3,X15] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_OatLeastAtMost(X15,X15,X3) = c_insert(X15,c_emptyset,X3) )
| ~ spl0_1192 ),
inference(avatar_component_clause,[],[f9448]) ).
fof(f11724,plain,
( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_764
| ~ spl0_1443 ),
inference(superposition,[],[f11722,f7129]) ).
fof(f11722,plain,
( ! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_plus(c_1,X25,tc_nat),tc_nat)
| ~ spl0_1443 ),
inference(avatar_component_clause,[],[f11721]) ).
fof(f30763,plain,
( spl0_2391
| ~ spl0_88
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11292,f10419,f10415,f10092,f6703,f3695,f3596,f30761]) ).
fof(f30761,plain,
( spl0_2391
<=> ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).
fof(f10419,plain,
( spl0_1341
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f11292,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_88
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1341 ),
inference(forward_demodulation,[],[f11290,f11235]) ).
fof(f11290,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_88
| ~ spl0_1341 ),
inference(resolution,[],[f10420,f3598]) ).
fof(f10420,plain,
( ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) )
| ~ spl0_1341 ),
inference(avatar_component_clause,[],[f10419]) ).
fof(f30759,plain,
( spl0_2390
| ~ spl0_54
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11291,f10419,f10415,f10092,f6703,f3695,f3426,f30757]) ).
fof(f30757,plain,
( spl0_2390
<=> ! [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_2390])]) ).
fof(f11291,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_plus(c_1,X0,tc_nat),tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1341 ),
inference(forward_demodulation,[],[f11289,f11235]) ).
fof(f11289,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_54
| ~ spl0_1341 ),
inference(resolution,[],[f10420,f3428]) ).
fof(f30754,plain,
( spl0_2389
| ~ spl0_787
| ~ spl0_1314 ),
inference(avatar_split_clause,[],[f10993,f10310,f7221,f30752]) ).
fof(f30752,plain,
( spl0_2389
<=> ! [X0,X1] :
( c_emptyset != c_uminus(X1,tc_set(X0))
| c_UNIV = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).
fof(f7221,plain,
( spl0_787
<=> ! [X3] : c_emptyset = c_uminus(c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f10310,plain,
( spl0_1314
<=> ! [X27,X3,X31] :
( X27 = X31
| c_uminus(X27,tc_set(X3)) != c_uminus(X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f10993,plain,
( ! [X0,X1] :
( c_emptyset != c_uminus(X1,tc_set(X0))
| c_UNIV = X1 )
| ~ spl0_787
| ~ spl0_1314 ),
inference(superposition,[],[f10311,f7222]) ).
fof(f7222,plain,
( ! [X3] : c_emptyset = c_uminus(c_UNIV,tc_set(X3))
| ~ spl0_787 ),
inference(avatar_component_clause,[],[f7221]) ).
fof(f10311,plain,
( ! [X31,X3,X27] :
( c_uminus(X27,tc_set(X3)) != c_uminus(X31,tc_set(X3))
| X27 = X31 )
| ~ spl0_1314 ),
inference(avatar_component_clause,[],[f10310]) ).
fof(f30749,plain,
( spl0_2388
| ~ spl0_788
| ~ spl0_1314 ),
inference(avatar_split_clause,[],[f10992,f10310,f7225,f30747]) ).
fof(f30747,plain,
( spl0_2388
<=> ! [X0,X1] :
( c_UNIV != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).
fof(f10992,plain,
( ! [X0,X1] :
( c_UNIV != c_uminus(X1,tc_set(X0))
| c_emptyset = X1 )
| ~ spl0_788
| ~ spl0_1314 ),
inference(superposition,[],[f10311,f7226]) ).
fof(f30719,plain,
( spl0_2387
| ~ spl0_24
| ~ spl0_668
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10953,f10282,f6707,f3276,f30717]) ).
fof(f3276,plain,
( spl0_24
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f6707,plain,
( spl0_668
<=> ! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f10953,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) )
| ~ spl0_668
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f6708]) ).
fof(f6708,plain,
( ! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ spl0_668 ),
inference(avatar_component_clause,[],[f6707]) ).
fof(f30696,plain,
( spl0_2386
| ~ spl0_24
| ~ spl0_668
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10902,f10238,f6707,f3276,f30694]) ).
fof(f10902,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) )
| ~ spl0_668
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f6708]) ).
fof(f30692,plain,
( spl0_2385
| ~ spl0_773
| ~ spl0_1264 ),
inference(avatar_split_clause,[],[f10687,f10104,f7164,f30690]) ).
fof(f30690,plain,
( spl0_2385
<=> ! [X0,X1] :
( c_plus(X1,X0,tc_nat) != X0
| c_0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f10104,plain,
( spl0_1264
<=> ! [X25,X9,X10] :
( X10 = X25
| c_plus(X25,X9,tc_nat) != c_plus(X10,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f10687,plain,
( ! [X0,X1] :
( c_plus(X1,X0,tc_nat) != X0
| c_0 = X1 )
| ~ spl0_773
| ~ spl0_1264 ),
inference(superposition,[],[f10105,f7165]) ).
fof(f10105,plain,
( ! [X10,X9,X25] :
( c_plus(X25,X9,tc_nat) != c_plus(X10,X9,tc_nat)
| X10 = X25 )
| ~ spl0_1264 ),
inference(avatar_component_clause,[],[f10104]) ).
fof(f30688,plain,
( spl0_2384
| ~ spl0_764
| ~ spl0_1264 ),
inference(avatar_split_clause,[],[f10686,f10104,f7128,f30686]) ).
fof(f30686,plain,
( spl0_2384
<=> ! [X0,X1] :
( c_plus(X1,c_0,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).
fof(f10686,plain,
( ! [X0,X1] :
( c_plus(X1,c_0,tc_nat) != X0
| X0 = X1 )
| ~ spl0_764
| ~ spl0_1264 ),
inference(superposition,[],[f10105,f7129]) ).
fof(f30684,plain,
( spl0_2383
| ~ spl0_773
| ~ spl0_1263 ),
inference(avatar_split_clause,[],[f10682,f10100,f7164,f30682]) ).
fof(f30682,plain,
( spl0_2383
<=> ! [X0,X1] :
( c_plus(c_0,X1,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).
fof(f10100,plain,
( spl0_1263
<=> ! [X25,X9,X10] :
( X10 = X25
| c_plus(X9,X25,tc_nat) != c_plus(X9,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f10682,plain,
( ! [X0,X1] :
( c_plus(c_0,X1,tc_nat) != X0
| X0 = X1 )
| ~ spl0_773
| ~ spl0_1263 ),
inference(superposition,[],[f10101,f7165]) ).
fof(f10101,plain,
( ! [X10,X9,X25] :
( c_plus(X9,X25,tc_nat) != c_plus(X9,X10,tc_nat)
| X10 = X25 )
| ~ spl0_1263 ),
inference(avatar_component_clause,[],[f10100]) ).
fof(f30680,plain,
( spl0_2382
| ~ spl0_764
| ~ spl0_1263 ),
inference(avatar_split_clause,[],[f10681,f10100,f7128,f30678]) ).
fof(f30678,plain,
( spl0_2382
<=> ! [X0,X1] :
( c_plus(X0,X1,tc_nat) != X0
| c_0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f10681,plain,
( ! [X0,X1] :
( c_plus(X0,X1,tc_nat) != X0
| c_0 = X1 )
| ~ spl0_764
| ~ spl0_1263 ),
inference(superposition,[],[f10101,f7129]) ).
fof(f30676,plain,
( spl0_2381
| ~ spl0_800
| ~ spl0_1256 ),
inference(avatar_split_clause,[],[f10633,f10072,f7277,f30674]) ).
fof(f30674,plain,
( spl0_2381
<=> ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).
fof(f7277,plain,
( spl0_800
<=> ! [X13,X8] : c_append(c_List_Olist_ONil,X8,X13) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f10072,plain,
( spl0_1256
<=> ! [X41,X42,X44,X3] :
( X42 = X44
| c_append(X41,X42,X3) != c_append(X41,X44,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f10633,plain,
( ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 )
| ~ spl0_800
| ~ spl0_1256 ),
inference(superposition,[],[f10073,f7278]) ).
fof(f7278,plain,
( ! [X8,X13] : c_append(c_List_Olist_ONil,X8,X13) = X8
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7277]) ).
fof(f10073,plain,
( ! [X41,X3,X44,X42] :
( c_append(X41,X42,X3) != c_append(X41,X44,X3)
| X42 = X44 )
| ~ spl0_1256 ),
inference(avatar_component_clause,[],[f10072]) ).
fof(f30672,plain,
( spl0_2380
| ~ spl0_761
| ~ spl0_1250 ),
inference(avatar_split_clause,[],[f10617,f10042,f7116,f30670]) ).
fof(f30670,plain,
( spl0_2380
<=> ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).
fof(f7116,plain,
( spl0_761
<=> ! [X41,X3] : c_append(X41,c_List_Olist_ONil,X3) = X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f10042,plain,
( spl0_1250
<=> ! [X41,X42,X44,X3] :
( X42 = X44
| c_append(X42,X41,X3) != c_append(X44,X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f10617,plain,
( ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 )
| ~ spl0_761
| ~ spl0_1250 ),
inference(superposition,[],[f10043,f7117]) ).
fof(f7117,plain,
( ! [X41,X3] : c_append(X41,c_List_Olist_ONil,X3) = X41
| ~ spl0_761 ),
inference(avatar_component_clause,[],[f7116]) ).
fof(f10043,plain,
( ! [X41,X3,X44,X42] :
( c_append(X42,X41,X3) != c_append(X44,X41,X3)
| X42 = X44 )
| ~ spl0_1250 ),
inference(avatar_component_clause,[],[f10042]) ).
fof(f30668,plain,
( spl0_2379
| ~ spl0_72
| ~ spl0_2288 ),
inference(avatar_split_clause,[],[f29807,f29326,f3516,f30666]) ).
fof(f30666,plain,
( spl0_2379
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).
fof(f29326,plain,
( spl0_2288
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f29807,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_nat)
| ~ spl0_72
| ~ spl0_2288 ),
inference(resolution,[],[f29327,f3518]) ).
fof(f29327,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_2288 ),
inference(avatar_component_clause,[],[f29326]) ).
fof(f30664,plain,
( spl0_2378
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1213 ),
inference(avatar_split_clause,[],[f9911,f9567,f8297,f3421,f30661]) ).
fof(f30661,plain,
( spl0_2378
<=> 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_2378])]) ).
fof(f9567,plain,
( spl0_1213
<=> ! [X3] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f9911,plain,
( c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1213 ),
inference(forward_demodulation,[],[f9910,f8587]) ).
fof(f9910,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_53
| ~ spl0_1213 ),
inference(resolution,[],[f9568,f3423]) ).
fof(f9568,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X3) )
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f9567]) ).
fof(f30659,plain,
( spl0_2377
| ~ spl0_775
| ~ spl0_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1205 ),
inference(avatar_split_clause,[],[f9888,f9505,f8309,f7540,f7272,f7172,f30656]) ).
fof(f30656,plain,
( spl0_2377
<=> 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_2377])]) ).
fof(f7540,plain,
( spl0_865
<=> 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_865])]) ).
fof(f9505,plain,
( spl0_1205
<=> ! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f9888,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_775
| ~ spl0_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1205 ),
inference(forward_demodulation,[],[f9887,f7174]) ).
fof(f9887,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_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1205 ),
inference(forward_demodulation,[],[f9886,f8310]) ).
fof(f9886,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_799
| ~ spl0_865
| ~ spl0_1205 ),
inference(forward_demodulation,[],[f9881,f7542]) ).
fof(f7542,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f7540]) ).
fof(f9881,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_799
| ~ spl0_1205 ),
inference(superposition,[],[f9506,f7274]) ).
fof(f9506,plain,
( ! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_Obit_OB0)
| ~ spl0_1205 ),
inference(avatar_component_clause,[],[f9505]) ).
fof(f30654,plain,
( spl0_2376
| ~ spl0_72
| ~ spl0_1192 ),
inference(avatar_split_clause,[],[f9848,f9448,f3516,f30652]) ).
fof(f30650,plain,
( spl0_2375
| ~ spl0_24
| ~ spl0_1192 ),
inference(avatar_split_clause,[],[f9847,f9448,f3276,f30648]) ).
fof(f9847,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_1192 ),
inference(resolution,[],[f9449,f3278]) ).
fof(f3278,plain,
( class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f3276]) ).
fof(f30645,plain,
( spl0_2374
| ~ spl0_715
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9824,f9432,f6918,f30643]) ).
fof(f30643,plain,
( spl0_2374
<=> ! [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_2374])]) ).
fof(f9432,plain,
( spl0_1188
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_OrderedGroup_Opprt(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f9824,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) )
| ~ spl0_715
| ~ spl0_1188 ),
inference(resolution,[],[f9433,f6919]) ).
fof(f9433,plain,
( ! [X3,X8] :
( ~ c_lessequals(c_0,X8,X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_OrderedGroup_Opprt(X8,X3) = X8 )
| ~ spl0_1188 ),
inference(avatar_component_clause,[],[f9432]) ).
fof(f30634,plain,
( spl0_2373
| ~ spl0_41
| ~ spl0_668
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9820,f9432,f6707,f3361,f30632]) ).
fof(f30632,plain,
( spl0_2373
<=> ! [X0] : c_IntDef_Oint(X0) = c_OrderedGroup_Opprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).
fof(f3361,plain,
( spl0_41
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f9820,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_668
| ~ spl0_1188 ),
inference(resolution,[],[f9433,f6708]) ).
fof(f30630,plain,
( spl0_2372
| ~ spl0_786
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9815,f9432,f7217,f30628]) ).
fof(f30628,plain,
( spl0_2372
<=> ! [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_2372])]) ).
fof(f9815,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_786
| ~ spl0_1188 ),
inference(resolution,[],[f9433,f7218]) ).
fof(f30626,plain,
( spl0_2371
| ~ spl0_918
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f9808,f9424,f7827,f30624]) ).
fof(f30624,plain,
( spl0_2371
<=> ! [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_2371])]) ).
fof(f7827,plain,
( spl0_918
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f9424,plain,
( spl0_1186
<=> ! [X11,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_OrderedGroup_Opprt(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f9808,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) )
| ~ spl0_918
| ~ spl0_1186 ),
inference(duplicate_literal_removal,[],[f9807]) ).
fof(f9807,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_918
| ~ spl0_1186 ),
inference(resolution,[],[f9425,f7828]) ).
fof(f7828,plain,
( ! [X3,X15] :
( c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_0,X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3) )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7827]) ).
fof(f9425,plain,
( ! [X3,X11] :
( ~ c_lessequals(X11,c_0,X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(X11,X3) )
| ~ spl0_1186 ),
inference(avatar_component_clause,[],[f9424]) ).
fof(f30622,plain,
( spl0_2370
| ~ spl0_719
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f9800,f9424,f6934,f30620]) ).
fof(f30620,plain,
( spl0_2370
<=> ! [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_2370])]) ).
fof(f9800,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) )
| ~ spl0_719
| ~ spl0_1186 ),
inference(resolution,[],[f9425,f6935]) ).
fof(f30618,plain,
( spl0_2369
| ~ spl0_24
| ~ spl0_2288 ),
inference(avatar_split_clause,[],[f29806,f29326,f3276,f30616]) ).
fof(f30616,plain,
( spl0_2369
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f29806,plain,
( ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_2288 ),
inference(resolution,[],[f29327,f3278]) ).
fof(f30614,plain,
( spl0_2368
| ~ spl0_719
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f9783,f9420,f6934,f30612]) ).
fof(f30612,plain,
( spl0_2368
<=> ! [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_2368])]) ).
fof(f9420,plain,
( spl0_1185
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X8,c_0,X3)
| c_OrderedGroup_Onprt(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f9783,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) )
| ~ spl0_719
| ~ spl0_1185 ),
inference(resolution,[],[f9421,f6935]) ).
fof(f9421,plain,
( ! [X3,X8] :
( ~ c_lessequals(X8,c_0,X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_OrderedGroup_Onprt(X8,X3) = X8 )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f9420]) ).
fof(f30610,plain,
( spl0_2367
| ~ spl0_919
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f9776,f9416,f7831,f30608]) ).
fof(f30608,plain,
( spl0_2367
<=> ! [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_2367])]) ).
fof(f7831,plain,
( spl0_919
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f9416,plain,
( spl0_1184
<=> ! [X11,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_0 = c_OrderedGroup_Onprt(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f9776,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) )
| ~ spl0_919
| ~ spl0_1184 ),
inference(duplicate_literal_removal,[],[f9770]) ).
fof(f9770,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_919
| ~ spl0_1184 ),
inference(resolution,[],[f9417,f7832]) ).
fof(f7832,plain,
( ! [X3,X15] :
( c_lessequals(c_0,c_OrderedGroup_Opprt(X15,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f7831]) ).
fof(f9417,plain,
( ! [X3,X11] :
( ~ c_lessequals(c_0,X11,X3)
| ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(X11,X3) )
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f9416]) ).
fof(f30605,plain,
( spl0_2366
| ~ spl0_715
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f9773,f9416,f6918,f30603]) ).
fof(f30603,plain,
( spl0_2366
<=> ! [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_2366])]) ).
fof(f9773,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) )
| ~ spl0_715
| ~ spl0_1184 ),
inference(resolution,[],[f9417,f6919]) ).
fof(f30601,plain,
( spl0_2365
| ~ spl0_786
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f9764,f9416,f7217,f30599]) ).
fof(f30599,plain,
( spl0_2365
<=> ! [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_2365])]) ).
fof(f9764,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_786
| ~ spl0_1184 ),
inference(resolution,[],[f9417,f7218]) ).
fof(f30597,plain,
( spl0_2361
| spl0_2364
| ~ spl0_850
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9757,f9412,f7479,f30595,f30584]) ).
fof(f30584,plain,
( spl0_2361
<=> ! [X1] : ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f30595,plain,
( spl0_2364
<=> ! [X0] :
( c_0 != X0
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f7479,plain,
( spl0_850
<=> ! [X8,X3] : c_minus(X8,c_emptyset,tc_set(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f9412,plain,
( spl0_1183
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_0 != c_minus(X15,X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f9757,plain,
( ! [X0,X1] :
( c_0 != X0
| c_emptyset = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_850
| ~ spl0_1183 ),
inference(superposition,[],[f9413,f7480]) ).
fof(f7480,plain,
( ! [X3,X8] : c_minus(X8,c_emptyset,tc_set(X3)) = X8
| ~ spl0_850 ),
inference(avatar_component_clause,[],[f7479]) ).
fof(f9413,plain,
( ! [X3,X16,X15] :
( c_0 != c_minus(X15,X16,X3)
| X15 = X16
| ~ class_OrderedGroup_Oab__group__add(X3) )
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9412]) ).
fof(f30593,plain,
( spl0_2361
| spl0_2362
| ~ spl0_2363
| ~ spl0_848
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9755,f9412,f7471,f30590,f30587,f30584]) ).
fof(f30587,plain,
( spl0_2362
<=> ! [X0] : c_UNIV = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).
fof(f30590,plain,
( spl0_2363
<=> c_0 = c_emptyset ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f7471,plain,
( spl0_848
<=> ! [X27,X3] : c_emptyset = c_minus(X27,c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f9755,plain,
( ! [X0,X1] :
( c_0 != c_emptyset
| c_UNIV = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_848
| ~ spl0_1183 ),
inference(superposition,[],[f9413,f7472]) ).
fof(f7472,plain,
( ! [X3,X27] : c_emptyset = c_minus(X27,c_UNIV,tc_set(X3))
| ~ spl0_848 ),
inference(avatar_component_clause,[],[f7471]) ).
fof(f30581,plain,
( spl0_2360
| ~ spl0_715
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9744,f9408,f6918,f30579]) ).
fof(f30579,plain,
( spl0_2360
<=> ! [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_2360])]) ).
fof(f9408,plain,
( spl0_1182
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_HOL_Oabs(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f9744,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) )
| ~ spl0_715
| ~ spl0_1182 ),
inference(resolution,[],[f9409,f6919]) ).
fof(f9409,plain,
( ! [X3,X8] :
( ~ c_lessequals(c_0,X8,X3)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X8,X3) = X8 )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f9408]) ).
fof(f30577,plain,
( spl0_2359
| ~ spl0_786
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9735,f9408,f7217,f30575]) ).
fof(f30575,plain,
( spl0_2359
<=> ! [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_2359])]) ).
fof(f9735,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_786
| ~ spl0_1182 ),
inference(resolution,[],[f9409,f7218]) ).
fof(f30573,plain,
( spl0_2358
| ~ spl0_72
| ~ spl0_2286 ),
inference(avatar_split_clause,[],[f29804,f29312,f3516,f30571]) ).
fof(f30571,plain,
( spl0_2358
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).
fof(f29312,plain,
( spl0_2286
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f29804,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_nat)
| ~ spl0_72
| ~ spl0_2286 ),
inference(resolution,[],[f29313,f3518]) ).
fof(f29313,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_2286 ),
inference(avatar_component_clause,[],[f29312]) ).
fof(f30569,plain,
( spl0_2357
| ~ spl0_44
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f9730,f9404,f3376,f30567]) ).
fof(f30567,plain,
( spl0_2357
<=> ! [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_2357])]) ).
fof(f3376,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f9404,plain,
( spl0_1181
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f9730,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_44
| ~ spl0_1181 ),
inference(resolution,[],[f9405,f3378]) ).
fof(f3378,plain,
( class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f9405,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_uminus(X15,X3),X3) )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f9404]) ).
fof(f30565,plain,
( spl0_2356
| ~ spl0_44
| ~ spl0_1179 ),
inference(avatar_split_clause,[],[f9724,f9396,f3376,f30563]) ).
fof(f30563,plain,
( spl0_2356
<=> ! [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_2356])]) ).
fof(f9396,plain,
( spl0_1179
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f9724,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_44
| ~ spl0_1179 ),
inference(resolution,[],[f9397,f3378]) ).
fof(f9397,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_HOL_Oabs(X15,X3),X3) )
| ~ spl0_1179 ),
inference(avatar_component_clause,[],[f9396]) ).
fof(f30561,plain,
( spl0_2355
| ~ spl0_775
| ~ spl0_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1177 ),
inference(avatar_split_clause,[],[f9721,f9388,f8309,f7540,f7272,f7172,f30558]) ).
fof(f30558,plain,
( spl0_2355
<=> 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_2355])]) ).
fof(f9388,plain,
( spl0_1177
<=> ! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35) = c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f9721,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_775
| ~ spl0_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1177 ),
inference(forward_demodulation,[],[f9720,f7174]) ).
fof(f9720,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_799
| ~ spl0_865
| ~ spl0_1008
| ~ spl0_1177 ),
inference(forward_demodulation,[],[f9719,f8310]) ).
fof(f9719,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_799
| ~ spl0_865
| ~ spl0_1177 ),
inference(forward_demodulation,[],[f9714,f7542]) ).
fof(f9714,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_799
| ~ spl0_1177 ),
inference(superposition,[],[f9389,f7274]) ).
fof(f9389,plain,
( ! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35) = c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0)
| ~ spl0_1177 ),
inference(avatar_component_clause,[],[f9388]) ).
fof(f30556,plain,
( spl0_2354
| ~ spl0_23
| ~ spl0_1148 ),
inference(avatar_split_clause,[],[f9578,f9272,f3271,f30554]) ).
fof(f30554,plain,
( spl0_2354
<=> ! [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_2354])]) ).
fof(f3271,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f9272,plain,
( spl0_1148
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_NatArith_Oof__nat(X10,X3) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X10,tc_IntDef_Oint),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f9578,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_23
| ~ spl0_1148 ),
inference(resolution,[],[f9273,f3273]) ).
fof(f3273,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3271]) ).
fof(f9273,plain,
( ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_NatArith_Oof__nat(X10,X3) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X10,tc_IntDef_Oint),X3) )
| ~ spl0_1148 ),
inference(avatar_component_clause,[],[f9272]) ).
fof(f30537,plain,
( ~ spl0_53
| spl0_2353
| ~ spl0_51
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1140 ),
inference(avatar_split_clause,[],[f9565,f9239,f8297,f3421,f3411,f30534,f3421]) ).
fof(f30534,plain,
( spl0_2353
<=> c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2353])]) ).
fof(f3411,plain,
( spl0_51
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f9239,plain,
( spl0_1140
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f9565,plain,
( c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1140 ),
inference(forward_demodulation,[],[f9564,f8587]) ).
fof(f9564,plain,
( ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_1140 ),
inference(resolution,[],[f9240,f3413]) ).
fof(f3413,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f3411]) ).
fof(f9240,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) )
| ~ spl0_1140 ),
inference(avatar_component_clause,[],[f9239]) ).
fof(f30531,plain,
( ~ spl0_2352
| ~ spl0_109
| ~ spl0_1204 ),
inference(avatar_split_clause,[],[f9501,f9497,f3695,f30528]) ).
fof(f9501,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1204 ),
inference(superposition,[],[f9498,f3697]) ).
fof(f30526,plain,
( spl0_2351
| ~ spl0_938
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9185,f8939,f7907,f30524]) ).
fof(f30524,plain,
( spl0_2351
<=> ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f9185,plain,
( ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_938
| ~ spl0_1115 ),
inference(superposition,[],[f8940,f7909]) ).
fof(f30522,plain,
( spl0_2350
| ~ spl0_832
| ~ spl0_1102 ),
inference(avatar_split_clause,[],[f9166,f8886,f7407,f30520]) ).
fof(f30520,plain,
( spl0_2350
<=> ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f8886,plain,
( spl0_1102
<=> ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f9166,plain,
( ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) )
| ~ spl0_832
| ~ spl0_1102 ),
inference(resolution,[],[f8887,f7408]) ).
fof(f8887,plain,
( ! [X10] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_nat),tc_nat)
| c_0 = X10 )
| ~ spl0_1102 ),
inference(avatar_component_clause,[],[f8886]) ).
fof(f30518,plain,
( spl0_2349
| ~ spl0_827
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f9137,f8842,f7387,f30516]) ).
fof(f30516,plain,
( spl0_2349
<=> ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f8842,plain,
( spl0_1091
<=> ! [X25,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_0 = c_minus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f9137,plain,
( ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_827
| ~ spl0_1091 ),
inference(resolution,[],[f8843,f7388]) ).
fof(f8843,plain,
( ! [X10,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_0 = c_minus(X25,X10,tc_nat) )
| ~ spl0_1091 ),
inference(avatar_component_clause,[],[f8842]) ).
fof(f30511,plain,
( spl0_2348
| ~ spl0_807
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f9136,f8842,f7307,f30509]) ).
fof(f30509,plain,
( spl0_2348
<=> ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).
fof(f7307,plain,
( spl0_807
<=> ! [X25,X10] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f9136,plain,
( ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_807
| ~ spl0_1091 ),
inference(resolution,[],[f8843,f7308]) ).
fof(f7308,plain,
( ! [X10,X25] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat)
| ~ spl0_807 ),
inference(avatar_component_clause,[],[f7307]) ).
fof(f30506,plain,
( spl0_2347
| ~ spl0_858
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f9093,f8786,f7511,f30504]) ).
fof(f8786,plain,
( spl0_1077
<=> ! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f9093,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_858
| ~ spl0_1077 ),
inference(resolution,[],[f8787,f7512]) ).
fof(f8787,plain,
( ! [X37,X35] :
( ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint) )
| ~ spl0_1077 ),
inference(avatar_component_clause,[],[f8786]) ).
fof(f30501,plain,
( spl0_2346
| ~ spl0_857
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f9092,f8786,f7507,f30499]) ).
fof(f9092,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_857
| ~ spl0_1077 ),
inference(resolution,[],[f8787,f7508]) ).
fof(f30497,plain,
( spl0_2345
| ~ spl0_818
| ~ spl0_1075 ),
inference(avatar_split_clause,[],[f9083,f8777,f7351,f30495]) ).
fof(f30495,plain,
( spl0_2345
<=> ! [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_2345])]) ).
fof(f7351,plain,
( spl0_818
<=> ! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f8777,plain,
( spl0_1075
<=> ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f9083,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_818
| ~ spl0_1075 ),
inference(resolution,[],[f8778,f7352]) ).
fof(f7352,plain,
( ! [X25] :
( ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint)
| c_0 = X25 )
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7351]) ).
fof(f8778,plain,
( ! [X37,X35] :
( c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint) )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f8777]) ).
fof(f30493,plain,
( spl0_2344
| ~ spl0_649
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9076,f8765,f5860,f30491]) ).
fof(f30491,plain,
( spl0_2344
<=> ! [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_2344])]) ).
fof(f5860,plain,
( spl0_649
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f9076,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) )
| ~ spl0_649
| ~ spl0_1072 ),
inference(superposition,[],[f8766,f5862]) ).
fof(f5862,plain,
( c_1 = c_IntDef_Onat(c_1)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f5860]) ).
fof(f30489,plain,
( spl0_2343
| ~ spl0_667
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f9063,f8761,f6703,f30487]) ).
fof(f30487,plain,
( spl0_2343
<=> ! [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_2343])]) ).
fof(f8761,plain,
( spl0_1071
<=> ! [X37,X35] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f9063,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) )
| ~ spl0_667
| ~ spl0_1071 ),
inference(superposition,[],[f8762,f6704]) ).
fof(f8762,plain,
( ! [X37,X35] :
( ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat)
| c_less(c_0,X37,tc_IntDef_Oint) )
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f8761]) ).
fof(f30485,plain,
( spl0_2342
| ~ spl0_109
| ~ spl0_1070 ),
inference(avatar_split_clause,[],[f9058,f8757,f3695,f30483]) ).
fof(f30483,plain,
( spl0_2342
<=> ! [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_2342])]) ).
fof(f8757,plain,
( spl0_1070
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f9058,plain,
( ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) )
| ~ spl0_109
| ~ spl0_1070 ),
inference(superposition,[],[f8758,f3697]) ).
fof(f8758,plain,
( ! [X10,X25] :
( c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ c_less(X25,X10,tc_nat) )
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f8757]) ).
fof(f30481,plain,
( spl0_2341
| ~ spl0_109
| ~ spl0_1069 ),
inference(avatar_split_clause,[],[f9052,f8753,f3695,f30479]) ).
fof(f30479,plain,
( spl0_2341
<=> ! [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_2341])]) ).
fof(f8753,plain,
( spl0_1069
<=> ! [X25,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f9052,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) )
| ~ spl0_109
| ~ spl0_1069 ),
inference(superposition,[],[f8754,f3697]) ).
fof(f8754,plain,
( ! [X10,X25] :
( ~ c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint)
| c_less(X25,X10,tc_nat) )
| ~ spl0_1069 ),
inference(avatar_component_clause,[],[f8753]) ).
fof(f30477,plain,
( spl0_2340
| ~ spl0_110
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9044,f8749,f3700,f30475]) ).
fof(f30475,plain,
( spl0_2340
<=> ! [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_2340])]) ).
fof(f8749,plain,
( spl0_1068
<=> ! [X25,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f9044,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_110
| ~ spl0_1068 ),
inference(superposition,[],[f8750,f3702]) ).
fof(f8750,plain,
( ! [X10,X25] :
( c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ c_lessequals(X25,X10,tc_nat) )
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f8749]) ).
fof(f30473,plain,
( spl0_2339
| ~ spl0_109
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9043,f8749,f3695,f30471]) ).
fof(f30471,plain,
( spl0_2339
<=> ! [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_2339])]) ).
fof(f9043,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_109
| ~ spl0_1068 ),
inference(superposition,[],[f8750,f3697]) ).
fof(f30469,plain,
( spl0_2338
| ~ spl0_1143
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f30298,f29519,f9252,f30467]) ).
fof(f30467,plain,
( spl0_2338
<=> ! [X0] : c_Main_Ozmod__eq__0D__dest__1(c_1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f9252,plain,
( spl0_1143
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f29519,plain,
( spl0_2316
<=> ! [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_2316])]) ).
fof(f30298,plain,
( ! [X0] : c_Main_Ozmod__eq__0D__dest__1(c_1,X0) = X0
| ~ spl0_1143
| ~ spl0_2316 ),
inference(superposition,[],[f29520,f9253]) ).
fof(f9253,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f9252]) ).
fof(f29520,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_2316 ),
inference(avatar_component_clause,[],[f29519]) ).
fof(f30465,plain,
( spl0_2337
| ~ spl0_109
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9041,f8749,f3695,f30463]) ).
fof(f30463,plain,
( spl0_2337
<=> ! [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_2337])]) ).
fof(f9041,plain,
( ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_109
| ~ spl0_1068 ),
inference(superposition,[],[f8750,f3697]) ).
fof(f30461,plain,
( spl0_2336
| ~ spl0_110
| ~ spl0_1067 ),
inference(avatar_split_clause,[],[f9039,f8745,f3700,f30459]) ).
fof(f30459,plain,
( spl0_2336
<=> ! [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_2336])]) ).
fof(f8745,plain,
( spl0_1067
<=> ! [X25,X10] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f9039,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_110
| ~ spl0_1067 ),
inference(superposition,[],[f8746,f3702]) ).
fof(f8746,plain,
( ! [X10,X25] :
( ~ c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint)
| c_lessequals(X25,X10,tc_nat) )
| ~ spl0_1067 ),
inference(avatar_component_clause,[],[f8745]) ).
fof(f30457,plain,
( spl0_2335
| ~ spl0_109
| ~ spl0_1067 ),
inference(avatar_split_clause,[],[f9038,f8745,f3695,f30455]) ).
fof(f30455,plain,
( spl0_2335
<=> ! [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_2335])]) ).
fof(f9038,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_109
| ~ spl0_1067 ),
inference(superposition,[],[f8746,f3697]) ).
fof(f30453,plain,
( spl0_2334
| ~ spl0_109
| ~ spl0_1067 ),
inference(avatar_split_clause,[],[f9036,f8745,f3695,f30451]) ).
fof(f30451,plain,
( spl0_2334
<=> ! [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_2334])]) ).
fof(f9036,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_109
| ~ spl0_1067 ),
inference(superposition,[],[f8746,f3697]) ).
fof(f30448,plain,
( spl0_95
| spl0_2333
| ~ spl0_109
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f9027,f8729,f3695,f30446,f3631]) ).
fof(f3631,plain,
( spl0_95
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f30446,plain,
( spl0_2333
<=> ! [X0] : c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).
fof(f8729,plain,
( spl0_1063
<=> ! [X25,X10] :
( c_0 = X10
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f9027,plain,
( ! [X0] :
( c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0)
| c_0 = c_1 )
| ~ spl0_109
| ~ spl0_1063 ),
inference(superposition,[],[f8730,f3697]) ).
fof(f8730,plain,
( ! [X10,X25] :
( c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint)
| c_0 = X10 )
| ~ spl0_1063 ),
inference(avatar_component_clause,[],[f8729]) ).
fof(f30444,plain,
( spl0_2332
| ~ spl0_832
| ~ spl0_1058 ),
inference(avatar_split_clause,[],[f9009,f8708,f7407,f30442]) ).
fof(f30442,plain,
( spl0_2332
<=> ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f8708,plain,
( spl0_1058
<=> ! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_1 = c_div(X10,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f9009,plain,
( ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 )
| ~ spl0_832
| ~ spl0_1058 ),
inference(resolution,[],[f8709,f7408]) ).
fof(f8709,plain,
( ! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_1 = c_div(X10,X10,tc_nat) )
| ~ spl0_1058 ),
inference(avatar_component_clause,[],[f8708]) ).
fof(f30440,plain,
( spl0_2331
| ~ spl0_876
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f8983,f8664,f7656,f30438]) ).
fof(f30438,plain,
( spl0_2331
<=> ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).
fof(f7656,plain,
( spl0_876
<=> ! [X3,X15] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X15,X3),tc_Datatype_Ooption(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f8983,plain,
( ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_876
| ~ spl0_1047 ),
inference(superposition,[],[f7657,f8665]) ).
fof(f7657,plain,
( ! [X3,X15] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X15,X3),tc_Datatype_Ooption(X3))
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f7656]) ).
fof(f30436,plain,
( spl0_2330
| ~ spl0_667
| ~ spl0_1041 ),
inference(avatar_split_clause,[],[f8661,f8442,f6703,f30434]) ).
fof(f30434,plain,
( spl0_2330
<=> ! [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_2330])]) ).
fof(f8442,plain,
( spl0_1041
<=> ! [X37] :
( ~ c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| c_less(c_1,X37,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f8661,plain,
( ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_667
| ~ spl0_1041 ),
inference(superposition,[],[f8443,f6704]) ).
fof(f8443,plain,
( ! [X37] :
( ~ c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| c_less(c_1,X37,tc_IntDef_Oint) )
| ~ spl0_1041 ),
inference(avatar_component_clause,[],[f8442]) ).
fof(f30432,plain,
( spl0_2329
| ~ spl0_667
| ~ spl0_1040 ),
inference(avatar_split_clause,[],[f8655,f8438,f6703,f30430]) ).
fof(f30430,plain,
( spl0_2329
<=> ! [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_2329])]) ).
fof(f8438,plain,
( spl0_1040
<=> ! [X37] :
( c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_1,X37,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f8655,plain,
( ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_667
| ~ spl0_1040 ),
inference(superposition,[],[f8439,f6704]) ).
fof(f8439,plain,
( ! [X37] :
( c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_1,X37,tc_IntDef_Oint) )
| ~ spl0_1040 ),
inference(avatar_component_clause,[],[f8438]) ).
fof(f30425,plain,
( spl0_2328
| ~ spl0_866
| ~ spl0_1037 ),
inference(avatar_split_clause,[],[f8645,f8426,f7545,f30423]) ).
fof(f30423,plain,
( spl0_2328
<=> ! [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_2328])]) ).
fof(f30421,plain,
( spl0_2327
| ~ spl0_992
| ~ spl0_993 ),
inference(avatar_split_clause,[],[f8549,f8248,f8244,f30419]) ).
fof(f30419,plain,
( spl0_2327
<=> ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).
fof(f8244,plain,
( spl0_992
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_0 != c_Nat_Osize(X41,tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f8549,plain,
( ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_992
| ~ spl0_993 ),
inference(superposition,[],[f8245,f8249]) ).
fof(f8245,plain,
( ! [X41,X3] :
( c_0 != c_Nat_Osize(X41,tc_List_Olist(X3))
| c_List_Olist_ONil = X41 )
| ~ spl0_992 ),
inference(avatar_component_clause,[],[f8244]) ).
fof(f30417,plain,
( spl0_2326
| ~ spl0_813
| ~ spl0_967 ),
inference(avatar_split_clause,[],[f8468,f8142,f7331,f30415]) ).
fof(f30415,plain,
( spl0_2326
<=> ! [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_2326])]) ).
fof(f7331,plain,
( spl0_813
<=> ! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f8142,plain,
( spl0_967
<=> ! [X37] :
( c_0 = X37
| ~ c_less(c_HOL_Oabs(X37,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f8468,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(X0) )
| ~ spl0_813
| ~ spl0_967 ),
inference(superposition,[],[f8143,f7332]) ).
fof(f7332,plain,
( ! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint)
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f7331]) ).
fof(f8143,plain,
( ! [X37] :
( ~ c_less(c_HOL_Oabs(X37,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| c_0 = X37 )
| ~ spl0_967 ),
inference(avatar_component_clause,[],[f8142]) ).
fof(f30256,plain,
( spl0_2325
| ~ spl0_1154
| ~ spl0_2313 ),
inference(avatar_split_clause,[],[f30067,f29476,f9296,f30254]) ).
fof(f30254,plain,
( spl0_2325
<=> ! [X0] : c_Main_Omod__eq__0D__dest__1(c_1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).
fof(f9296,plain,
( spl0_1154
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f29476,plain,
( spl0_2313
<=> ! [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_2313])]) ).
fof(f30067,plain,
( ! [X0] : c_Main_Omod__eq__0D__dest__1(c_1,X0) = X0
| ~ spl0_1154
| ~ spl0_2313 ),
inference(superposition,[],[f29477,f9297]) ).
fof(f9297,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_1154 ),
inference(avatar_component_clause,[],[f9296]) ).
fof(f29477,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_2313 ),
inference(avatar_component_clause,[],[f29476]) ).
fof(f29844,plain,
( spl0_2324
| ~ spl0_24
| ~ spl0_2286 ),
inference(avatar_split_clause,[],[f29803,f29312,f3276,f29842]) ).
fof(f29842,plain,
( spl0_2324
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).
fof(f29803,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,X0,tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_2286 ),
inference(resolution,[],[f29313,f3278]) ).
fof(f29685,plain,
( spl0_2323
| ~ spl0_1145
| ~ spl0_2310 ),
inference(avatar_split_clause,[],[f29496,f29461,f9260,f29683]) ).
fof(f29683,plain,
( spl0_2323
<=> ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).
fof(f9260,plain,
( spl0_1145
<=> ! [X37,X35] :
( ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f29461,plain,
( spl0_2310
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f29496,plain,
( ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1145
| ~ spl0_2310 ),
inference(resolution,[],[f29462,f9261]) ).
fof(f9261,plain,
( ! [X37,X35] :
( c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X35,X37,tc_IntDef_Oint) )
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f9260]) ).
fof(f29462,plain,
( ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ spl0_2310 ),
inference(avatar_component_clause,[],[f29461]) ).
fof(f29629,plain,
( spl0_2322
| ~ spl0_10
| ~ spl0_1142
| ~ spl0_1752
| ~ spl0_2270 ),
inference(avatar_split_clause,[],[f29163,f29159,f17547,f9248,f3206,f29626]) ).
fof(f29626,plain,
( spl0_2322
<=> 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_2322])]) ).
fof(f29159,plain,
( spl0_2270
<=> 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_2270])]) ).
fof(f29163,plain,
( c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_1142
| ~ spl0_1752
| ~ spl0_2270 ),
inference(forward_demodulation,[],[f29161,f18256]) ).
fof(f29161,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2270 ),
inference(avatar_component_clause,[],[f29159]) ).
fof(f29589,plain,
( spl0_2321
| ~ spl0_1146
| ~ spl0_1810 ),
inference(avatar_split_clause,[],[f29446,f17933,f9264,f29587]) ).
fof(f29587,plain,
( spl0_2321
<=> ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).
fof(f9264,plain,
( spl0_1146
<=> ! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f17933,plain,
( spl0_1810
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f29446,plain,
( ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1146
| ~ spl0_1810 ),
inference(resolution,[],[f17934,f9265]) ).
fof(f9265,plain,
( ! [X37,X35] :
( ~ c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X35,X37,tc_IntDef_Oint) )
| ~ spl0_1146 ),
inference(avatar_component_clause,[],[f9264]) ).
fof(f17934,plain,
( ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ spl0_1810 ),
inference(avatar_component_clause,[],[f17933]) ).
fof(f29537,plain,
( spl0_2320
| ~ spl0_118
| ~ spl0_2053 ),
inference(avatar_split_clause,[],[f24267,f23618,f3736,f29535]) ).
fof(f29535,plain,
( spl0_2320
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).
fof(f23618,plain,
( spl0_2053
<=> ! [X17,X16,X20,X27,X3] :
( ~ c_in(X16,c_Relation_OImage(X20,X27,X17,X3),X3)
| c_in(c_Pair(c_Main_OImageE__1(X27,X16,X20,X17,X3),X16,X17,X3),X20,tc_prod(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f24267,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
| ~ spl0_118
| ~ spl0_2053 ),
inference(resolution,[],[f23619,f3737]) ).
fof(f23619,plain,
( ! [X3,X16,X27,X17,X20] :
( c_in(c_Pair(c_Main_OImageE__1(X27,X16,X20,X17,X3),X16,X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(X16,c_Relation_OImage(X20,X27,X17,X3),X3) )
| ~ spl0_2053 ),
inference(avatar_component_clause,[],[f23618]) ).
fof(f29533,plain,
( spl0_2319
| ~ spl0_886
| ~ spl0_1721
| ~ spl0_1831 ),
inference(avatar_split_clause,[],[f19352,f18908,f16846,f7697,f29531]) ).
fof(f29531,plain,
( spl0_2319
<=> ! [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_2319])]) ).
fof(f7697,plain,
( spl0_886
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f16846,plain,
( spl0_1721
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f18908,plain,
( spl0_1831
<=> ! [X11,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f19352,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_886
| ~ spl0_1721
| ~ spl0_1831 ),
inference(forward_demodulation,[],[f19349,f16848]) ).
fof(f16848,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_1721 ),
inference(avatar_component_clause,[],[f16846]) ).
fof(f19349,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_886
| ~ spl0_1831 ),
inference(trivial_inequality_removal,[],[f19346]) ).
fof(f19346,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_886
| ~ spl0_1831 ),
inference(superposition,[],[f18909,f7698]) ).
fof(f7698,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_886 ),
inference(avatar_component_clause,[],[f7697]) ).
fof(f18909,plain,
( ! [X11,X8] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1831 ),
inference(avatar_component_clause,[],[f18908]) ).
fof(f29529,plain,
( spl0_2318
| ~ spl0_765
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f14437,f14433,f7132,f29527]) ).
fof(f29527,plain,
( spl0_2318
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).
fof(f14437,plain,
( ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat)
| ~ spl0_765
| ~ spl0_1601 ),
inference(superposition,[],[f14434,f7133]) ).
fof(f29525,plain,
( spl0_2317
| ~ spl0_748
| ~ spl0_1520 ),
inference(avatar_split_clause,[],[f13981,f13123,f7064,f29523]) ).
fof(f7064,plain,
( spl0_748
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f13123,plain,
( spl0_1520
<=> ! [X25,X81] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_IntDef_Oint)
| c_times(X81,c_Main_Ozmod__eq__0D__dest__1(X81,X25),tc_IntDef_Oint) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f13981,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_748
| ~ spl0_1520 ),
inference(trivial_inequality_removal,[],[f13966]) ).
fof(f13966,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 )
| ~ spl0_748
| ~ spl0_1520 ),
inference(superposition,[],[f13124,f7065]) ).
fof(f7065,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,X15,tc_IntDef_Oint)
| ~ spl0_748 ),
inference(avatar_component_clause,[],[f7064]) ).
fof(f13124,plain,
( ! [X81,X25] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_IntDef_Oint)
| c_times(X81,c_Main_Ozmod__eq__0D__dest__1(X81,X25),tc_IntDef_Oint) = X25 )
| ~ spl0_1520 ),
inference(avatar_component_clause,[],[f13123]) ).
fof(f29521,plain,
( spl0_2316
| ~ spl0_747
| ~ spl0_1520 ),
inference(avatar_split_clause,[],[f13980,f13123,f7060,f29519]) ).
fof(f7060,plain,
( spl0_747
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f13980,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_747
| ~ spl0_1520 ),
inference(trivial_inequality_removal,[],[f13968]) ).
fof(f13968,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_747
| ~ spl0_1520 ),
inference(superposition,[],[f13124,f7061]) ).
fof(f7061,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_IntDef_Oint)
| ~ spl0_747 ),
inference(avatar_component_clause,[],[f7060]) ).
fof(f29517,plain,
( spl0_2315
| ~ spl0_749
| ~ spl0_1520 ),
inference(avatar_split_clause,[],[f13978,f13123,f7068,f29515]) ).
fof(f29515,plain,
( spl0_2315
<=> ! [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_2315])]) ).
fof(f7068,plain,
( spl0_749
<=> ! [X16] : c_0 = c_Divides_Oop_Amod(c_0,X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f13978,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint)
| ~ spl0_749
| ~ spl0_1520 ),
inference(trivial_inequality_removal,[],[f13970]) ).
fof(f13970,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_749
| ~ spl0_1520 ),
inference(superposition,[],[f13124,f7069]) ).
fof(f7069,plain,
( ! [X16] : c_0 = c_Divides_Oop_Amod(c_0,X16,tc_IntDef_Oint)
| ~ spl0_749 ),
inference(avatar_component_clause,[],[f7068]) ).
fof(f29483,plain,
( ~ spl0_51
| ~ spl0_24
| ~ spl0_2309 ),
inference(avatar_split_clause,[],[f29464,f29418,f3276,f3411]) ).
fof(f29418,plain,
( spl0_2309
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f29464,plain,
( ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_2309 ),
inference(resolution,[],[f29419,f3278]) ).
fof(f29419,plain,
( ! [X1] :
( ~ class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_2309 ),
inference(avatar_component_clause,[],[f29418]) ).
fof(f29482,plain,
( spl0_2314
| ~ spl0_736
| ~ spl0_1519 ),
inference(avatar_split_clause,[],[f13964,f13119,f7015,f29480]) ).
fof(f13119,plain,
( spl0_1519
<=> ! [X25,X81] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_nat)
| c_times(X81,c_Main_Omod__eq__0D__dest__1(X81,X25),tc_nat) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f13964,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_736
| ~ spl0_1519 ),
inference(trivial_inequality_removal,[],[f13952]) ).
fof(f13952,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 )
| ~ spl0_736
| ~ spl0_1519 ),
inference(superposition,[],[f13120,f7016]) ).
fof(f13120,plain,
( ! [X81,X25] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_nat)
| c_times(X81,c_Main_Omod__eq__0D__dest__1(X81,X25),tc_nat) = X25 )
| ~ spl0_1519 ),
inference(avatar_component_clause,[],[f13119]) ).
fof(f29478,plain,
( spl0_2313
| ~ spl0_802
| ~ spl0_1519 ),
inference(avatar_split_clause,[],[f13963,f13119,f7286,f29476]) ).
fof(f7286,plain,
( spl0_802
<=> ! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f13963,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_802
| ~ spl0_1519 ),
inference(trivial_inequality_removal,[],[f13953]) ).
fof(f13953,plain,
( ! [X0] :
( c_0 != c_0
| c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 )
| ~ spl0_802
| ~ spl0_1519 ),
inference(superposition,[],[f13120,f7287]) ).
fof(f7287,plain,
( ! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_1,tc_nat)
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7286]) ).
fof(f29474,plain,
( spl0_2312
| ~ spl0_735
| ~ spl0_1519 ),
inference(avatar_split_clause,[],[f13962,f13119,f7011,f29472]) ).
fof(f29472,plain,
( spl0_2312
<=> ! [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_2312])]) ).
fof(f7011,plain,
( spl0_735
<=> ! [X25] : c_0 = c_Divides_Oop_Amod(c_0,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f13962,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat)
| ~ spl0_735
| ~ spl0_1519 ),
inference(trivial_inequality_removal,[],[f13954]) ).
fof(f13954,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) )
| ~ spl0_735
| ~ spl0_1519 ),
inference(superposition,[],[f13120,f7012]) ).
fof(f7012,plain,
( ! [X25] : c_0 = c_Divides_Oop_Amod(c_0,X25,tc_nat)
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f7011]) ).
fof(f29470,plain,
( spl0_2311
| ~ spl0_123
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f13248,f12888,f3756,f29468]) ).
fof(f29468,plain,
( spl0_2311
<=> ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).
fof(f3756,plain,
( spl0_123
<=> ! [X10] : ~ c_less(X10,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f12888,plain,
( spl0_1464
<=> ! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f13248,plain,
( ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) )
| ~ spl0_123
| ~ spl0_1464 ),
inference(resolution,[],[f12889,f3757]) ).
fof(f3757,plain,
( ! [X10] : ~ c_less(X10,X10,tc_nat)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f3756]) ).
fof(f12889,plain,
( ! [X37,X35] :
( c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(X35,X37,tc_IntDef_Oint) )
| ~ spl0_1464 ),
inference(avatar_component_clause,[],[f12888]) ).
fof(f29463,plain,
( spl0_2309
| spl0_2310
| ~ spl0_776
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f13233,f12884,f7177,f29461,f29418]) ).
fof(f7177,plain,
( spl0_776
<=> ! [X11,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X11,X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f12884,plain,
( spl0_1463
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,X37,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f13233,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_776
| ~ spl0_1463 ),
inference(resolution,[],[f12885,f7178]) ).
fof(f7178,plain,
( ! [X3,X11] :
( ~ c_less(X11,X11,X3)
| ~ class_Orderings_Oorder(X3) )
| ~ spl0_776 ),
inference(avatar_component_clause,[],[f7177]) ).
fof(f12885,plain,
( ! [X3,X37,X35] :
( c_less(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3)
| ~ c_less(X35,X37,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_1463 ),
inference(avatar_component_clause,[],[f12884]) ).
fof(f29420,plain,
( spl0_2309
| spl0_1810
| ~ spl0_795
| ~ spl0_1460 ),
inference(avatar_split_clause,[],[f13203,f12872,f7253,f17933,f29418]) ).
fof(f7253,plain,
( spl0_795
<=> ! [X11,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f12872,plain,
( spl0_1460
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f13203,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_795
| ~ spl0_1460 ),
inference(resolution,[],[f12873,f7254]) ).
fof(f7254,plain,
( ! [X3,X11] :
( c_lessequals(X11,X11,X3)
| ~ class_Orderings_Oorder(X3) )
| ~ spl0_795 ),
inference(avatar_component_clause,[],[f7253]) ).
fof(f12873,plain,
( ! [X3,X37,X35] :
( ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3)
| c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_1460 ),
inference(avatar_component_clause,[],[f12872]) ).
fof(f29415,plain,
( spl0_2308
| ~ spl0_789
| ~ spl0_1440 ),
inference(avatar_split_clause,[],[f12775,f11708,f7229,f29413]) ).
fof(f29413,plain,
( spl0_2308
<=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).
fof(f7229,plain,
( spl0_789
<=> ! [X3,X31] : c_UNIV = c_union(c_UNIV,X31,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f11708,plain,
( spl0_1440
<=> ! [X3,X79] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f12775,plain,
( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_789
| ~ spl0_1440 ),
inference(superposition,[],[f11709,f7230]) ).
fof(f7230,plain,
( ! [X31,X3] : c_UNIV = c_union(c_UNIV,X31,X3)
| ~ spl0_789 ),
inference(avatar_component_clause,[],[f7229]) ).
fof(f11709,plain,
( ! [X3,X79] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3)
| ~ spl0_1440 ),
inference(avatar_component_clause,[],[f11708]) ).
fof(f29410,plain,
( spl0_2307
| ~ spl0_789
| ~ spl0_1439 ),
inference(avatar_split_clause,[],[f12767,f11704,f7229,f29408]) ).
fof(f29408,plain,
( spl0_2307
<=> ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).
fof(f11704,plain,
( spl0_1439
<=> ! [X3,X79] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f12767,plain,
( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_789
| ~ spl0_1439 ),
inference(superposition,[],[f11705,f7230]) ).
fof(f11705,plain,
( ! [X3,X79] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3)
| ~ spl0_1439 ),
inference(avatar_component_clause,[],[f11704]) ).
fof(f29406,plain,
( spl0_2306
| ~ spl0_854
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25300,f25139,f7495,f29404]) ).
fof(f29404,plain,
( spl0_2306
<=> ! [X0,X1] : c_IntDef_ONats = c_Sum__Type_OPlus(c_IntDef_ONats,c_IntDef_ONats,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).
fof(f7495,plain,
( spl0_854
<=> ! [X17,X3] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f25300,plain,
( ! [X0,X1] : c_IntDef_ONats = c_Sum__Type_OPlus(c_IntDef_ONats,c_IntDef_ONats,X0,X1)
| ~ spl0_854
| ~ spl0_2095 ),
inference(superposition,[],[f7496,f25141]) ).
fof(f7496,plain,
( ! [X3,X17] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X3,X17)
| ~ spl0_854 ),
inference(avatar_component_clause,[],[f7495]) ).
fof(f29400,plain,
( spl0_2305
| ~ spl0_715
| ~ spl0_1436 ),
inference(avatar_split_clause,[],[f12747,f11688,f6918,f29398]) ).
fof(f29398,plain,
( spl0_2305
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2305])]) ).
fof(f11688,plain,
( spl0_1436
<=> ! [X27,X3,X31] :
( X27 = X31
| ~ c_lessequals(X27,X31,tc_set(X3))
| ~ c_lessequals(X31,X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f12747,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_715
| ~ spl0_1436 ),
inference(resolution,[],[f11689,f6919]) ).
fof(f11689,plain,
( ! [X31,X3,X27] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| ~ c_lessequals(X27,X31,tc_set(X3))
| X27 = X31 )
| ~ spl0_1436 ),
inference(avatar_component_clause,[],[f11688]) ).
fof(f29396,plain,
( spl0_2304
| ~ spl0_719
| ~ spl0_1434 ),
inference(avatar_split_clause,[],[f12720,f11680,f6934,f29394]) ).
fof(f29394,plain,
( spl0_2304
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f11680,plain,
( spl0_1434
<=> ! [X27,X3,X31] :
( X27 = X31
| ~ c_lessequals(X27,X31,tc_set(X3))
| c_less(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f12720,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_719
| ~ spl0_1434 ),
inference(resolution,[],[f11681,f6935]) ).
fof(f11681,plain,
( ! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| X27 = X31
| c_less(X27,X31,tc_set(X3)) )
| ~ spl0_1434 ),
inference(avatar_component_clause,[],[f11680]) ).
fof(f29390,plain,
( spl0_2303
| ~ spl0_715
| ~ spl0_1434 ),
inference(avatar_split_clause,[],[f12707,f11680,f6918,f29388]) ).
fof(f29388,plain,
( spl0_2303
<=> ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f12707,plain,
( ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) )
| ~ spl0_715
| ~ spl0_1434 ),
inference(resolution,[],[f11681,f6919]) ).
fof(f29386,plain,
( spl0_2302
| ~ spl0_720
| ~ spl0_1429 ),
inference(avatar_split_clause,[],[f12675,f11660,f6938,f29384]) ).
fof(f29384,plain,
( spl0_2302
<=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f6938,plain,
( spl0_720
<=> ! [X27,X3] : c_lessequals(X27,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f11660,plain,
( spl0_1429
<=> ! [X11,X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f12675,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| ~ spl0_720
| ~ spl0_1429 ),
inference(resolution,[],[f11661,f6939]) ).
fof(f6939,plain,
( ! [X3,X27] : c_lessequals(X27,X27,tc_set(X3))
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f6938]) ).
fof(f11661,plain,
( ! [X31,X3,X11,X27] :
( ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) )
| ~ spl0_1429 ),
inference(avatar_component_clause,[],[f11660]) ).
fof(f29382,plain,
( spl0_2301
| ~ spl0_720
| ~ spl0_1426 ),
inference(avatar_split_clause,[],[f12660,f11648,f6938,f29380]) ).
fof(f29380,plain,
( spl0_2301
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f11648,plain,
( spl0_1426
<=> ! [X80,X27,X3,X31] :
( c_lessequals(X31,X80,tc_set(X3))
| ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f12660,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| ~ spl0_720
| ~ spl0_1426 ),
inference(resolution,[],[f11649,f6939]) ).
fof(f11649,plain,
( ! [X31,X3,X80,X27] :
( ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3))
| c_lessequals(X31,X80,tc_set(X3)) )
| ~ spl0_1426 ),
inference(avatar_component_clause,[],[f11648]) ).
fof(f29378,plain,
( spl0_2300
| ~ spl0_720
| ~ spl0_1425 ),
inference(avatar_split_clause,[],[f12649,f11644,f6938,f29376]) ).
fof(f29376,plain,
( spl0_2300
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f12649,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_720
| ~ spl0_1425 ),
inference(resolution,[],[f11645,f6939]) ).
fof(f29374,plain,
( spl0_2299
| ~ spl0_1028
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f12534,f11573,f8390,f29372]) ).
fof(f29372,plain,
( spl0_2299
<=> ! [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_2299])]) ).
fof(f8390,plain,
( spl0_1028
<=> ! [X25,X10] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f12534,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1411 ),
inference(superposition,[],[f8391,f11574]) ).
fof(f8391,plain,
( ! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X25,tc_nat)
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8390]) ).
fof(f29370,plain,
( spl0_2298
| ~ spl0_1029
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f12533,f11573,f8394,f29368]) ).
fof(f29368,plain,
( spl0_2298
<=> ! [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_2298])]) ).
fof(f8394,plain,
( spl0_1029
<=> ! [X25,X10] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f12533,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1029
| ~ spl0_1411 ),
inference(superposition,[],[f8395,f11574]) ).
fof(f8395,plain,
( ! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X10,tc_nat)
| ~ spl0_1029 ),
inference(avatar_component_clause,[],[f8394]) ).
fof(f29365,plain,
( spl0_2297
| ~ spl0_1028
| ~ spl0_1410 ),
inference(avatar_split_clause,[],[f12528,f11569,f8390,f29363]) ).
fof(f29363,plain,
( spl0_2297
<=> ! [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_2297])]) ).
fof(f11569,plain,
( spl0_1410
<=> ! [X17,X8,X3] : c_Pair(c_fst(X8,X3,X17),c_snd(X8,X3,X17),X3,X17) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f12528,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1410 ),
inference(superposition,[],[f8391,f11570]) ).
fof(f11570,plain,
( ! [X3,X8,X17] : c_Pair(c_fst(X8,X3,X17),c_snd(X8,X3,X17),X3,X17) = X8
| ~ spl0_1410 ),
inference(avatar_component_clause,[],[f11569]) ).
fof(f29360,plain,
( spl0_2296
| ~ spl0_1029
| ~ spl0_1410 ),
inference(avatar_split_clause,[],[f12527,f11569,f8394,f29358]) ).
fof(f29358,plain,
( spl0_2296
<=> ! [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_2296])]) ).
fof(f12527,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1029
| ~ spl0_1410 ),
inference(superposition,[],[f8395,f11570]) ).
fof(f29356,plain,
( spl0_2295
| ~ spl0_848
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25299,f25139,f7471,f29354]) ).
fof(f29354,plain,
( spl0_2295
<=> ! [X0,X1] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).
fof(f25299,plain,
( ! [X0,X1] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(X1))
| ~ spl0_848
| ~ spl0_2095 ),
inference(superposition,[],[f7472,f25141]) ).
fof(f29352,plain,
( spl0_2294
| ~ spl0_794
| ~ spl0_1374 ),
inference(avatar_split_clause,[],[f12000,f11409,f7249,f29350]) ).
fof(f29350,plain,
( spl0_2294
<=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f12000,plain,
( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
| ~ spl0_794
| ~ spl0_1374 ),
inference(superposition,[],[f7250,f11410]) ).
fof(f29348,plain,
( spl0_2293
| ~ spl0_756
| ~ spl0_1367 ),
inference(avatar_split_clause,[],[f11935,f11381,f7096,f29346]) ).
fof(f29346,plain,
( spl0_2293
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).
fof(f7096,plain,
( spl0_756
<=> ! [X41,X11,X3] : c_List_Olist_OCons(X11,X41,X3) != X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f11935,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 )
| ~ spl0_756
| ~ spl0_1367 ),
inference(superposition,[],[f7097,f11382]) ).
fof(f7097,plain,
( ! [X41,X3,X11] : c_List_Olist_OCons(X11,X41,X3) != X41
| ~ spl0_756 ),
inference(avatar_component_clause,[],[f7096]) ).
fof(f29344,plain,
( spl0_2292
| ~ spl0_956
| ~ spl0_1360 ),
inference(avatar_split_clause,[],[f11880,f11353,f7981,f29342]) ).
fof(f29342,plain,
( spl0_2292
<=> ! [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_2292])]) ).
fof(f7981,plain,
( spl0_956
<=> ! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f11353,plain,
( spl0_1360
<=> ! [X25,X9,X10] :
( c_Divides_Oop_Advd(X9,X25,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f11880,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) )
| ~ spl0_956
| ~ spl0_1360 ),
inference(superposition,[],[f11354,f7982]) ).
fof(f7982,plain,
( ! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_1,tc_nat,tc_nat))
| ~ spl0_956 ),
inference(avatar_component_clause,[],[f7981]) ).
fof(f11354,plain,
( ! [X10,X9,X25] :
( ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(X9,X25,tc_nat) )
| ~ spl0_1360 ),
inference(avatar_component_clause,[],[f11353]) ).
fof(f29340,plain,
( spl0_2291
| ~ spl0_764
| ~ spl0_828
| ~ spl0_1447 ),
inference(avatar_split_clause,[],[f11766,f11743,f7391,f7128,f29338]) ).
fof(f29338,plain,
( spl0_2291
<=> ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).
fof(f7391,plain,
( spl0_828
<=> ! [X24] :
( c_0 = X24
| ~ c_lessequals(X24,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f11743,plain,
( spl0_1447
<=> ! [X52,X24] :
( c_List_Olist_ONil = c_List_Oupt(X24,c_plus(c_1,X52,tc_nat))
| c_lessequals(X24,X52,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f11766,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 )
| ~ spl0_764
| ~ spl0_828
| ~ spl0_1447 ),
inference(forward_demodulation,[],[f11753,f7129]) ).
fof(f11753,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
| c_0 = X0 )
| ~ spl0_828
| ~ spl0_1447 ),
inference(resolution,[],[f11744,f7392]) ).
fof(f7392,plain,
( ! [X24] :
( ~ c_lessequals(X24,c_0,tc_nat)
| c_0 = X24 )
| ~ spl0_828 ),
inference(avatar_component_clause,[],[f7391]) ).
fof(f11744,plain,
( ! [X52,X24] :
( c_lessequals(X24,X52,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,c_plus(c_1,X52,tc_nat)) )
| ~ spl0_1447 ),
inference(avatar_component_clause,[],[f11743]) ).
fof(f29336,plain,
( spl0_2290
| ~ spl0_944
| ~ spl0_1443 ),
inference(avatar_split_clause,[],[f11726,f11721,f7932,f29334]) ).
fof(f29334,plain,
( spl0_2290
<=> ! [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_2290])]) ).
fof(f7932,plain,
( spl0_944
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f11726,plain,
( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_944
| ~ spl0_1443 ),
inference(superposition,[],[f7933,f11722]) ).
fof(f7933,plain,
( ! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f7932]) ).
fof(f29332,plain,
( spl0_2289
| ~ spl0_850
| ~ spl0_1315 ),
inference(avatar_split_clause,[],[f11001,f10314,f7479,f29330]) ).
fof(f29330,plain,
( spl0_2289
<=> ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).
fof(f10314,plain,
( spl0_1315
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| c_emptyset != c_minus(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f11001,plain,
( ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) )
| ~ spl0_850
| ~ spl0_1315 ),
inference(superposition,[],[f10315,f7480]) ).
fof(f10315,plain,
( ! [X31,X3,X27] :
( c_emptyset != c_minus(X27,X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) )
| ~ spl0_1315 ),
inference(avatar_component_clause,[],[f10314]) ).
fof(f29328,plain,
( spl0_2288
| ~ spl0_795
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10970,f10282,f7253,f29326]) ).
fof(f10970,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_795
| ~ spl0_1307 ),
inference(duplicate_literal_removal,[],[f10939]) ).
fof(f10939,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_795
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f7254]) ).
fof(f29318,plain,
( spl0_2287
| ~ spl0_72
| ~ spl0_122
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10944,f10282,f3752,f3516,f29316]) ).
fof(f29316,plain,
( spl0_2287
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f3752,plain,
( spl0_122
<=> ! [X10] : c_lessequals(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f10944,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
| ~ spl0_122
| ~ spl0_1307 ),
inference(resolution,[],[f10283,f3753]) ).
fof(f3753,plain,
( ! [X10] : c_lessequals(c_0,X10,tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f3752]) ).
fof(f29314,plain,
( spl0_2286
| ~ spl0_795
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10919,f10238,f7253,f29312]) ).
fof(f10919,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_795
| ~ spl0_1296 ),
inference(duplicate_literal_removal,[],[f10888]) ).
fof(f10888,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_795
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f7254]) ).
fof(f29244,plain,
( spl0_2285
| ~ spl0_72
| ~ spl0_122
| ~ spl0_1296 ),
inference(avatar_split_clause,[],[f10893,f10238,f3752,f3516,f29242]) ).
fof(f29242,plain,
( spl0_2285
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f10893,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
| ~ spl0_122
| ~ spl0_1296 ),
inference(resolution,[],[f10239,f3753]) ).
fof(f29236,plain,
( spl0_2284
| ~ spl0_24
| ~ spl0_652
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10867,f10234,f5874,f3276,f29233]) ).
fof(f29233,plain,
( spl0_2284
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f5874,plain,
( spl0_652
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f10867,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_652
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f5876]) ).
fof(f5876,plain,
( c_less(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f5874]) ).
fof(f29226,plain,
( spl0_2283
| ~ spl0_72
| ~ spl0_115
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10866,f10234,f3722,f3516,f29223]) ).
fof(f29223,plain,
( spl0_2283
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).
fof(f10866,plain,
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
| ~ spl0_115
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f3724]) ).
fof(f29219,plain,
( spl0_2281
| ~ spl0_2282
| ~ spl0_771
| ~ spl0_1210 ),
inference(avatar_split_clause,[],[f9906,f9525,f7156,f29216,f29213]) ).
fof(f29213,plain,
( spl0_2281
<=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f29216,plain,
( spl0_2282
<=> c_lessequals(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f7156,plain,
( spl0_771
<=> ! [X25] : c_0 = c_times(X25,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f9525,plain,
( spl0_1210
<=> ! [X25,X10] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f9906,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_0,tc_nat)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_771
| ~ spl0_1210 ),
inference(superposition,[],[f9526,f7157]) ).
fof(f7157,plain,
( ! [X25] : c_0 = c_times(X25,c_0,tc_nat)
| ~ spl0_771 ),
inference(avatar_component_clause,[],[f7156]) ).
fof(f9526,plain,
( ! [X10,X25] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X25,tc_nat) )
| ~ spl0_1210 ),
inference(avatar_component_clause,[],[f9525]) ).
fof(f29203,plain,
( spl0_2280
| ~ spl0_41
| ~ spl0_668
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f9769,f9416,f6707,f3361,f29201]) ).
fof(f29201,plain,
( spl0_2280
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).
fof(f9769,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_668
| ~ spl0_1184 ),
inference(resolution,[],[f9417,f6708]) ).
fof(f29199,plain,
( spl0_2279
| ~ spl0_1024
| ~ spl0_2213 ),
inference(avatar_split_clause,[],[f28465,f28072,f8374,f29197]) ).
fof(f29197,plain,
( spl0_2279
<=> ! [X0] : c_IntDef_ONats = c_uminus(c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f8374,plain,
( spl0_1024
<=> ! [X8,X3] : c_uminus(c_uminus(X8,tc_set(X3)),tc_set(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f28072,plain,
( spl0_2213
<=> ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f28465,plain,
( ! [X0] : c_IntDef_ONats = c_uminus(c_emptyset,tc_set(X0))
| ~ spl0_1024
| ~ spl0_2213 ),
inference(superposition,[],[f8375,f28073]) ).
fof(f28073,plain,
( ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0))
| ~ spl0_2213 ),
inference(avatar_component_clause,[],[f28072]) ).
fof(f8375,plain,
( ! [X3,X8] : c_uminus(c_uminus(X8,tc_set(X3)),tc_set(X3)) = X8
| ~ spl0_1024 ),
inference(avatar_component_clause,[],[f8374]) ).
fof(f29195,plain,
( spl0_2278
| ~ spl0_10
| ~ spl0_1099 ),
inference(avatar_split_clause,[],[f9159,f8874,f3206,f29193]) ).
fof(f29193,plain,
( spl0_2278
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).
fof(f8874,plain,
( spl0_1099
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(X15,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f9159,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_1099 ),
inference(resolution,[],[f8875,f3208]) ).
fof(f8875,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(X15,c_uminus(X15,X3),X3) )
| ~ spl0_1099 ),
inference(avatar_component_clause,[],[f8874]) ).
fof(f29191,plain,
( spl0_2277
| ~ spl0_10
| ~ spl0_1094 ),
inference(avatar_split_clause,[],[f9148,f8854,f3206,f29189]) ).
fof(f29189,plain,
( spl0_2277
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f8854,plain,
( spl0_1094
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(X15,X3) = c_minus(c_0,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f9148,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_1094 ),
inference(resolution,[],[f8855,f3208]) ).
fof(f8855,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(X15,X3) = c_minus(c_0,X15,X3) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f8854]) ).
fof(f29187,plain,
( spl0_2276
| ~ spl0_10
| ~ spl0_1092 ),
inference(avatar_split_clause,[],[f9144,f8846,f3206,f29185]) ).
fof(f29185,plain,
( spl0_2276
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f8846,plain,
( spl0_1092
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(c_uminus(X15,X3),X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f9144,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_1092 ),
inference(resolution,[],[f8847,f3208]) ).
fof(f8847,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(c_uminus(X15,X3),X15,X3) )
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f8846]) ).
fof(f29183,plain,
( spl0_2275
| ~ spl0_23
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f9034,f8741,f3271,f29181]) ).
fof(f29181,plain,
( spl0_2275
<=> ! [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_2275])]) ).
fof(f8741,plain,
( spl0_1066
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_IntDef_Oint(X10),X3) = c_NatArith_Oof__nat(X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f9034,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_1066 ),
inference(resolution,[],[f8742,f3273]) ).
fof(f8742,plain,
( ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_IntDef_Oint(X10),X3) = c_NatArith_Oof__nat(X10,X3) )
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f8741]) ).
fof(f29179,plain,
( spl0_2274
| ~ spl0_92
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f9025,f8720,f3616,f29177]) ).
fof(f29177,plain,
( spl0_2274
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f8720,plain,
( spl0_1061
<=> ! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f9025,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_92
| ~ spl0_1061 ),
inference(resolution,[],[f8721,f3618]) ).
fof(f8721,plain,
( ! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X3),X3) = X8 )
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f8720]) ).
fof(f29175,plain,
( spl0_2273
| ~ spl0_28
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f9024,f8720,f3296,f29173]) ).
fof(f29173,plain,
( spl0_2273
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f9024,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_1061 ),
inference(resolution,[],[f8721,f3298]) ).
fof(f29171,plain,
( spl0_2272
| ~ spl0_92
| ~ spl0_1060 ),
inference(avatar_split_clause,[],[f9023,f8716,f3616,f29169]) ).
fof(f29169,plain,
( spl0_2272
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f8716,plain,
( spl0_1060
<=> ! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f9023,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_92
| ~ spl0_1060 ),
inference(resolution,[],[f8717,f3618]) ).
fof(f8717,plain,
( ! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X3),X3) = X8 )
| ~ spl0_1060 ),
inference(avatar_component_clause,[],[f8716]) ).
fof(f29167,plain,
( spl0_2271
| ~ spl0_28
| ~ spl0_1060 ),
inference(avatar_split_clause,[],[f9022,f8716,f3296,f29165]) ).
fof(f29165,plain,
( spl0_2271
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f9022,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_1060 ),
inference(resolution,[],[f8717,f3298]) ).
fof(f29162,plain,
( spl0_2270
| ~ spl0_109
| ~ spl0_1119 ),
inference(avatar_split_clause,[],[f8960,f8957,f3695,f29159]) ).
fof(f8957,plain,
( spl0_1119
<=> ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f8960,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1119 ),
inference(superposition,[],[f8958,f3697]) ).
fof(f8958,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1119 ),
inference(avatar_component_clause,[],[f8957]) ).
fof(f29157,plain,
( spl0_2269
| ~ spl0_939
| ~ spl0_1019 ),
inference(avatar_split_clause,[],[f8603,f8353,f7912,f29155]) ).
fof(f29155,plain,
( spl0_2269
<=> ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f7912,plain,
( spl0_939
<=> ! [X8,X3] : c_Set_Ocontents(c_insert(X8,c_emptyset,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f8603,plain,
( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_939
| ~ spl0_1019 ),
inference(superposition,[],[f7913,f8354]) ).
fof(f7913,plain,
( ! [X3,X8] : c_Set_Ocontents(c_insert(X8,c_emptyset,X3),X3) = X8
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f7912]) ).
fof(f29153,plain,
( spl0_2268
| ~ spl0_827
| ~ spl0_1002 ),
inference(avatar_split_clause,[],[f8574,f8285,f7387,f29151]) ).
fof(f29151,plain,
( spl0_2268
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f8285,plain,
( spl0_1002
<=> ! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f8574,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
| ~ spl0_827
| ~ spl0_1002 ),
inference(resolution,[],[f8286,f7388]) ).
fof(f8286,plain,
( ! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) )
| ~ spl0_1002 ),
inference(avatar_component_clause,[],[f8285]) ).
fof(f29149,plain,
( spl0_2267
| ~ spl0_807
| ~ spl0_1002 ),
inference(avatar_split_clause,[],[f8573,f8285,f7307,f29147]) ).
fof(f29147,plain,
( spl0_2267
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f8573,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
| ~ spl0_807
| ~ spl0_1002 ),
inference(resolution,[],[f8286,f7308]) ).
fof(f29145,plain,
( spl0_2266
| ~ spl0_939
| ~ spl0_994 ),
inference(avatar_split_clause,[],[f8554,f8252,f7912,f29143]) ).
fof(f29143,plain,
( spl0_2266
<=> ! [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_2266])]) ).
fof(f8554,plain,
( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_939
| ~ spl0_994 ),
inference(superposition,[],[f7913,f8253]) ).
fof(f29141,plain,
( spl0_2265
| ~ spl0_813
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8516,f8179,f7331,f29139]) ).
fof(f29139,plain,
( spl0_2265
<=> ! [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_2265])]) ).
fof(f8179,plain,
( spl0_976
<=> ! [X11,X10] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f8516,plain,
( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_813
| ~ spl0_976 ),
inference(superposition,[],[f8180,f7332]) ).
fof(f8180,plain,
( ! [X10,X11] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f8179]) ).
fof(f29137,plain,
( spl0_2264
| ~ spl0_832
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8490,f8163,f7407,f29135]) ).
fof(f29135,plain,
( spl0_2264
<=> ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f8163,plain,
( spl0_972
<=> ! [X37] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8490,plain,
( ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) )
| ~ spl0_832
| ~ spl0_972 ),
inference(resolution,[],[f8164,f7408]) ).
fof(f8164,plain,
( ! [X37] :
( ~ c_less(c_0,c_IntDef_Onat(X37),tc_nat)
| c_less(c_0,X37,tc_IntDef_Oint) )
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8163]) ).
fof(f29124,plain,
( spl0_2263
| ~ spl0_41
| ~ spl0_883
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8066,f7827,f7685,f3361,f29122]) ).
fof(f29122,plain,
( spl0_2263
<=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f7685,plain,
( spl0_883
<=> ! [X37] :
( ~ c_lessequals(X37,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f8066,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
| ~ spl0_883
| ~ spl0_918 ),
inference(resolution,[],[f7828,f7686]) ).
fof(f7686,plain,
( ! [X37] :
( ~ c_lessequals(X37,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X37) )
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f7685]) ).
fof(f29120,plain,
( spl0_2262
| ~ spl0_822
| ~ spl0_889 ),
inference(avatar_split_clause,[],[f8023,f7709,f7367,f29118]) ).
fof(f29118,plain,
( spl0_2262
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f7709,plain,
( spl0_889
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orev(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f8023,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_822
| ~ spl0_889 ),
inference(superposition,[],[f7710,f7368]) ).
fof(f7710,plain,
( ! [X41,X3] :
( c_List_Olist_ONil != c_List_Orev(X41,X3)
| c_List_Olist_ONil = X41 )
| ~ spl0_889 ),
inference(avatar_component_clause,[],[f7709]) ).
fof(f29107,plain,
spl0_2261,
inference(avatar_split_clause,[],[f1583,f29105]) ).
fof(f29105,plain,
( spl0_2261
<=> ! [X17,X3,X20,X18,X22,X23,X19,X21] :
( ~ c_in(c_Pair(X19,X23,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X18,X19,X3,X17),c_Datatype__Universe_OScons(X22,X23,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f1583,axiom,
! [X21,X3,X18,X19,X17,X22,X23,X20] :
( ~ c_in(c_Pair(X19,X23,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X18,X19,X3,X17),c_Datatype__Universe_OScons(X22,X23,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f29103,plain,
( ~ spl0_2260
| ~ spl0_794
| ~ spl0_2232 ),
inference(avatar_split_clause,[],[f28957,f28378,f7249,f29100]) ).
fof(f29100,plain,
( spl0_2260
<=> c_emptyset = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f28378,plain,
( spl0_2232
<=> ! [X0,X1] : c_IntDef_ONats = c_insert(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f28957,plain,
( c_emptyset != c_IntDef_ONats
| ~ spl0_794
| ~ spl0_2232 ),
inference(superposition,[],[f7250,f28379]) ).
fof(f28379,plain,
( ! [X0,X1] : c_IntDef_ONats = c_insert(X0,c_IntDef_ONats,X1)
| ~ spl0_2232 ),
inference(avatar_component_clause,[],[f28378]) ).
fof(f29079,plain,
spl0_2259,
inference(avatar_split_clause,[],[f1587,f29077]) ).
fof(f29077,plain,
( spl0_2259
<=> ! [X17,X20,X3,X35,X21] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdsumE__3(X21,X35,X3,X17),c_Main_OdsumE__4(X21,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdsumE__1(X20,X35,X3,X17),c_Main_OdsumE__2(X20,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f1587,axiom,
! [X21,X3,X17,X35,X20] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdsumE__3(X21,X35,X3,X17),c_Main_OdsumE__4(X21,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdsumE__1(X20,X35,X3,X17),c_Main_OdsumE__2(X20,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f29037,plain,
spl0_2258,
inference(avatar_split_clause,[],[f1586,f29035]) ).
fof(f29035,plain,
( spl0_2258
<=> ! [X17,X20,X3,X35,X21] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X21,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X21,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_in(c_Pair(c_Main_OdsumE__1(X20,X35,X3,X17),c_Main_OdsumE__2(X20,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f1586,axiom,
! [X21,X3,X17,X35,X20] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X21,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X21,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_in(c_Pair(c_Main_OdsumE__1(X20,X35,X3,X17),c_Main_OdsumE__2(X20,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f29033,plain,
spl0_2257,
inference(avatar_split_clause,[],[f1585,f29031]) ).
fof(f29031,plain,
( spl0_2257
<=> ! [X17,X20,X3,X35,X21] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_in(c_Pair(c_Main_OdsumE__3(X21,X35,X3,X17),c_Main_OdsumE__4(X21,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f1585,axiom,
! [X21,X3,X17,X35,X20] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_in(c_Pair(c_Main_OdsumE__3(X21,X35,X3,X17),c_Main_OdsumE__4(X21,X35,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f29010,plain,
spl0_2256,
inference(avatar_split_clause,[],[f1584,f29008]) ).
fof(f29008,plain,
( spl0_2256
<=> ! [X17,X20,X3,X35,X21] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X21,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X21,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f1584,axiom,
! [X21,X3,X17,X35,X20] :
( ~ c_in(X35,c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X21,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X21,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X35,X3,X17),X3,X17),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X35,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f28989,plain,
spl0_2255,
inference(avatar_split_clause,[],[f1580,f28987]) ).
fof(f28987,plain,
( spl0_2255
<=> ! [X17,X20,X3,X21,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X26,X20,X21,X3,X17),c_Main_OdprodE__2(X26,X20,X21,X3,X17),X3,X17),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X26,X20,X21,X3,X17),c_Main_OdprodE__4(X26,X20,X21,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).
fof(f1580,axiom,
! [X21,X3,X26,X17,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X26,X20,X21,X3,X17),c_Main_OdprodE__2(X26,X20,X21,X3,X17),X3,X17),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X26,X20,X21,X3,X17),c_Main_OdprodE__4(X26,X20,X21,X3,X17),X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f28944,plain,
spl0_2254,
inference(avatar_split_clause,[],[f1589,f28942]) ).
fof(f28942,plain,
( spl0_2254
<=> ! [X17,X3,X20,X23,X19,X21] :
( ~ c_in(c_Pair(X19,X23,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X19,X3,X17),c_Datatype__Universe_OIn1(X23,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).
fof(f1589,axiom,
! [X21,X3,X19,X17,X23,X20] :
( ~ c_in(c_Pair(X19,X23,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X19,X3,X17),c_Datatype__Universe_OIn1(X23,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f28940,plain,
spl0_2253,
inference(avatar_split_clause,[],[f1588,f28938]) ).
fof(f28938,plain,
( spl0_2253
<=> ! [X17,X20,X18,X3,X21,X22] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X18,X3,X17),c_Datatype__Universe_OIn0(X22,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f1588,axiom,
! [X21,X3,X18,X17,X22,X20] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X18,X3,X17),c_Datatype__Universe_OIn0(X22,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f28896,plain,
( spl0_2252
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1654
| ~ spl0_1655
| ~ spl0_2251 ),
inference(avatar_split_clause,[],[f28892,f28887,f15688,f15684,f14075,f9388,f8309,f7172,f3421,f28894]) ).
fof(f28894,plain,
( spl0_2252
<=> ! [X36,X35] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f14075,plain,
( spl0_1539
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f15684,plain,
( spl0_1654
<=> ! [X36,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X35),X3) = c_plus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f15688,plain,
( spl0_1655
<=> ! [X36,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X35),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f28887,plain,
( spl0_2251
<=> ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f28892,plain,
( ! [X36,X35] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1654
| ~ spl0_1655
| ~ spl0_2251 ),
inference(forward_demodulation,[],[f28891,f16771]) ).
fof(f16771,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_53
| ~ spl0_1654 ),
inference(resolution,[],[f15685,f3423]) ).
fof(f15685,plain,
( ! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X35),X3) = c_plus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) )
| ~ spl0_1654 ),
inference(avatar_component_clause,[],[f15684]) ).
fof(f28891,plain,
( ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2251 ),
inference(forward_demodulation,[],[f28890,f14260]) ).
fof(f14260,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_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539 ),
inference(forward_demodulation,[],[f14259,f7174]) ).
fof(f14259,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_1008
| ~ spl0_1177
| ~ spl0_1539 ),
inference(forward_demodulation,[],[f14258,f8310]) ).
fof(f14258,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_1177
| ~ spl0_1539 ),
inference(superposition,[],[f9389,f14076]) ).
fof(f14076,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_1539 ),
inference(avatar_component_clause,[],[f14075]) ).
fof(f28890,plain,
( ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X36),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1655
| ~ spl0_2251 ),
inference(forward_demodulation,[],[f28888,f16772]) ).
fof(f16772,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_53
| ~ spl0_1655 ),
inference(resolution,[],[f15689,f3423]) ).
fof(f15689,plain,
( ! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X35),X3) )
| ~ spl0_1655 ),
inference(avatar_component_clause,[],[f15688]) ).
fof(f28888,plain,
( ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2251 ),
inference(avatar_component_clause,[],[f28887]) ).
fof(f28889,plain,
spl0_2251,
inference(avatar_split_clause,[],[f3137,f28887]) ).
fof(f3137,plain,
! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3136,f1006]) ).
fof(f1006,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3136,plain,
! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3135,f1004]) ).
fof(f1004,axiom,
! [X35] : c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3135,plain,
! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f302,f1006]) ).
fof(f302,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
fof(f28736,plain,
spl0_2250,
inference(avatar_split_clause,[],[f1582,f28734]) ).
fof(f28734,plain,
( spl0_2250
<=> ! [X17,X20,X3,X21,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdprodE__1(X26,X20,X21,X3,X17),c_Main_OdprodE__3(X26,X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f1582,axiom,
! [X21,X3,X26,X17,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdprodE__1(X26,X20,X21,X3,X17),c_Main_OdprodE__3(X26,X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f28732,plain,
spl0_2249,
inference(avatar_split_clause,[],[f1581,f28730]) ).
fof(f28730,plain,
( spl0_2249
<=> ! [X17,X20,X3,X21,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdprodE__2(X26,X20,X21,X3,X17),c_Main_OdprodE__4(X26,X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f1581,axiom,
! [X21,X3,X26,X17,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))))
| c_in(c_Pair(c_Main_OdprodE__2(X26,X20,X21,X3,X17),c_Main_OdprodE__4(X26,X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X21,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f28728,plain,
spl0_2248,
inference(avatar_split_clause,[],[f470,f28726]) ).
fof(f28726,plain,
( spl0_2248
<=> ! [X15,X11,X20,X8,X16,X3] :
( c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X11,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f470,axiom,
! [X3,X11,X8,X16,X15,X20] :
( c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X11,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
fof(f28724,plain,
spl0_2247,
inference(avatar_split_clause,[],[f351,f28722]) ).
fof(f28722,plain,
( spl0_2247
<=> ! [X42,X11,X20,X41,X3,X8] :
( c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f351,axiom,
! [X3,X41,X11,X8,X42,X20] :
( c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
fof(f28684,plain,
spl0_2246,
inference(avatar_split_clause,[],[f353,f28682]) ).
fof(f28682,plain,
( spl0_2246
<=> ! [X41,X11,X42,X20,X3,X8] :
( c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(X42,tc_List_Olist(X3))
| c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f353,axiom,
! [X41,X3,X11,X8,X42,X20] :
( c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(X42,tc_List_Olist(X3))
| c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
fof(f28680,plain,
spl0_2245,
inference(avatar_split_clause,[],[f219,f28678]) ).
fof(f28678,plain,
( spl0_2245
<=> ! [X11,X8] :
( ~ c_in(c_Pair(X11,X8,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(X11,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(X8,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_2245])]) ).
fof(f219,axiom,
! [X11,X8] :
( ~ c_in(c_Pair(X11,X8,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(X11,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(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
fof(f28643,plain,
spl0_2244,
inference(avatar_split_clause,[],[f218,f28641]) ).
fof(f28641,plain,
( spl0_2244
<=> ! [X11,X8] :
( c_in(c_Pair(X11,X8,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(X11,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(X8,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_2244])]) ).
fof(f218,axiom,
! [X11,X8] :
( c_in(c_Pair(X11,X8,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(X11,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(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
fof(f28625,plain,
( spl0_2243
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2242 ),
inference(avatar_split_clause,[],[f28621,f28617,f15688,f14075,f9388,f8309,f7172,f3421,f28623]) ).
fof(f28623,plain,
( spl0_2243
<=> ! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f28617,plain,
( spl0_2242
<=> ! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f28621,plain,
( ! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2242 ),
inference(forward_demodulation,[],[f28620,f14260]) ).
fof(f28620,plain,
( ! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X36),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1655
| ~ spl0_2242 ),
inference(forward_demodulation,[],[f28618,f16772]) ).
fof(f28618,plain,
( ! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2242 ),
inference(avatar_component_clause,[],[f28617]) ).
fof(f28619,plain,
spl0_2242,
inference(avatar_split_clause,[],[f3131,f28617]) ).
fof(f3131,plain,
! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3130,f1006]) ).
fof(f3130,plain,
! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3129,f1004]) ).
fof(f3129,plain,
! [X36,X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f311,f1006]) ).
fof(f311,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
fof(f28580,plain,
spl0_2241,
inference(avatar_split_clause,[],[f641,f28578]) ).
fof(f28578,plain,
( spl0_2241
<=> ! [X17,X41,X42,X3,X45,X46] :
( c_Nat_Osize(X42,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X17))
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X45,tc_List_Olist(X17))
| c_List_Ozip(c_append(X41,X42,X3),c_append(X45,X46,X17),X3,X17) = c_append(c_List_Ozip(X41,X45,X3,X17),c_List_Ozip(X42,X46,X3,X17),tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f641,axiom,
! [X3,X41,X46,X45,X17,X42] :
( c_Nat_Osize(X42,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X17))
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X45,tc_List_Olist(X17))
| c_List_Ozip(c_append(X41,X42,X3),c_append(X45,X46,X17),X3,X17) = c_append(c_List_Ozip(X41,X45,X3,X17),c_List_Ozip(X42,X46,X3,X17),tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
fof(f28561,plain,
( spl0_2240
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2239 ),
inference(avatar_split_clause,[],[f28557,f28553,f15688,f14075,f9388,f8309,f7172,f3421,f28559]) ).
fof(f28559,plain,
( spl0_2240
<=> ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f28553,plain,
( spl0_2239
<=> ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f28557,plain,
( ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2239 ),
inference(forward_demodulation,[],[f28556,f14260]) ).
fof(f28556,plain,
( ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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)),X35),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1655
| ~ spl0_2239 ),
inference(forward_demodulation,[],[f28554,f16772]) ).
fof(f28554,plain,
( ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2239 ),
inference(avatar_component_clause,[],[f28553]) ).
fof(f28555,plain,
spl0_2239,
inference(avatar_split_clause,[],[f3134,f28553]) ).
fof(f3134,plain,
! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3133,f1006]) ).
fof(f3133,plain,
! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3132,f1004]) ).
fof(f3132,plain,
! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f300,f1006]) ).
fof(f300,axiom,
! [X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
fof(f28464,plain,
( spl0_2238
| ~ spl0_53
| ~ spl0_1654
| ~ spl0_1721
| ~ spl0_2237 ),
inference(avatar_split_clause,[],[f28460,f28455,f16846,f15684,f3421,f28462]) ).
fof(f28462,plain,
( spl0_2238
<=> ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).
fof(f28455,plain,
( spl0_2237
<=> ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f28460,plain,
( ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1654
| ~ spl0_1721
| ~ spl0_2237 ),
inference(forward_demodulation,[],[f28459,f16848]) ).
fof(f28459,plain,
( ! [X36,X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1654
| ~ spl0_2237 ),
inference(forward_demodulation,[],[f28458,f16771]) ).
fof(f28458,plain,
( ! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X35,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1654
| ~ spl0_2237 ),
inference(forward_demodulation,[],[f28456,f16771]) ).
fof(f28456,plain,
( ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2237 ),
inference(avatar_component_clause,[],[f28455]) ).
fof(f28457,plain,
spl0_2237,
inference(avatar_split_clause,[],[f301,f28455]) ).
fof(f301,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,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(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
fof(f28422,plain,
spl0_2236,
inference(avatar_split_clause,[],[f354,f28420]) ).
fof(f28420,plain,
( spl0_2236
<=> ! [X41,X11,X42,X20,X3,X8] :
( c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| ~ c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
fof(f354,axiom,
! [X41,X3,X11,X8,X42,X20] :
( c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| ~ c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
fof(f28394,plain,
( spl0_2235
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2234 ),
inference(avatar_split_clause,[],[f28390,f28386,f15688,f14075,f9388,f8309,f7172,f3421,f28392]) ).
fof(f28392,plain,
( spl0_2235
<=> ! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
fof(f28386,plain,
( spl0_2234
<=> ! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f28390,plain,
( ! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_775
| ~ spl0_1008
| ~ spl0_1177
| ~ spl0_1539
| ~ spl0_1655
| ~ spl0_2234 ),
inference(forward_demodulation,[],[f28389,f14260]) ).
fof(f28389,plain,
( ! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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)),X35),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1655
| ~ spl0_2234 ),
inference(forward_demodulation,[],[f28387,f16772]) ).
fof(f28387,plain,
( ! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2234 ),
inference(avatar_component_clause,[],[f28386]) ).
fof(f28388,plain,
spl0_2234,
inference(avatar_split_clause,[],[f3128,f28386]) ).
fof(f3128,plain,
! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3127,f1006]) ).
fof(f3127,plain,
! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3126,f1004]) ).
fof(f3126,plain,
! [X35] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f309,f1006]) ).
fof(f309,axiom,
! [X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
fof(f28384,plain,
spl0_2233,
inference(avatar_split_clause,[],[f1631,f28382]) ).
fof(f28382,plain,
( spl0_2233
<=> ! [X42,X41,X20,X3,X8] :
( ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X20,X41,X8,X42,X3),X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f1631,axiom,
! [X41,X3,X8,X42,X20] :
( ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X20,X41,X8,X42,X3),X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
fof(f28380,plain,
( spl0_2232
| ~ spl0_1620
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25305,f25139,f15533,f28378]) ).
fof(f15533,plain,
( spl0_1620
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f25305,plain,
( ! [X0,X1] : c_IntDef_ONats = c_insert(X0,c_IntDef_ONats,X1)
| ~ spl0_1620
| ~ spl0_2095 ),
inference(superposition,[],[f15534,f25141]) ).
fof(f15534,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_1620 ),
inference(avatar_component_clause,[],[f15533]) ).
fof(f28376,plain,
spl0_2231,
inference(avatar_split_clause,[],[f1628,f28374]) ).
fof(f28374,plain,
( spl0_2231
<=> ! [X41,X42,X20,X3,X8] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(X42,c_Main_Olistrel__Cons1__2(X20,X41,X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f1628,axiom,
! [X3,X41,X8,X42,X20] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(X42,c_Main_Olistrel__Cons1__2(X20,X41,X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
fof(f28343,plain,
( spl0_2230
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2225 ),
inference(avatar_split_clause,[],[f28240,f28237,f11573,f8898,f28341]) ).
fof(f28341,plain,
( spl0_2230
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f28237,plain,
( spl0_2225
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f28240,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2225 ),
inference(forward_demodulation,[],[f28238,f12529]) ).
fof(f28238,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2225 ),
inference(avatar_component_clause,[],[f28237]) ).
fof(f28339,plain,
( spl0_2229
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2224 ),
inference(avatar_split_clause,[],[f28235,f28232,f11573,f8894,f28337]) ).
fof(f28337,plain,
( spl0_2229
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f28232,plain,
( spl0_2224
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f28235,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2224 ),
inference(forward_demodulation,[],[f28233,f12530]) ).
fof(f28233,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2224 ),
inference(avatar_component_clause,[],[f28232]) ).
fof(f28335,plain,
( spl0_2228
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2223 ),
inference(avatar_split_clause,[],[f28230,f28227,f11573,f8898,f28333]) ).
fof(f28333,plain,
( spl0_2228
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).
fof(f28227,plain,
( spl0_2223
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f28230,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2223 ),
inference(forward_demodulation,[],[f28228,f12529]) ).
fof(f28228,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2223 ),
inference(avatar_component_clause,[],[f28227]) ).
fof(f28331,plain,
( spl0_2227
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2222 ),
inference(avatar_split_clause,[],[f28225,f28222,f11573,f8894,f28329]) ).
fof(f28329,plain,
( spl0_2227
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).
fof(f28222,plain,
( spl0_2222
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f28225,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2222 ),
inference(forward_demodulation,[],[f28223,f12530]) ).
fof(f28223,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2222 ),
inference(avatar_component_clause,[],[f28222]) ).
fof(f28306,plain,
( spl0_2226
| ~ spl0_790
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25298,f25139,f7233,f28304]) ).
fof(f28304,plain,
( spl0_2226
<=> ! [X0,X1] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f25298,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,X1)
| ~ spl0_790
| ~ spl0_2095 ),
inference(superposition,[],[f7234,f25141]) ).
fof(f28239,plain,
spl0_2225,
inference(avatar_split_clause,[],[f3125,f28237]) ).
fof(f3125,plain,
! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f296,f306]) ).
fof(f306,axiom,
! [X39,X20] : c_IntDiv_OnegateSnd(c_Pair(X39,X20,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X39,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f296,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f28234,plain,
spl0_2224,
inference(avatar_split_clause,[],[f3124,f28232]) ).
fof(f3124,plain,
! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f286,f306]) ).
fof(f286,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f28229,plain,
spl0_2223,
inference(avatar_split_clause,[],[f3123,f28227]) ).
fof(f3123,plain,
! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f293,f306]) ).
fof(f293,axiom,
! [X36,X35] :
( ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f28224,plain,
spl0_2222,
inference(avatar_split_clause,[],[f3122,f28222]) ).
fof(f3122,plain,
! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,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(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f283,f306]) ).
fof(f283,axiom,
! [X36,X35] :
( ~ c_lessequals(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f28220,plain,
spl0_2221,
inference(avatar_split_clause,[],[f472,f28218]) ).
fof(f28218,plain,
( spl0_2221
<=> ! [X55,X11,X20,X3,X8] :
( ~ c_in(c_Pair(X55,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_List_Olist_OCons(X11,X55,X3),c_List_Olist_OCons(X11,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f472,axiom,
! [X3,X11,X8,X55,X20] :
( ~ c_in(c_Pair(X55,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_List_Olist_OCons(X11,X55,X3),c_List_Olist_OCons(X11,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
fof(f28216,plain,
spl0_2220,
inference(avatar_split_clause,[],[f355,f28214]) ).
fof(f28214,plain,
( spl0_2220
<=> ! [X41,X11,X42,X20,X3] :
( ~ c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X11,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f355,axiom,
! [X41,X3,X11,X42,X20] :
( ~ c_in(c_Pair(X41,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
| c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X11,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
fof(f28212,plain,
spl0_2219,
inference(avatar_split_clause,[],[f38,f28210]) ).
fof(f28210,plain,
( spl0_2219
<=> ! [X17,X20,X3,X21] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Relation_ODomain(X21,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f38,axiom,
! [X21,X3,X17,X20] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Relation_ODomain(X21,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f28208,plain,
( spl0_2218
| ~ spl0_789
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25297,f25139,f7229,f28206]) ).
fof(f28206,plain,
( spl0_2218
<=> ! [X0,X1] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f25297,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,X1)
| ~ spl0_789
| ~ spl0_2095 ),
inference(superposition,[],[f7230,f25141]) ).
fof(f28204,plain,
spl0_2217,
inference(avatar_split_clause,[],[f37,f28202]) ).
fof(f28202,plain,
( spl0_2217
<=> ! [X17,X20,X3,X21] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Relation_ODomain(X21,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f37,axiom,
! [X21,X3,X17,X20] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X20,X21,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),c_Relation_ODomain(X21,tc_set(tc_Datatype__Universe_Onode(X3,X17)),tc_set(tc_Datatype__Universe_Onode(X3,X17))),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f28175,plain,
( spl0_2216
| ~ spl0_1721
| ~ spl0_2214 ),
inference(avatar_split_clause,[],[f28167,f28164,f16846,f28173]) ).
fof(f28173,plain,
( spl0_2216
<=> ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f28164,plain,
( spl0_2214
<=> ! [X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f28167,plain,
( ! [X35] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1721
| ~ spl0_2214 ),
inference(forward_demodulation,[],[f28165,f16848]) ).
fof(f28165,plain,
( ! [X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2214 ),
inference(avatar_component_clause,[],[f28164]) ).
fof(f28171,plain,
spl0_2215,
inference(avatar_split_clause,[],[f555,f28169]) ).
fof(f28169,plain,
( spl0_2215
<=> ! [X17,X41,X42,X3,X24] :
( ~ c_less(X24,c_Nat_Osize(X42,tc_List_Olist(X17)),tc_nat)
| ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Ozip(X41,X42,X3,X17),X24,tc_prod(X3,X17)) = c_Pair(c_List_Onth(X41,X24,X3),c_List_Onth(X42,X24,X17),X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f555,axiom,
! [X41,X3,X17,X24,X42] :
( ~ c_less(X24,c_Nat_Osize(X42,tc_List_Olist(X17)),tc_nat)
| ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Ozip(X41,X42,X3,X17),X24,tc_prod(X3,X17)) = c_Pair(c_List_Onth(X41,X24,X3),c_List_Onth(X42,X24,X17),X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f28166,plain,
spl0_2214,
inference(avatar_split_clause,[],[f299,f28164]) ).
fof(f299,axiom,
! [X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f28074,plain,
( spl0_2213
| ~ spl0_787
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25296,f25139,f7221,f28072]) ).
fof(f25296,plain,
( ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0))
| ~ spl0_787
| ~ spl0_2095 ),
inference(superposition,[],[f7222,f25141]) ).
fof(f28013,plain,
spl0_2212,
inference(avatar_split_clause,[],[f1662,f28011]) ).
fof(f28011,plain,
( spl0_2212
<=> ! [X15,X17,X3,X20,X21,X16,X26,X85] :
( ~ c_in(c_Pair(X16,X26,X17,X85),X20,tc_prod(X17,X85))
| ~ c_in(c_Pair(X15,X16,X3,X17),X21,tc_prod(X3,X17))
| c_in(c_Pair(X15,X26,X3,X85),c_Relation_Orel__comp(X20,X21,X17,X85,X3),tc_prod(X3,X85)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f1662,axiom,
! [X21,X3,X26,X16,X17,X15,X85,X20] :
( ~ c_in(c_Pair(X16,X26,X17,X85),X20,tc_prod(X17,X85))
| ~ c_in(c_Pair(X15,X16,X3,X17),X21,tc_prod(X3,X17))
| c_in(c_Pair(X15,X26,X3,X85),c_Relation_Orel__comp(X20,X21,X17,X85,X3),tc_prod(X3,X85)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f28009,plain,
spl0_2211,
inference(avatar_split_clause,[],[f1630,f28007]) ).
fof(f28007,plain,
( spl0_2211
<=> ! [X41,X42,X20,X3,X8] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X20,X41,X8,X42,X3),c_Main_Olistrel__Cons2__2(X20,X41,X8,X42,X3),X3) = X41
| ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f1630,axiom,
! [X41,X3,X8,X42,X20] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X20,X41,X8,X42,X3),c_Main_Olistrel__Cons2__2(X20,X41,X8,X42,X3),X3) = X41
| ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f28005,plain,
spl0_2210,
inference(avatar_split_clause,[],[f1627,f28003]) ).
fof(f28003,plain,
( spl0_2210
<=> ! [X41,X42,X20,X3,X8] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X20,X41,X8,X42,X3),c_Main_Olistrel__Cons1__2(X20,X41,X8,X42,X3),X3) = X41
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f1627,axiom,
! [X41,X3,X8,X42,X20] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X20,X41,X8,X42,X3),c_Main_Olistrel__Cons1__2(X20,X41,X8,X42,X3),X3) = X41
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f28001,plain,
spl0_2209,
inference(avatar_split_clause,[],[f469,f27999]) ).
fof(f27999,plain,
( spl0_2209
<=> ! [X15,X11,X20,X8,X16,X3] :
( X15 = X16
| c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f469,axiom,
! [X3,X11,X8,X16,X15,X20] :
( X15 = X16
| c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
fof(f27997,plain,
spl0_2208,
inference(avatar_split_clause,[],[f350,f27995]) ).
fof(f27995,plain,
( spl0_2208
<=> ! [X42,X11,X20,X41,X3,X8] :
( X8 = X11
| c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f350,axiom,
! [X3,X41,X11,X8,X42,X20] :
( X8 = X11
| c_in(c_Pair(X11,X8,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
fof(f27993,plain,
spl0_2207,
inference(avatar_split_clause,[],[f233,f27991]) ).
fof(f27991,plain,
( spl0_2207
<=> ! [X38,X11,X36,X8] :
( c_plus(X11,X36,tc_nat) != c_plus(X38,X8,tc_nat)
| c_in(c_Pair(c_Pair(X11,X8,tc_nat,tc_nat),c_Pair(X38,X36,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_2207])]) ).
fof(f233,axiom,
! [X38,X11,X36,X8] :
( c_plus(X11,X36,tc_nat) != c_plus(X38,X8,tc_nat)
| c_in(c_Pair(c_Pair(X11,X8,tc_nat,tc_nat),c_Pair(X38,X36,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
fof(f27989,plain,
spl0_2206,
inference(avatar_split_clause,[],[f232,f27987]) ).
fof(f27987,plain,
( spl0_2206
<=> ! [X38,X11,X36,X8] :
( c_plus(X11,X36,tc_nat) = c_plus(X38,X8,tc_nat)
| ~ c_in(c_Pair(c_Pair(X11,X8,tc_nat,tc_nat),c_Pair(X38,X36,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_2206])]) ).
fof(f232,axiom,
! [X38,X11,X36,X8] :
( c_plus(X11,X36,tc_nat) = c_plus(X38,X8,tc_nat)
| ~ c_in(c_Pair(c_Pair(X11,X8,tc_nat,tc_nat),c_Pair(X38,X36,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
fof(f27924,plain,
( spl0_2205
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2198 ),
inference(avatar_split_clause,[],[f27874,f27871,f11573,f8898,f27922]) ).
fof(f27922,plain,
( spl0_2205
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f27871,plain,
( spl0_2198
<=> ! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f27874,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2198 ),
inference(forward_demodulation,[],[f27872,f12529]) ).
fof(f27872,plain,
( ! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2198 ),
inference(avatar_component_clause,[],[f27871]) ).
fof(f27920,plain,
( spl0_2204
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2197 ),
inference(avatar_split_clause,[],[f27869,f27866,f11573,f8898,f27918]) ).
fof(f27918,plain,
( spl0_2204
<=> ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f27866,plain,
( spl0_2197
<=> ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f27869,plain,
( ! [X36,X35] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2197 ),
inference(forward_demodulation,[],[f27867,f12529]) ).
fof(f27867,plain,
( ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2197 ),
inference(avatar_component_clause,[],[f27866]) ).
fof(f27916,plain,
( spl0_2203
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2196 ),
inference(avatar_split_clause,[],[f27864,f27861,f11573,f8894,f27914]) ).
fof(f27914,plain,
( spl0_2203
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f27861,plain,
( spl0_2196
<=> ! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f27864,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2196 ),
inference(forward_demodulation,[],[f27862,f12530]) ).
fof(f27862,plain,
( ! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2196 ),
inference(avatar_component_clause,[],[f27861]) ).
fof(f27890,plain,
( spl0_2202
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2195 ),
inference(avatar_split_clause,[],[f27859,f27856,f11573,f8894,f27888]) ).
fof(f27888,plain,
( spl0_2202
<=> ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f27856,plain,
( spl0_2195
<=> ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f27859,plain,
( ! [X36,X35] :
( c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2195 ),
inference(forward_demodulation,[],[f27857,f12530]) ).
fof(f27857,plain,
( ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2195 ),
inference(avatar_component_clause,[],[f27856]) ).
fof(f27886,plain,
spl0_2201,
inference(avatar_split_clause,[],[f1632,f27884]) ).
fof(f27884,plain,
( spl0_2201
<=> ! [X42,X41,X20,X3,X8] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X20,X41,X8,X42,X3),X8,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f1632,axiom,
! [X41,X3,X8,X42,X20] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X20,X41,X8,X42,X3),X8,X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(X41,c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f27882,plain,
spl0_2200,
inference(avatar_split_clause,[],[f1629,f27880]) ).
fof(f27880,plain,
( spl0_2200
<=> ! [X42,X41,X20,X3,X8] :
( c_in(c_Pair(X8,c_Main_Olistrel__Cons1__1(X20,X41,X8,X42,X3),X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f1629,axiom,
! [X41,X3,X8,X42,X20] :
( c_in(c_Pair(X8,c_Main_Olistrel__Cons1__1(X20,X41,X8,X42,X3),X3,X3),X20,tc_prod(X3,X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X42,X3),X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f27878,plain,
spl0_2199,
inference(avatar_split_clause,[],[f352,f27876]) ).
fof(f27876,plain,
( spl0_2199
<=> ! [X42,X41,X11,X3,X8,X20] :
( X8 = X11
| c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(X42,tc_List_Olist(X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f352,axiom,
! [X41,X3,X11,X8,X42,X20] :
( X8 = X11
| c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(X42,tc_List_Olist(X3))
| ~ c_in(c_Pair(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
fof(f27873,plain,
spl0_2198,
inference(avatar_split_clause,[],[f298,f27871]) ).
fof(f298,axiom,
! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f27868,plain,
spl0_2197,
inference(avatar_split_clause,[],[f294,f27866]) ).
fof(f294,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f27863,plain,
spl0_2196,
inference(avatar_split_clause,[],[f288,f27861]) ).
fof(f288,axiom,
! [X36,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f27858,plain,
spl0_2195,
inference(avatar_split_clause,[],[f284,f27856]) ).
fof(f284,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f27706,plain,
spl0_2194,
inference(avatar_split_clause,[],[f1660,f27704]) ).
fof(f27704,plain,
( spl0_2194
<=> ! [X17,X20,X84,X3,X21,X85] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_Orel__compE__1(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__2(X20,X21,X84,X85,X17,X3),X3,X85),X21,tc_prod(X3,X85)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f1660,axiom,
! [X21,X3,X84,X17,X85,X20] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_Orel__compE__1(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__2(X20,X21,X84,X85,X17,X3),X3,X85),X21,tc_prod(X3,X85)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f27702,plain,
spl0_2193,
inference(avatar_split_clause,[],[f1659,f27700]) ).
fof(f27700,plain,
( spl0_2193
<=> ! [X17,X20,X84,X3,X21,X85] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_Orel__compE__2(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__3(X20,X21,X84,X85,X17,X3),X85,X17),X20,tc_prod(X85,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f1659,axiom,
! [X21,X3,X84,X17,X85,X20] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_Orel__compE__2(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__3(X20,X21,X84,X85,X17,X3),X85,X17),X20,tc_prod(X85,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f27698,plain,
spl0_2192,
inference(avatar_split_clause,[],[f1597,f27696]) ).
fof(f27696,plain,
( spl0_2192
<=> ! [X38,X17,X31,X27,X3] :
( ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__2(X31,X38,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__1(X27,X38,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f1597,axiom,
! [X31,X38,X3,X27,X17] :
( ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__2(X31,X38,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__1(X27,X38,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f27694,plain,
spl0_2191,
inference(avatar_split_clause,[],[f320,f27692]) ).
fof(f27692,plain,
( spl0_2191
<=> ! [X36,X16,X35] :
( c_Numeral_Obit_OB0 = X16
| c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,X16),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f320,axiom,
! [X36,X16,X35] :
( c_Numeral_Obit_OB0 = X16
| c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,X16),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f27545,plain,
spl0_2190,
inference(avatar_split_clause,[],[f3031,f27543]) ).
fof(f27543,plain,
( spl0_2190
<=> ! [X36,X25] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f3031,plain,
! [X36,X25] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3030,f1006]) ).
fof(f3030,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3029,f2796]) ).
fof(f2796,plain,
! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat),
inference(definition_unfolding,[],[f951,f1394,f1394]) ).
fof(f1394,axiom,
! [X38] : c_Suc(X38) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X38,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f951,axiom,
! [X10,X25] : c_Suc(c_plus(X25,X10,tc_nat)) = c_plus(c_Suc(X25),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3029,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2846,f2996]) ).
fof(f2996,plain,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X10,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2995,f1006]) ).
fof(f2995,plain,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X10,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,[],[f2994,f1004]) ).
fof(f2994,plain,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X10,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,[],[f2815,f1006]) ).
fof(f2815,plain,
! [X10] : c_plus(X10,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(X10,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f732,f1394,f1394]) ).
fof(f732,axiom,
! [X10] : c_Suc(c_Suc(X10)) = c_plus(X10,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/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f2846,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,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(X25,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
inference(definition_unfolding,[],[f730,f1394,f1394,f1394]) ).
fof(f730,axiom,
! [X36,X25] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X25))),c_Numeral_Onumber__of(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f27523,plain,
( spl0_2189
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2188 ),
inference(avatar_split_clause,[],[f27519,f27515,f19031,f10415,f10092,f6703,f3695,f27521]) ).
fof(f27521,plain,
( spl0_2189
<=> ! [X36,X25] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X25,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f19031,plain,
( spl0_1859
<=> ! [X10] : c_plus(X10,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,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f27515,plain,
( spl0_2188
<=> ! [X36,X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f27519,plain,
( ! [X36,X25] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X25,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2188 ),
inference(forward_demodulation,[],[f27518,f19032]) ).
fof(f19032,plain,
( ! [X10] : c_plus(X10,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,X10,tc_nat),tc_nat)
| ~ spl0_1859 ),
inference(avatar_component_clause,[],[f19031]) ).
fof(f27518,plain,
( ! [X36,X25] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X25,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(X36,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2188 ),
inference(forward_demodulation,[],[f27516,f11235]) ).
fof(f27516,plain,
( ! [X36,X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ spl0_2188 ),
inference(avatar_component_clause,[],[f27515]) ).
fof(f27517,plain,
spl0_2188,
inference(avatar_split_clause,[],[f3028,f27515]) ).
fof(f3028,plain,
! [X36,X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3027,f1006]) ).
fof(f3027,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,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(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3026,f2796]) ).
fof(f3026,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X36,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2845,f2996]) ).
fof(f2845,plain,
! [X36,X25] : 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),X25,tc_nat),c_Numeral_Onumber__of(X36,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(X25,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
inference(definition_unfolding,[],[f729,f1394,f1394,f1394]) ).
fof(f729,axiom,
! [X36,X25] : c_div(c_Suc(c_Suc(c_Suc(X25))),c_Numeral_Onumber__of(X36,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),X25,tc_nat),c_Numeral_Onumber__of(X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f27513,plain,
spl0_2187,
inference(avatar_split_clause,[],[f2923,f27511]) ).
fof(f27511,plain,
( spl0_2187
<=> ! [X11,X20,X3,X8] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f2923,plain,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f1574,f1566]) ).
fof(f1566,axiom,
! [X3,X20] : c_Transitive__Closure_Ortrancl(X20,X3) = c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1574,axiom,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f27509,plain,
spl0_2186,
inference(avatar_split_clause,[],[f2922,f27507]) ).
fof(f27507,plain,
( spl0_2186
<=> ! [X11,X20,X3,X8] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f2922,plain,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f1571,f1566]) ).
fof(f1571,axiom,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f27505,plain,
spl0_2185,
inference(avatar_split_clause,[],[f1596,f27503]) ).
fof(f27503,plain,
( spl0_2185
<=> ! [X38,X17,X31,X3,X27] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X31,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__1(X27,X38,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f1596,axiom,
! [X31,X38,X3,X27,X17] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X31,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__1(X27,X38,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f27501,plain,
spl0_2184,
inference(avatar_split_clause,[],[f1595,f27499]) ).
fof(f27499,plain,
( spl0_2184
<=> ! [X38,X17,X31,X27,X3] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X27,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__2(X31,X38,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f1595,axiom,
! [X31,X38,X3,X27,X17] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X27,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OusumE__2(X31,X38,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f27492,plain,
spl0_2183,
inference(avatar_split_clause,[],[f471,f27490]) ).
fof(f27490,plain,
( spl0_2183
<=> ! [X15,X11,X20,X8,X16,X3] :
( ~ c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f471,axiom,
! [X3,X11,X8,X16,X15,X20] :
( ~ c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(c_List_Olist_OCons(X15,X11,X3),c_List_Olist_OCons(X16,X8,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f27488,plain,
spl0_2182,
inference(avatar_split_clause,[],[f310,f27486]) ).
fof(f27486,plain,
( spl0_2182
<=> ! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f310,axiom,
! [X36,X35] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f27413,plain,
spl0_2181,
inference(avatar_split_clause,[],[f2894,f27411]) ).
fof(f27411,plain,
( spl0_2181
<=> ! [X41,X11,X36,X3] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),X3) = c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f2894,plain,
! [X41,X3,X36,X11] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),X3) = c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),tc_nat),X3),X3) ),
inference(definition_unfolding,[],[f618,f616,f616]) ).
fof(f616,axiom,
! [X3,X10,X74] : c_List_Osublist(X74,c_SetInterval_OlessThan(X10,tc_nat),X3) = c_List_Otake(X10,X74,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f618,axiom,
! [X41,X3,X36,X11] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X36,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Olist_OCons(X11,c_List_Otake(c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f27409,plain,
spl0_2180,
inference(avatar_split_clause,[],[f1594,f27407]) ).
fof(f27407,plain,
( spl0_2180
<=> ! [X38,X17,X31,X3,X27] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X31,X38,X3,X17),X3,X17) = X38
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X27,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f1594,axiom,
! [X31,X38,X3,X27,X17] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X31,X38,X3,X17),X3,X17) = X38
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X27,X38,X3,X17),X3,X17) = X38
| ~ c_in(X38,c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f27092,plain,
spl0_2179,
inference(avatar_split_clause,[],[f2842,f27090]) ).
fof(f27090,plain,
( spl0_2179
<=> ! [X42,X41,X10,X3] : c_List_Osublist(c_append(X41,X42,X3),c_SetInterval_OlessThan(X10,tc_nat),X3) = c_append(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),c_List_Osublist(X42,c_SetInterval_OlessThan(c_minus(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),tc_nat),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f2842,plain,
! [X41,X3,X10,X42] : c_List_Osublist(c_append(X41,X42,X3),c_SetInterval_OlessThan(X10,tc_nat),X3) = c_append(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),c_List_Osublist(X42,c_SetInterval_OlessThan(c_minus(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),tc_nat),X3),X3),
inference(definition_unfolding,[],[f621,f616,f616,f616]) ).
fof(f621,axiom,
! [X41,X10,X3,X42] : c_List_Otake(X10,c_append(X41,X42,X3),X3) = c_append(c_List_Otake(X10,X41,X3),c_List_Otake(c_minus(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f27088,plain,
spl0_2178,
inference(avatar_split_clause,[],[f1692,f27086]) ).
fof(f27086,plain,
( spl0_2178
<=> ! [X38,X17,X31,X27,X3] :
( ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X31,X38,X17,X3),X17,X3) = X38
| c_Sum__Type_OInl(c_Main_OPlusE__1(X27,X38,X3,X17),X3,X17) = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f1692,axiom,
! [X31,X38,X3,X27,X17] :
( ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X31,X38,X17,X3),X17,X3) = X38
| c_Sum__Type_OInl(c_Main_OPlusE__1(X27,X38,X3,X17),X3,X17) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f27084,plain,
spl0_2177,
inference(avatar_split_clause,[],[f1661,f27082]) ).
fof(f27082,plain,
( spl0_2177
<=> ! [X17,X20,X84,X3,X21,X85] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_Pair(c_Main_Orel__compE__1(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__3(X20,X21,X84,X85,X17,X3),X3,X17) = X84 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f1661,axiom,
! [X21,X3,X84,X17,X85,X20] :
( ~ c_in(X84,c_Relation_Orel__comp(X20,X21,X85,X17,X3),tc_prod(X3,X17))
| c_Pair(c_Main_Orel__compE__1(X20,X21,X84,X85,X17,X3),c_Main_Orel__compE__3(X20,X21,X84,X85,X17,X3),X3,X17) = X84 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f27080,plain,
spl0_2176,
inference(avatar_split_clause,[],[f848,f27078]) ).
fof(f27078,plain,
( spl0_2176
<=> ! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f848,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f27076,plain,
spl0_2175,
inference(avatar_split_clause,[],[f842,f27074]) ).
fof(f27074,plain,
( spl0_2175
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f842,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f27072,plain,
spl0_2174,
inference(avatar_split_clause,[],[f836,f27070]) ).
fof(f27070,plain,
( spl0_2174
<=> ! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f836,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f27068,plain,
spl0_2173,
inference(avatar_split_clause,[],[f830,f27066]) ).
fof(f27066,plain,
( spl0_2173
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f830,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f26979,plain,
( spl0_2172
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_2171 ),
inference(avatar_split_clause,[],[f26975,f26972,f19031,f7164,f7128,f26977]) ).
fof(f26977,plain,
( spl0_2172
<=> ! [X15,X3,X10] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_plus(c_1,c_1,tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_plus(c_1,c_1,tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f26972,plain,
( spl0_2171
<=> ! [X15,X3,X10] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f26975,plain,
( ! [X3,X10,X15] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_plus(c_1,c_1,tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_plus(c_1,c_1,tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) )
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_2171 ),
inference(forward_demodulation,[],[f26973,f19114]) ).
fof(f19114,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_764
| ~ spl0_773
| ~ spl0_1859 ),
inference(forward_demodulation,[],[f19035,f7129]) ).
fof(f19035,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_773
| ~ spl0_1859 ),
inference(superposition,[],[f19032,f7165]) ).
fof(f26973,plain,
( ! [X3,X10,X15] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) )
| ~ spl0_2171 ),
inference(avatar_component_clause,[],[f26972]) ).
fof(f26974,plain,
spl0_2171,
inference(avatar_split_clause,[],[f3119,f26972]) ).
fof(f3119,plain,
! [X3,X10,X15] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(forward_demodulation,[],[f3118,f1006]) ).
fof(f3118,plain,
! [X3,X10,X15] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(forward_demodulation,[],[f3117,f1004]) ).
fof(f3117,plain,
! [X3,X10,X15] :
( c_Nat_Opower(c_uminus(X15,X3),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X10,tc_nat),X3) = c_Nat_Opower(X15,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X10,tc_nat),X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(forward_demodulation,[],[f725,f1006]) ).
fof(f725,axiom,
! [X3,X10,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Nat_Opower(c_uminus(X15,X3),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),X10,tc_nat),X3) = c_Nat_Opower(X15,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),X10,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f26970,plain,
spl0_2170,
inference(avatar_split_clause,[],[f2910,f26968]) ).
fof(f26968,plain,
( spl0_2170
<=> ! [X11,X20,X3,X8] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f2910,plain,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f1573,f1566]) ).
fof(f1573,axiom,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f26966,plain,
spl0_2169,
inference(avatar_split_clause,[],[f2909,f26964]) ).
fof(f26964,plain,
( spl0_2169
<=> ! [X11,X20,X3,X8] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f2909,plain,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f1570,f1566]) ).
fof(f1570,axiom,
! [X3,X11,X8,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X11,X8,X3,X3),c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f26962,plain,
spl0_2168,
inference(avatar_split_clause,[],[f2816,f26960]) ).
fof(f26960,plain,
( spl0_2168
<=> ! [X3,X79] : c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f2816,plain,
! [X3,X79] : c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3,X3),
inference(definition_unfolding,[],[f1561,f1566,f1566,f1566]) ).
fof(f1561,axiom,
! [X3,X79] : c_Transitive__Closure_Ortrancl(X79,X3) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X79,X3),c_Transitive__Closure_Ortrancl(X79,X3),X3,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f26958,plain,
( spl0_2167
| ~ spl0_1126
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25303,f25139,f9046,f26955]) ).
fof(f26955,plain,
( spl0_2167
<=> c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f9046,plain,
( spl0_1126
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f25303,plain,
( c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat)
| ~ spl0_1126
| ~ spl0_2095 ),
inference(superposition,[],[f9048,f25141]) ).
fof(f9048,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| ~ spl0_1126 ),
inference(avatar_component_clause,[],[f9046]) ).
fof(f26953,plain,
spl0_2166,
inference(avatar_split_clause,[],[f1593,f26951]) ).
fof(f26951,plain,
( spl0_2166
<=> ! [X17,X18,X31,X3,X27,X19] :
( ~ c_in(X19,X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| ~ c_in(X18,X27,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OScons(X18,X19,X3,X17),c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f1593,axiom,
! [X31,X3,X18,X19,X27,X17] :
( ~ c_in(X19,X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| ~ c_in(X18,X27,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OScons(X18,X19,X3,X17),c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f26929,plain,
( spl0_2165
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2160 ),
inference(avatar_split_clause,[],[f26151,f26148,f11573,f8898,f26927]) ).
fof(f26927,plain,
( spl0_2165
<=> ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f26148,plain,
( spl0_2160
<=> ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f26151,plain,
( ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2160 ),
inference(forward_demodulation,[],[f26149,f12529]) ).
fof(f26149,plain,
( ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2160 ),
inference(avatar_component_clause,[],[f26148]) ).
fof(f26925,plain,
( spl0_2164
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2159 ),
inference(avatar_split_clause,[],[f26146,f26143,f11573,f8894,f26923]) ).
fof(f26923,plain,
( spl0_2164
<=> ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f26143,plain,
( spl0_2159
<=> ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f26146,plain,
( ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2159 ),
inference(forward_demodulation,[],[f26144,f12530]) ).
fof(f26144,plain,
( ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2159 ),
inference(avatar_component_clause,[],[f26143]) ).
fof(f26864,plain,
( spl0_2163
| ~ spl0_715
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25295,f25139,f6918,f26862]) ).
fof(f26862,plain,
( spl0_2163
<=> ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f25295,plain,
( ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1))
| ~ spl0_715
| ~ spl0_2095 ),
inference(superposition,[],[f6919,f25141]) ).
fof(f26532,plain,
( spl0_2162
| ~ spl0_712
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25294,f25139,f6906,f26530]) ).
fof(f26530,plain,
( spl0_2162
<=> ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f6906,plain,
( spl0_712
<=> ! [X3] : c_UNIV = c_Union(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f25294,plain,
( ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0)
| ~ spl0_712
| ~ spl0_2095 ),
inference(superposition,[],[f6907,f25141]) ).
fof(f6907,plain,
( ! [X3] : c_UNIV = c_Union(c_UNIV,X3)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f6906]) ).
fof(f26155,plain,
( spl0_2161
| ~ spl0_711
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25293,f25139,f6902,f26153]) ).
fof(f26153,plain,
( spl0_2161
<=> ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f6902,plain,
( spl0_711
<=> ! [X3] : c_UNIV = c_Pow(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f25293,plain,
( ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0)
| ~ spl0_711
| ~ spl0_2095 ),
inference(superposition,[],[f6903,f25141]) ).
fof(f6903,plain,
( ! [X3] : c_UNIV = c_Pow(c_UNIV,X3)
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f6902]) ).
fof(f26150,plain,
spl0_2160,
inference(avatar_split_clause,[],[f3076,f26148]) ).
fof(f3076,plain,
! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f295,f306]) ).
fof(f295,axiom,
! [X35] :
( ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f26145,plain,
spl0_2159,
inference(avatar_split_clause,[],[f3075,f26143]) ).
fof(f3075,plain,
! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f285,f306]) ).
fof(f285,axiom,
! [X35] :
( ~ c_less(c_Numeral_Onumber__of(X35,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X35,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(X35,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f26132,plain,
( spl0_2158
| ~ spl0_109
| ~ spl0_667
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2157 ),
inference(avatar_split_clause,[],[f26128,f26124,f19031,f10415,f10092,f7164,f7128,f6703,f3695,f26130]) ).
fof(f26130,plain,
( spl0_2158
<=> ! [X25] : c_div(c_plus(X25,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(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f26124,plain,
( spl0_2157
<=> ! [X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X25,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(X25,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_2157])]) ).
fof(f26128,plain,
( ! [X25] : c_div(c_plus(X25,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(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f26127,f11235]) ).
fof(f26127,plain,
( ! [X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X25,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f26125,f19114]) ).
fof(f26125,plain,
( ! [X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X25,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(X25,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_2157 ),
inference(avatar_component_clause,[],[f26124]) ).
fof(f26126,plain,
spl0_2157,
inference(avatar_split_clause,[],[f3025,f26124]) ).
fof(f3025,plain,
! [X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X25,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(X25,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,[],[f3024,f2996]) ).
fof(f3024,plain,
! [X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X25,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,[],[f3023,f1006]) ).
fof(f3023,plain,
! [X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X25,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,[],[f3022,f1004]) ).
fof(f3022,plain,
! [X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X25,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,[],[f2844,f1006]) ).
fof(f2844,plain,
! [X25] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,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(X25,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,[],[f734,f1394,f1394,f1394]) ).
fof(f734,axiom,
! [X25] : c_div(c_Suc(c_Suc(X25)),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(X25,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/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f26077,plain,
( spl0_2156
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2155 ),
inference(avatar_split_clause,[],[f26073,f26069,f19031,f10415,f10092,f6703,f3695,f26075]) ).
fof(f26075,plain,
( spl0_2156
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_plus(c_1,c_plus(c_1,c_plus(c_1,X10,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f26069,plain,
( spl0_2155
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f26073,plain,
( ! [X10,X25] : c_Divides_Oop_Amod(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_plus(c_1,c_plus(c_1,c_plus(c_1,X10,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2155 ),
inference(forward_demodulation,[],[f26072,f19032]) ).
fof(f26072,plain,
( ! [X10,X25] : c_Divides_Oop_Amod(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_plus(c_1,c_plus(X10,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2155 ),
inference(forward_demodulation,[],[f26070,f11235]) ).
fof(f26070,plain,
( ! [X10,X25] : c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat)
| ~ spl0_2155 ),
inference(avatar_component_clause,[],[f26069]) ).
fof(f26071,plain,
spl0_2155,
inference(avatar_split_clause,[],[f3017,f26069]) ).
fof(f3017,plain,
! [X10,X25] : c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3016,f1006]) ).
fof(f3016,plain,
! [X10,X25] : c_Divides_Oop_Amod(X25,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),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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,[],[f3015,f2796]) ).
fof(f3015,plain,
! [X10,X25] : c_Divides_Oop_Amod(X25,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),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,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,[],[f2839,f2996]) ).
fof(f2839,plain,
! [X10,X25] : c_Divides_Oop_Amod(X25,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),X10,tc_nat),tc_nat) = c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f827,f1394,f1394,f1394]) ).
fof(f827,axiom,
! [X10,X25] : c_Divides_Oop_Amod(X25,c_Suc(c_Suc(c_Suc(X10))),tc_nat) = c_Divides_Oop_Amod(X25,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),X10,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f26055,plain,
( spl0_2154
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2152 ),
inference(avatar_split_clause,[],[f26047,f26043,f19031,f10415,f10092,f6703,f3695,f26053]) ).
fof(f26053,plain,
( spl0_2154
<=> ! [X25,X10] : c_div(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_div(X25,c_plus(c_1,c_plus(c_1,c_plus(c_1,X10,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f26043,plain,
( spl0_2152
<=> ! [X25,X10] : c_div(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f26047,plain,
( ! [X10,X25] : c_div(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_div(X25,c_plus(c_1,c_plus(c_1,c_plus(c_1,X10,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2152 ),
inference(forward_demodulation,[],[f26046,f19032]) ).
fof(f26046,plain,
( ! [X10,X25] : c_div(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat) = c_div(X25,c_plus(c_1,c_plus(X10,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2152 ),
inference(forward_demodulation,[],[f26044,f11235]) ).
fof(f26044,plain,
( ! [X10,X25] : c_div(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat)
| ~ spl0_2152 ),
inference(avatar_component_clause,[],[f26043]) ).
fof(f26051,plain,
( spl0_2153
| ~ spl0_709
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25292,f25139,f6894,f26049]) ).
fof(f26049,plain,
( spl0_2153
<=> ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f6894,plain,
( spl0_709
<=> ! [X3] : c_emptyset = c_Inter(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f25292,plain,
( ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0)
| ~ spl0_709
| ~ spl0_2095 ),
inference(superposition,[],[f6895,f25141]) ).
fof(f6895,plain,
( ! [X3] : c_emptyset = c_Inter(c_UNIV,X3)
| ~ spl0_709 ),
inference(avatar_component_clause,[],[f6894]) ).
fof(f26045,plain,
spl0_2152,
inference(avatar_split_clause,[],[f3014,f26043]) ).
fof(f3014,plain,
! [X10,X25] : c_div(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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(X25,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X10,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3013,f1006]) ).
fof(f3013,plain,
! [X10,X25] : c_div(X25,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),X10,tc_nat),tc_nat) = c_div(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X10,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,[],[f3012,f2796]) ).
fof(f3012,plain,
! [X10,X25] : c_div(X25,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),X10,tc_nat),tc_nat) = c_div(X25,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,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,[],[f2838,f2996]) ).
fof(f2838,plain,
! [X10,X25] : c_div(X25,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),X10,tc_nat),tc_nat) = c_div(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f735,f1394,f1394,f1394]) ).
fof(f735,axiom,
! [X10,X25] : c_div(X25,c_Suc(c_Suc(c_Suc(X10))),tc_nat) = c_div(X25,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),X10,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f26037,plain,
( spl0_2151
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2150 ),
inference(avatar_split_clause,[],[f26033,f26029,f19031,f10415,f10092,f6703,f3695,f26035]) ).
fof(f26035,plain,
( spl0_2151
<=> ! [X18,X17,X9,X3] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f26029,plain,
( spl0_2150
<=> ! [X18,X17,X9,X3] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f26033,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X18,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2150 ),
inference(forward_demodulation,[],[f26032,f11235]) ).
fof(f26032,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17)
| ~ spl0_1859
| ~ spl0_2150 ),
inference(forward_demodulation,[],[f26030,f19032]) ).
fof(f26030,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17)
| ~ spl0_2150 ),
inference(avatar_component_clause,[],[f26029]) ).
fof(f26031,plain,
spl0_2150,
inference(avatar_split_clause,[],[f3011,f26029]) ).
fof(f3011,plain,
! [X3,X18,X9,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2837,f2996]) ).
fof(f2837,plain,
! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f54,f1394,f1394,f1394]) ).
fof(f54,axiom,
! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X9),X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f26023,plain,
( spl0_2149
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2148 ),
inference(avatar_split_clause,[],[f26019,f26015,f19031,f10415,f10092,f6703,f3695,f26021]) ).
fof(f26021,plain,
( spl0_2149
<=> ! [X18,X17,X9,X3] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f26015,plain,
( spl0_2148
<=> ! [X18,X17,X9,X3] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f26019,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X18,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1859
| ~ spl0_2148 ),
inference(forward_demodulation,[],[f26018,f11235]) ).
fof(f26018,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17)
| ~ spl0_1859
| ~ spl0_2148 ),
inference(forward_demodulation,[],[f26016,f19032]) ).
fof(f26016,plain,
( ! [X3,X18,X9,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17)
| ~ spl0_2148 ),
inference(avatar_component_clause,[],[f26015]) ).
fof(f26017,plain,
spl0_2148,
inference(avatar_split_clause,[],[f3010,f26015]) ).
fof(f3010,plain,
! [X3,X18,X9,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2836,f2996]) ).
fof(f2836,plain,
! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f55,f1394,f1394,f1394]) ).
fof(f55,axiom,
! [X3,X18,X9,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X9),X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f26013,plain,
spl0_2147,
inference(avatar_split_clause,[],[f2741,f26011]) ).
fof(f26011,plain,
( spl0_2147
<=> ! [X93,X3] :
( ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3)
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3)
| c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(X93,X3,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f2741,axiom,
! [X3,X93] :
( ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3)
| ~ c_Relation_Otrans(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3)
| c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| ~ c_Relation_Orefl(c_Tarski_Opotype_Opset(X93,X3,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_3) ).
fof(f26009,plain,
spl0_2146,
inference(avatar_split_clause,[],[f1694,f26007]) ).
fof(f26007,plain,
( spl0_2146
<=> ! [X38,X17,X31,X27,X3] :
( c_in(c_Main_OPlusE__1(X27,X38,X3,X17),X27,X3)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X31,X38,X17,X3),X17,X3) = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f1694,axiom,
! [X31,X38,X3,X27,X17] :
( c_in(c_Main_OPlusE__1(X27,X38,X3,X17),X27,X3)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X31,X38,X17,X3),X17,X3) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f26005,plain,
spl0_2145,
inference(avatar_split_clause,[],[f1693,f26003]) ).
fof(f26003,plain,
( spl0_2145
<=> ! [X38,X17,X31,X3,X27] :
( c_in(c_Main_OPlusE__2(X31,X38,X17,X3),X31,X17)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X27,X38,X3,X17),X3,X17) = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f1693,axiom,
! [X31,X38,X3,X27,X17] :
( c_in(c_Main_OPlusE__2(X31,X38,X17,X3),X31,X17)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X27,X38,X3,X17),X3,X17) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f26001,plain,
( spl0_2144
| ~ spl0_672
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25291,f25139,f6723,f25999]) ).
fof(f25999,plain,
( spl0_2144
<=> ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f6723,plain,
( spl0_672
<=> ! [X3] : c_UNIV = c_List_Olists(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f25291,plain,
( ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0)
| ~ spl0_672
| ~ spl0_2095 ),
inference(superposition,[],[f6724,f25141]) ).
fof(f6724,plain,
( ! [X3] : c_UNIV = c_List_Olists(c_UNIV,X3)
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f6723]) ).
fof(f25997,plain,
spl0_2143,
inference(avatar_split_clause,[],[f1590,f25995]) ).
fof(f25995,plain,
( spl0_2143
<=> ! [X17,X31,X27,X3,X26] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X27,X31,X26,X3,X17),c_Main_OuprodE__2(X27,X31,X26,X3,X17),X3,X17) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f1590,axiom,
! [X31,X3,X26,X27,X17] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X27,X31,X26,X3,X17),c_Main_OuprodE__2(X27,X31,X26,X3,X17),X3,X17) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f25993,plain,
spl0_2142,
inference(avatar_split_clause,[],[f853,f25991]) ).
fof(f25991,plain,
( spl0_2142
<=> ! [X17,X36,X16,X26] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Osemiring(X17)
| c_times(c_Numeral_Onumber__of(X36,X17),c_plus(X16,X26,X17),X17) = c_plus(c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),c_times(c_Numeral_Onumber__of(X36,X17),X26,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f853,axiom,
! [X36,X26,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Osemiring(X17)
| c_times(c_Numeral_Onumber__of(X36,X17),c_plus(X16,X26,X17),X17) = c_plus(c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),c_times(c_Numeral_Onumber__of(X36,X17),X26,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f25989,plain,
spl0_2141,
inference(avatar_split_clause,[],[f852,f25987]) ).
fof(f25987,plain,
( spl0_2141
<=> ! [X17,X36,X16,X26] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Oring(X17)
| c_times(c_Numeral_Onumber__of(X36,X17),c_minus(X16,X26,X17),X17) = c_minus(c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),c_times(c_Numeral_Onumber__of(X36,X17),X26,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f852,axiom,
! [X36,X26,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Oring(X17)
| c_times(c_Numeral_Onumber__of(X36,X17),c_minus(X16,X26,X17),X17) = c_minus(c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),c_times(c_Numeral_Onumber__of(X36,X17),X26,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f25985,plain,
spl0_2140,
inference(avatar_split_clause,[],[f850,f25983]) ).
fof(f25983,plain,
( spl0_2140
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f850,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f25981,plain,
spl0_2139,
inference(avatar_split_clause,[],[f849,f25979]) ).
fof(f25979,plain,
( spl0_2139
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X16,X15,X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f849,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X16,X15,X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f25977,plain,
spl0_2138,
inference(avatar_split_clause,[],[f847,f25975]) ).
fof(f25975,plain,
( spl0_2138
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X16,X15,X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f847,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X16,X15,X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f25973,plain,
spl0_2137,
inference(avatar_split_clause,[],[f846,f25971]) ).
fof(f25971,plain,
( spl0_2137
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X15,X16,X17)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f846,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X15,X16,X17)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f25969,plain,
spl0_2136,
inference(avatar_split_clause,[],[f844,f25967]) ).
fof(f25967,plain,
( spl0_2136
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f844,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f25965,plain,
spl0_2135,
inference(avatar_split_clause,[],[f843,f25963]) ).
fof(f25963,plain,
( spl0_2135
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X16,X15,X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f843,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X16,X15,X17)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f25961,plain,
spl0_2134,
inference(avatar_split_clause,[],[f841,f25959]) ).
fof(f25959,plain,
( spl0_2134
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X16,X15,X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f841,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X16,X15,X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f25957,plain,
( ~ spl0_2133
| spl0_665
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25290,f25139,f6694,f25954]) ).
fof(f25954,plain,
( spl0_2133
<=> c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f6694,plain,
( spl0_665
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f25290,plain,
( ~ c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_665
| ~ spl0_2095 ),
inference(superposition,[],[f6696,f25141]) ).
fof(f6696,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_665 ),
inference(avatar_component_clause,[],[f6694]) ).
fof(f25952,plain,
spl0_2132,
inference(avatar_split_clause,[],[f840,f25950]) ).
fof(f25950,plain,
( spl0_2132
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X15,X16,X17)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f840,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_less(X15,X16,X17)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f25948,plain,
spl0_2131,
inference(avatar_split_clause,[],[f838,f25946]) ).
fof(f25946,plain,
( spl0_2131
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f838,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f25944,plain,
spl0_2130,
inference(avatar_split_clause,[],[f837,f25942]) ).
fof(f25942,plain,
( spl0_2130
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X16,X15,X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f837,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X16,X15,X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f25940,plain,
spl0_2129,
inference(avatar_split_clause,[],[f835,f25938]) ).
fof(f25938,plain,
( spl0_2129
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X16,X15,X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f835,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X16,X15,X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f25936,plain,
spl0_2128,
inference(avatar_split_clause,[],[f834,f25934]) ).
fof(f25934,plain,
( spl0_2128
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X15,X16,X17)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f834,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X15,X16,X17)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f25932,plain,
spl0_2127,
inference(avatar_split_clause,[],[f832,f25930]) ).
fof(f25930,plain,
( spl0_2127
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f832,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f25928,plain,
spl0_2126,
inference(avatar_split_clause,[],[f831,f25926]) ).
fof(f25926,plain,
( spl0_2126
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X16,X15,X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f831,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X16,X15,X17)
| c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f25924,plain,
spl0_2125,
inference(avatar_split_clause,[],[f829,f25922]) ).
fof(f25922,plain,
( spl0_2125
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X16,X15,X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f829,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X16,X15,X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_0,X17)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f25920,plain,
spl0_2124,
inference(avatar_split_clause,[],[f828,f25918]) ).
fof(f25918,plain,
( spl0_2124
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X15,X16,X17)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f828,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| c_lessequals(X15,X16,X17)
| ~ c_less(c_0,c_Numeral_Onumber__of(X36,X17),X17)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f25916,plain,
spl0_2123,
inference(avatar_split_clause,[],[f798,f25914]) ).
fof(f25914,plain,
( spl0_2123
<=> ! [X15,X17,X36,X16] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Osemiring(X17)
| c_times(c_plus(X15,X16,X17),c_Numeral_Onumber__of(X36,X17),X17) = c_plus(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f798,axiom,
! [X36,X16,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Osemiring(X17)
| c_times(c_plus(X15,X16,X17),c_Numeral_Onumber__of(X36,X17),X17) = c_plus(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f25899,plain,
spl0_2122,
inference(avatar_split_clause,[],[f797,f25897]) ).
fof(f25897,plain,
( spl0_2122
<=> ! [X15,X17,X36,X16] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Oring(X17)
| c_times(c_minus(X15,X16,X17),c_Numeral_Onumber__of(X36,X17),X17) = c_minus(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f797,axiom,
! [X36,X16,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_Ring__and__Field_Oring(X17)
| c_times(c_minus(X15,X16,X17),c_Numeral_Onumber__of(X36,X17),X17) = c_minus(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f25895,plain,
spl0_2121,
inference(avatar_split_clause,[],[f712,f25893]) ).
fof(f25893,plain,
( spl0_2121
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f712,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f25755,plain,
( spl0_2120
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2119 ),
inference(avatar_split_clause,[],[f25751,f25748,f10415,f10092,f6703,f3695,f25753]) ).
fof(f25753,plain,
( spl0_2120
<=> ! [X18,X9,X17,X3,X19] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f25748,plain,
( spl0_2119
<=> ! [X18,X9,X17,X3,X19] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f25751,plain,
( ! [X3,X18,X19,X9,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2119 ),
inference(forward_demodulation,[],[f25749,f11235]) ).
fof(f25749,plain,
( ! [X3,X18,X19,X9,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17)
| ~ spl0_2119 ),
inference(avatar_component_clause,[],[f25748]) ).
fof(f25750,plain,
spl0_2119,
inference(avatar_split_clause,[],[f2843,f25748]) ).
fof(f2843,plain,
! [X3,X18,X19,X9,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17),
inference(definition_unfolding,[],[f58,f1394]) ).
fof(f58,axiom,
! [X3,X18,X19,X9,X17] : c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OScons(X18,X19,X3,X17),X3,X17) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X18,X3,X17),c_Datatype__Universe_Ontrunc(X9,X19,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f25746,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1654,f25744]) ).
fof(f1654,axiom,
! [X3,X83,X17,X20] :
( ~ c_in(X83,c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17))
| c_in(c_Pair(c_Main_OconverseE__1(X20,X83,X17,X3),c_Main_OconverseE__2(X20,X83,X17,X3),X17,X3),X20,tc_prod(X17,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f25742,plain,
( spl0_2117
| ~ spl0_124
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25289,f25139,f3760,f25740]) ).
fof(f25740,plain,
( spl0_2117
<=> ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f3760,plain,
( spl0_124
<=> ! [X11,X3] : c_in(X11,c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f25289,plain,
( ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1)
| ~ spl0_124
| ~ spl0_2095 ),
inference(superposition,[],[f3761,f25141]) ).
fof(f3761,plain,
( ! [X3,X11] : c_in(X11,c_UNIV,X3)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f3760]) ).
fof(f25738,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1181,f25736]) ).
fof(f25736,plain,
( spl0_2116
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X11,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f1181,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X11,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f25734,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1171,f25732]) ).
fof(f25732,plain,
( spl0_2115
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f1171,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f25730,plain,
spl0_2114,
inference(avatar_split_clause,[],[f319,f25728]) ).
fof(f25728,plain,
( spl0_2114
<=> ! [X36,X16,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,X16),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f319,axiom,
! [X36,X16,X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,X16),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
fof(f25359,plain,
spl0_2113,
inference(avatar_split_clause,[],[f2964,f25357]) ).
fof(f25357,plain,
( spl0_2113
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f2964,plain,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f690,f979]) ).
fof(f979,axiom,
! [X35] : c_Numeral_Obin__minus(X35) = c_Numeral_Obin__mult(c_Numeral_OMin,X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f690,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f25355,plain,
spl0_2112,
inference(avatar_split_clause,[],[f2963,f25353]) ).
fof(f25353,plain,
( spl0_2112
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) != c_Numeral_Onumber__of(X77,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f2963,plain,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) != c_Numeral_Onumber__of(X77,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f689,f979]) ).
fof(f689,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) != c_Numeral_Onumber__of(X77,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f25351,plain,
( spl0_2111
| ~ spl0_1456
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f25304,f25139,f12809,f25349]) ).
fof(f25349,plain,
( spl0_2111
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f12809,plain,
( spl0_1456
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f25304,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0)
| ~ spl0_1456
| ~ spl0_2095 ),
inference(superposition,[],[f12810,f25141]) ).
fof(f12810,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_1456 ),
inference(avatar_component_clause,[],[f12809]) ).
fof(f25347,plain,
spl0_2110,
inference(avatar_split_clause,[],[f2962,f25345]) ).
fof(f25345,plain,
( spl0_2110
<=> ! [X77,X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f2962,plain,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f692,f979]) ).
fof(f692,axiom,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f25343,plain,
spl0_2109,
inference(avatar_split_clause,[],[f2961,f25341]) ).
fof(f25341,plain,
( spl0_2109
<=> ! [X77,X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f2961,plain,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f694,f979]) ).
fof(f694,axiom,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f25339,plain,
spl0_2108,
inference(avatar_split_clause,[],[f2959,f25337]) ).
fof(f25337,plain,
( spl0_2108
<=> ! [X77,X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f2959,plain,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f696,f979]) ).
fof(f696,axiom,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f25335,plain,
spl0_2107,
inference(avatar_split_clause,[],[f1695,f25333]) ).
fof(f25333,plain,
( spl0_2107
<=> ! [X38,X17,X31,X3,X27] :
( c_in(c_Main_OPlusE__2(X31,X38,X17,X3),X31,X17)
| c_in(c_Main_OPlusE__1(X27,X38,X3,X17),X27,X3)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f1695,axiom,
! [X31,X38,X3,X27,X17] :
( c_in(c_Main_OPlusE__2(X31,X38,X17,X3),X31,X17)
| c_in(c_Main_OPlusE__1(X27,X38,X3,X17),X27,X3)
| ~ c_in(X38,c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f25331,plain,
spl0_2106,
inference(avatar_split_clause,[],[f851,f25329]) ).
fof(f25329,plain,
( spl0_2106
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| ~ c_less(X16,X15,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f851,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| ~ c_less(X16,X15,X17)
| c_less(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f25327,plain,
spl0_2105,
inference(avatar_split_clause,[],[f845,f25325]) ).
fof(f25325,plain,
( spl0_2105
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| ~ c_less(X16,X15,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f845,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_less(X15,X16,X17)
| ~ c_less(X16,X15,X17)
| c_less(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f25323,plain,
spl0_2104,
inference(avatar_split_clause,[],[f839,f25321]) ).
fof(f25321,plain,
( spl0_2104
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| ~ c_lessequals(X16,X15,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f839,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| ~ c_lessequals(X16,X15,X17)
| c_lessequals(c_times(X15,c_Numeral_Onumber__of(X36,X17),X17),c_times(X16,c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f25319,plain,
spl0_2103,
inference(avatar_split_clause,[],[f833,f25317]) ).
fof(f25317,plain,
( spl0_2103
<=> ! [X15,X17,X36,X16] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| ~ c_lessequals(X16,X15,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f833,axiom,
! [X36,X16,X17,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ class_Numeral_Onumber(X17)
| ~ c_lessequals(X15,X16,X17)
| ~ c_lessequals(X16,X15,X17)
| c_lessequals(c_times(c_Numeral_Onumber__of(X36,X17),X15,X17),c_times(c_Numeral_Onumber__of(X36,X17),X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f25315,plain,
spl0_2102,
inference(avatar_split_clause,[],[f644,f25313]) ).
fof(f25313,plain,
( spl0_2102
<=> ! [X41,X42,X11,X3,X17] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X17))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X41,X42,X3,X17),X11,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f644,axiom,
! [X41,X3,X11,X17,X42] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X17))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X41,X42,X3,X17),X11,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f25311,plain,
spl0_2101,
inference(avatar_split_clause,[],[f643,f25309]) ).
fof(f25309,plain,
( spl0_2101
<=> ! [X41,X42,X11,X3,X17] :
( ~ c_in(X11,c_List_Oset(X41,X3),X3)
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X17))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X41,X42,X3,X17),X11,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f643,axiom,
! [X41,X3,X11,X17,X42] :
( ~ c_in(X11,c_List_Oset(X41,X3),X3)
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X17))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X41,X42,X3,X17),X11,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f25288,plain,
spl0_2100,
inference(avatar_split_clause,[],[f639,f25286]) ).
fof(f25286,plain,
( spl0_2100
<=> ! [X41,X11,X42,X17,X3,X8] : c_List_Ozip(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X17),X3,X17) = c_List_Olist_OCons(c_Pair(X11,X8,X3,X17),c_List_Ozip(X41,X42,X3,X17),tc_prod(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f639,axiom,
! [X41,X3,X11,X8,X17,X42] : c_List_Ozip(c_List_Olist_OCons(X11,X41,X3),c_List_Olist_OCons(X8,X42,X17),X3,X17) = c_List_Olist_OCons(c_Pair(X11,X8,X3,X17),c_List_Ozip(X41,X42,X3,X17),tc_prod(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f25284,plain,
spl0_2099,
inference(avatar_split_clause,[],[f466,f25282]) ).
fof(f25282,plain,
( spl0_2099
<=> ! [X20,X8,X3] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X8,X3),c_Main_Olexord__Nil__left__2(X8,X3),X3) = X8
| ~ c_in(c_Pair(c_List_Olist_ONil,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f466,axiom,
! [X3,X8,X20] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X8,X3),c_Main_Olexord__Nil__left__2(X8,X3),X3) = X8
| ~ c_in(c_Pair(c_List_Olist_ONil,X8,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f25280,plain,
spl0_2098,
inference(avatar_split_clause,[],[f308,f25278]) ).
fof(f25278,plain,
( spl0_2098
<=> ! [X35] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,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_2098])]) ).
fof(f308,axiom,
! [X35] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f25150,plain,
spl0_2097,
inference(avatar_split_clause,[],[f2958,f25148]) ).
fof(f25148,plain,
( spl0_2097
<=> ! [X41,X3,X42] :
( ~ c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(X42,X3)
| c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X41,X3),X3),c_List_Oset(X42,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f2958,plain,
! [X41,X3,X42] :
( ~ c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(X42,X3)
| c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X41,X3),X3),c_List_Oset(X42,X3),X3,X3) ),
inference(definition_unfolding,[],[f408,f1223]) ).
fof(f1223,axiom,
! [X31,X3,X27] : c_inter(X27,X31,X3) = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f408,axiom,
! [X41,X3,X42] :
( ~ c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(X42,X3)
| c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset != c_inter(c_List_Oset(X41,X3),c_List_Oset(X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f25146,plain,
spl0_2096,
inference(avatar_split_clause,[],[f2930,f25144]) ).
fof(f25144,plain,
( spl0_2096
<=> ! [X3,X31,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f2930,plain,
! [X31,X3,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1529,f1223,f1223]) ).
fof(f1529,axiom,
! [X31,X3,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_inter(X27,X31,X3)
| c_emptyset = c_inter(c_insert(X15,X27,X3),X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
fof(f25142,plain,
( spl0_2095
| ~ spl0_788
| ~ spl0_792
| ~ spl0_1423
| ~ spl0_1671
| ~ spl0_2088 ),
inference(avatar_split_clause,[],[f24987,f24703,f15752,f11636,f7241,f7225,f25139]) ).
fof(f7241,plain,
( spl0_792
<=> ! [X8,X3] : c_union(c_emptyset,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f11636,plain,
( spl0_1423
<=> ! [X27,X3,X31] : c_union(c_minus(X31,X27,tc_set(X3)),X27,X3) = c_union(X31,X27,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f24703,plain,
( spl0_2088
<=> ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f24987,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_788
| ~ spl0_792
| ~ spl0_1423
| ~ spl0_1671
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f24986,f24984]) ).
fof(f24984,plain,
( ! [X0] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_792
| ~ spl0_1423
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f24969,f7242]) ).
fof(f7242,plain,
( ! [X3,X8] : c_union(c_emptyset,X8,X3) = X8
| ~ spl0_792 ),
inference(avatar_component_clause,[],[f7241]) ).
fof(f24969,plain,
( ! [X0] : c_union(X0,c_IntDef_ONats,tc_nat) = c_union(c_emptyset,c_IntDef_ONats,tc_nat)
| ~ spl0_1423
| ~ spl0_2088 ),
inference(superposition,[],[f11637,f24704]) ).
fof(f24704,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_2088 ),
inference(avatar_component_clause,[],[f24703]) ).
fof(f11637,plain,
( ! [X31,X3,X27] : c_union(c_minus(X31,X27,tc_set(X3)),X27,X3) = c_union(X31,X27,X3)
| ~ spl0_1423 ),
inference(avatar_component_clause,[],[f11636]) ).
fof(f24986,plain,
( ! [X0] : c_UNIV = c_union(c_uminus(X0,tc_set(tc_nat)),c_IntDef_ONats,tc_nat)
| ~ spl0_788
| ~ spl0_1671
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f24974,f7226]) ).
fof(f24974,plain,
( ! [X0] : c_union(c_uminus(X0,tc_set(tc_nat)),c_IntDef_ONats,tc_nat) = c_uminus(c_emptyset,tc_set(tc_nat))
| ~ spl0_1671
| ~ spl0_2088 ),
inference(superposition,[],[f15753,f24704]) ).
fof(f25137,plain,
spl0_2094,
inference(avatar_split_clause,[],[f2928,f25135]) ).
fof(f25135,plain,
( spl0_2094
<=> ! [X3,X31,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X31,X3),X27,X3,X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X31,X3),c_insert(X15,X27,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f2928,plain,
! [X31,X3,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X31,X3),X27,X3,X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X31,X3),c_insert(X15,X27,X3),X3,X3) ),
inference(definition_unfolding,[],[f1513,f1223,f1223]) ).
fof(f1513,axiom,
! [X31,X3,X27,X15] :
( c_in(X15,X31,X3)
| c_emptyset != c_inter(X31,X27,X3)
| c_emptyset = c_inter(X31,c_insert(X15,X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
fof(f25133,plain,
spl0_2093,
inference(avatar_split_clause,[],[f642,f25131]) ).
fof(f25131,plain,
( spl0_2093
<=> ! [X17,X11,X3,X24,X8,X52] : c_List_Ozip(c_List_Oreplicate(X24,X11,X3),c_List_Oreplicate(X52,X8,X17),X3,X17) = c_List_Oreplicate(c_Orderings_Omin(X24,X52,tc_nat),c_Pair(X11,X8,X3,X17),tc_prod(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f642,axiom,
! [X3,X11,X8,X52,X17,X24] : c_List_Ozip(c_List_Oreplicate(X24,X11,X3),c_List_Oreplicate(X52,X8,X17),X3,X17) = c_List_Oreplicate(c_Orderings_Omin(X24,X52,tc_nat),c_Pair(X11,X8,X3,X17),tc_prod(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f25129,plain,
spl0_2092,
inference(avatar_split_clause,[],[f548,f25127]) ).
fof(f25127,plain,
( spl0_2092
<=> ! [X41,X10,X3,X24] :
( ~ c_lessequals(c_plus(X10,X24,tc_nat),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Odrop(X10,X41,X3),X24,X3) = c_List_Onth(X41,c_plus(X10,X24,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f548,axiom,
! [X41,X10,X3,X24] :
( ~ c_lessequals(c_plus(X10,X24,tc_nat),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Odrop(X10,X41,X3),X24,X3) = c_List_Onth(X41,c_plus(X10,X24,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f25081,plain,
( spl0_2091
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_2087 ),
inference(avatar_split_clause,[],[f24649,f24646,f11729,f3421,f25079]) ).
fof(f25079,plain,
( spl0_2091
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f11729,plain,
( spl0_1444
<=> ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X35),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f24646,plain,
( spl0_2087
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f24649,plain,
( ! [X36,X77] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_2087 ),
inference(forward_demodulation,[],[f24647,f12793]) ).
fof(f12793,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_53
| ~ spl0_1444 ),
inference(resolution,[],[f11730,f3423]) ).
fof(f11730,plain,
( ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X35),X3) )
| ~ spl0_1444 ),
inference(avatar_component_clause,[],[f11729]) ).
fof(f24647,plain,
( ! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_2087 ),
inference(avatar_component_clause,[],[f24646]) ).
fof(f24713,plain,
( spl0_2090
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2070 ),
inference(avatar_split_clause,[],[f24482,f24479,f11573,f8898,f24711]) ).
fof(f24711,plain,
( spl0_2090
<=> ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f24479,plain,
( spl0_2070
<=> ! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f24482,plain,
( ! [X35] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1105
| ~ spl0_1411
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f24480,f12529]) ).
fof(f24480,plain,
( ! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2070 ),
inference(avatar_component_clause,[],[f24479]) ).
fof(f24709,plain,
( spl0_2089
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2069 ),
inference(avatar_split_clause,[],[f24477,f24474,f11573,f8894,f24707]) ).
fof(f24707,plain,
( spl0_2089
<=> ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f24474,plain,
( spl0_2069
<=> ! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f24477,plain,
( ! [X35] :
( c_div(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1104
| ~ spl0_1411
| ~ spl0_2069 ),
inference(forward_demodulation,[],[f24475,f12530]) ).
fof(f24475,plain,
( ! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2069 ),
inference(avatar_component_clause,[],[f24474]) ).
fof(f24705,plain,
( spl0_2088
| ~ spl0_1316
| ~ spl0_1386 ),
inference(avatar_split_clause,[],[f11503,f11457,f10318,f24703]) ).
fof(f11457,plain,
( spl0_1386
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f11503,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1316
| ~ spl0_1386 ),
inference(resolution,[],[f11458,f10319]) ).
fof(f11458,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1386 ),
inference(avatar_component_clause,[],[f11457]) ).
fof(f24648,plain,
spl0_2087,
inference(avatar_split_clause,[],[f2937,f24646]) ).
fof(f2937,plain,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f709,f979,f979]) ).
fof(f709,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f24644,plain,
spl0_2086,
inference(avatar_split_clause,[],[f2852,f24642]) ).
fof(f24642,plain,
( spl0_2086
<=> ! [X35,X36,X3,X26] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_minus(X26,c_Numeral_Onumber__of(X35,X3),X3),X3) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3),X26,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f2852,plain,
! [X3,X36,X26,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_minus(X26,c_Numeral_Onumber__of(X35,X3),X3),X3) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3),X26,X3) ),
inference(definition_unfolding,[],[f957,f979]) ).
fof(f957,axiom,
! [X3,X36,X26,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_minus(X26,c_Numeral_Onumber__of(X35,X3),X3),X3) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X35)),X3),X26,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f24634,plain,
( spl0_2085
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2084 ),
inference(avatar_split_clause,[],[f24630,f24627,f10415,f10092,f6703,f3695,f24632]) ).
fof(f24632,plain,
( spl0_2085
<=> ! [X13,X79,X10] : c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13) = c_Nat_Opower(X79,c_plus(c_1,X10,tc_nat),tc_set(tc_prod(X13,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f24627,plain,
( spl0_2084
<=> ! [X13,X79,X10] : c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13) = c_Nat_Opower(X79,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_set(tc_prod(X13,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f24630,plain,
( ! [X10,X79,X13] : c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13) = c_Nat_Opower(X79,c_plus(c_1,X10,tc_nat),tc_set(tc_prod(X13,X13)))
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2084 ),
inference(forward_demodulation,[],[f24628,f11235]) ).
fof(f24628,plain,
( ! [X10,X79,X13] : c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13) = c_Nat_Opower(X79,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_set(tc_prod(X13,X13)))
| ~ spl0_2084 ),
inference(avatar_component_clause,[],[f24627]) ).
fof(f24629,plain,
spl0_2084,
inference(avatar_split_clause,[],[f2840,f24627]) ).
fof(f2840,plain,
! [X10,X79,X13] : c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13) = c_Nat_Opower(X79,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_set(tc_prod(X13,X13))),
inference(definition_unfolding,[],[f1241,f1394]) ).
fof(f1241,axiom,
! [X10,X79,X13] : c_Nat_Opower(X79,c_Suc(X10),tc_set(tc_prod(X13,X13))) = c_Relation_Orel__comp(X79,c_Nat_Opower(X79,X10,tc_set(tc_prod(X13,X13))),X13,X13,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f24624,plain,
spl0_2083,
inference(avatar_split_clause,[],[f2835,f24622]) ).
fof(f24622,plain,
( spl0_2083
<=> ! [X3,X31,X27,X15] : c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),c_insert(X15,X31,X3),X3,X3) = c_insert(X15,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f2835,plain,
! [X31,X3,X27,X15] : c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),c_insert(X15,X31,X3),X3,X3) = c_insert(X15,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3),
inference(definition_unfolding,[],[f1536,f1223,f1223]) ).
fof(f1536,axiom,
! [X31,X3,X27,X15] : c_inter(c_insert(X15,X27,X3),c_insert(X15,X31,X3),X3) = c_insert(X15,c_inter(X27,X31,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f24620,plain,
spl0_2082,
inference(avatar_split_clause,[],[f2829,f24618]) ).
fof(f24618,plain,
( spl0_2082
<=> ! [X27,X3,X31] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X27,X3),tc_List_Olist(X3)),c_List_Olists(X31,X3),tc_List_Olist(X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f2829,plain,
! [X31,X3,X27] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X27,X3),tc_List_Olist(X3)),c_List_Olists(X31,X3),tc_List_Olist(X3),tc_List_Olist(X3)),
inference(definition_unfolding,[],[f487,f1223,f1223]) ).
fof(f487,axiom,
! [X31,X3,X27] : c_List_Olists(c_inter(X27,X31,X3),X3) = c_inter(c_List_Olists(X27,X3),c_List_Olists(X31,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f24616,plain,
spl0_2081,
inference(avatar_split_clause,[],[f2828,f24614]) ).
fof(f24614,plain,
( spl0_2081
<=> ! [X27,X3,X31] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X27,X3),tc_set(X3)),c_Pow(X31,X3),tc_set(X3),tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f2828,plain,
! [X31,X3,X27] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X27,X3),tc_set(X3)),c_Pow(X31,X3),tc_set(X3),tc_set(X3)),
inference(definition_unfolding,[],[f1474,f1223,f1223]) ).
fof(f1474,axiom,
! [X31,X3,X27] : c_Pow(c_inter(X27,X31,X3),X3) = c_inter(c_Pow(X27,X3),c_Pow(X31,X3),tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f24534,plain,
( spl0_2080
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f24530,f24526,f10415,f10092,f6703,f3695,f24532]) ).
fof(f24532,plain,
( spl0_2080
<=> ! [X9,X10] : c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X10,tc_nat),c_plus(c_1,X9,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f24526,plain,
( spl0_2079
<=> ! [X9,X10] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f24530,plain,
( ! [X10,X9] : c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X10,tc_nat),c_plus(c_1,X9,tc_nat))
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2079 ),
inference(forward_demodulation,[],[f24529,f11235]) ).
fof(f24529,plain,
( ! [X10,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat)) = c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_plus(c_1,X9,tc_nat)),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2079 ),
inference(forward_demodulation,[],[f24527,f11235]) ).
fof(f24527,plain,
( ! [X10,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2079 ),
inference(avatar_component_clause,[],[f24526]) ).
fof(f24528,plain,
spl0_2079,
inference(avatar_split_clause,[],[f2822,f24526]) ).
fof(f2822,plain,
! [X10,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f12,f1394,f1394,f1394]) ).
fof(f12,axiom,
! [X10,X9] : c_Binomial_Obinomial(c_Suc(X10),c_Suc(X9)) = c_plus(c_Binomial_Obinomial(X10,X9),c_Binomial_Obinomial(X10,c_Suc(X9)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f24522,plain,
spl0_2078,
inference(avatar_split_clause,[],[f2786,f24520]) ).
fof(f24520,plain,
( spl0_2078
<=> ! [X20,X3] : c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),c_Relation_OId,tc_prod(X3,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f2786,plain,
! [X3,X20] : c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),c_Relation_OId,tc_prod(X3,X3)),X3),
inference(definition_unfolding,[],[f1560,f1566,f1566,f1566]) ).
fof(f1560,axiom,
! [X3,X20] : c_Transitive__Closure_Ortrancl(X20,X3) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X20,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f24518,plain,
spl0_2077,
inference(avatar_split_clause,[],[f1655,f24516]) ).
fof(f24516,plain,
( spl0_2077
<=> ! [X17,X20,X3,X83] :
( ~ c_in(X83,c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17))
| c_Pair(c_Main_OconverseE__2(X20,X83,X17,X3),c_Main_OconverseE__1(X20,X83,X17,X3),X3,X17) = X83 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f1655,axiom,
! [X3,X83,X17,X20] :
( ~ c_in(X83,c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17))
| c_Pair(c_Main_OconverseE__2(X20,X83,X17,X3),c_Main_OconverseE__1(X20,X83,X17,X3),X3,X17) = X83 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f24514,plain,
spl0_2076,
inference(avatar_split_clause,[],[f1166,f24512]) ).
fof(f24512,plain,
( spl0_2076
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X11,X3),c_Numeral_Onumber__of(X35,tc_nat),X3) = c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f1166,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X11,X3),c_Numeral_Onumber__of(X35,tc_nat),X3) = c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f24510,plain,
spl0_2075,
inference(avatar_split_clause,[],[f676,f24508]) ).
fof(f24508,plain,
( spl0_2075
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X77),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f676,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X77),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f24498,plain,
spl0_2074,
inference(avatar_split_clause,[],[f545,f24496]) ).
fof(f24496,plain,
( spl0_2074
<=> ! [X41,X36,X11,X3] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Numeral_Onumber__of(X36,tc_nat),X3) = c_List_Onth(X41,c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f545,axiom,
! [X41,X3,X36,X11] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Numeral_Onumber__of(X36,tc_nat),X3) = c_List_Onth(X41,c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f24494,plain,
spl0_2073,
inference(avatar_split_clause,[],[f423,f24492]) ).
fof(f24492,plain,
( spl0_2073
<=> ! [X41,X42,X10,X3] : c_List_Odrop(X10,c_append(X41,X42,X3),X3) = c_append(c_List_Odrop(X10,X41,X3),c_List_Odrop(c_minus(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f423,axiom,
! [X41,X10,X3,X42] : c_List_Odrop(X10,c_append(X41,X42,X3),X3) = c_append(c_List_Odrop(X10,X41,X3),c_List_Odrop(c_minus(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f24490,plain,
spl0_2072,
inference(avatar_split_clause,[],[f421,f24488]) ).
fof(f24488,plain,
( spl0_2072
<=> ! [X41,X11,X36,X3] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X36,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f421,axiom,
! [X41,X3,X36,X11] :
( c_0 = c_Numeral_Onumber__of(X36,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X36,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X36,tc_nat),c_1,tc_nat),X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f24486,plain,
spl0_2071,
inference(avatar_split_clause,[],[f376,f24484]) ).
fof(f24484,plain,
( spl0_2071
<=> ! [X41,X42,X27,X3] :
( ~ c_in(X42,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f376,axiom,
! [X3,X41,X27,X42] :
( ~ c_in(X42,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f24481,plain,
spl0_2070,
inference(avatar_split_clause,[],[f297,f24479]) ).
fof(f297,axiom,
! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f24476,plain,
spl0_2069,
inference(avatar_split_clause,[],[f287,f24474]) ).
fof(f287,axiom,
! [X35] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f24472,plain,
spl0_2068,
inference(avatar_split_clause,[],[f231,f24470]) ).
fof(f24470,plain,
( spl0_2068
<=> ! [X11,X8] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X11,X8,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_2068])]) ).
fof(f231,axiom,
! [X11,X8] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X11,X8,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/sandbox2/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(f24468,plain,
spl0_2067,
inference(avatar_split_clause,[],[f119,f24466]) ).
fof(f24466,plain,
( spl0_2067
<=> ! [X11,X30,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_less(X11,X30,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_less(X11,c_Finite__Set_OMin(X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f119,axiom,
! [X3,X11,X27,X30] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_less(X11,X30,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_less(X11,c_Finite__Set_OMin(X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f24464,plain,
spl0_2066,
inference(avatar_split_clause,[],[f116,f24462]) ).
fof(f24462,plain,
( spl0_2066
<=> ! [X11,X30,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_lessequals(X11,X30,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f116,axiom,
! [X3,X11,X27,X30] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_lessequals(X11,X30,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f24460,plain,
spl0_2065,
inference(avatar_split_clause,[],[f112,f24458]) ).
fof(f24458,plain,
( spl0_2065
<=> ! [X11,X30,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_less(X30,X11,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_less(c_Finite__Set_OMax(X27,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f112,axiom,
! [X3,X11,X27,X30] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_less(X30,X11,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_less(c_Finite__Set_OMax(X27,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f24446,plain,
spl0_2064,
inference(avatar_split_clause,[],[f109,f24444]) ).
fof(f24444,plain,
( spl0_2064
<=> ! [X11,X30,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_lessequals(X30,X11,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f109,axiom,
! [X3,X11,X27,X30] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X30,X27,X3)
| c_lessequals(X30,X11,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f23814,plain,
( ~ spl0_53
| ~ spl0_2063
| ~ spl0_834
| ~ spl0_1721 ),
inference(avatar_split_clause,[],[f20648,f16846,f7415,f23811,f3421]) ).
fof(f23811,plain,
( spl0_2063
<=> c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f7415,plain,
( spl0_834
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f20648,plain,
( ~ c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_834
| ~ spl0_1721 ),
inference(superposition,[],[f7416,f16848]) ).
fof(f7416,plain,
( ! [X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f7415]) ).
fof(f23726,plain,
( spl0_2062
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_2061 ),
inference(avatar_split_clause,[],[f23722,f23719,f19031,f7164,f7128,f23724]) ).
fof(f23724,plain,
( spl0_2062
<=> ! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_plus(c_1,c_1,tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f23719,plain,
( spl0_2061
<=> ! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f23722,plain,
( ! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_plus(c_1,c_1,tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) )
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f23720,f19114]) ).
fof(f23720,plain,
( ! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) )
| ~ spl0_2061 ),
inference(avatar_component_clause,[],[f23719]) ).
fof(f23721,plain,
spl0_2061,
inference(avatar_split_clause,[],[f3116,f23719]) ).
fof(f3116,plain,
! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) ),
inference(forward_demodulation,[],[f3115,f1006]) ).
fof(f3115,plain,
! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) ),
inference(forward_demodulation,[],[f3114,f1004]) ).
fof(f3114,plain,
! [X17,X35] :
( c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) = c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X17)
| ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17) ),
inference(forward_demodulation,[],[f724,f1006]) ).
fof(f724,axiom,
! [X17,X35] :
( ~ class_Power_Orecpower(X17)
| ~ class_Numeral_Onumber(X17)
| c_Nat_Opower(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X17) = c_times(c_Numeral_Onumber__of(X35,X17),c_Numeral_Onumber__of(X35,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f23717,plain,
spl0_2060,
inference(avatar_split_clause,[],[f3054,f23715]) ).
fof(f23715,plain,
( spl0_2060
<=> ! [X9,X52,X25] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X25,tc_nat),X52,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X25,c_minus(X52,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f3054,plain,
! [X9,X52,X25] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X25,tc_nat),X52,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X25,c_minus(X52,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ),
inference(forward_demodulation,[],[f3053,f2801]) ).
fof(f2801,plain,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X38,tc_nat),tc_nat),X74,tc_nat),
inference(definition_unfolding,[],[f1390,f1394]) ).
fof(f1390,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_Suc(X38),X74,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3053,plain,
! [X9,X52,X25] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X52,X9,tc_nat),tc_nat),tc_nat),X25,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X25,tc_nat),X52,tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ),
inference(forward_demodulation,[],[f2872,f2801]) ).
fof(f2872,plain,
! [X9,X52,X25] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X52,X9,tc_nat),tc_nat),tc_nat),X25,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat),c_plus(X9,X25,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f648,f1394,f1394]) ).
fof(f648,axiom,
! [X9,X52,X25] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(c_Suc(c_minus(X52,X9,tc_nat)),X25,tc_nat) = c_minus(c_Suc(X52),c_plus(X9,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f23713,plain,
spl0_2059,
inference(avatar_split_clause,[],[f3052,f23711]) ).
fof(f23711,plain,
( spl0_2059
<=> ! [X25,X9,X52] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X52,c_plus(X25,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X52,X9,tc_nat),X25,tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f3052,plain,
! [X9,X52,X25] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X52,c_plus(X25,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X52,X9,tc_nat),X25,tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ),
inference(forward_demodulation,[],[f3051,f2800]) ).
fof(f2800,plain,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X74,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1397,f1394]) ).
fof(f1397,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_Suc(X74),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3051,plain,
! [X9,X52,X25] :
( c_minus(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X52,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X52,c_plus(X25,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X52,tc_nat) ),
inference(forward_demodulation,[],[f2871,f2800]) ).
fof(f2871,plain,
! [X9,X52,X25] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X52,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X25,X9,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f647,f1394,f1394]) ).
fof(f647,axiom,
! [X9,X52,X25] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(X25,c_Suc(c_minus(X52,X9,tc_nat)),tc_nat) = c_minus(c_plus(X25,X9,tc_nat),c_Suc(X52),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f23663,plain,
( spl0_2058
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2057 ),
inference(avatar_split_clause,[],[f23659,f23656,f10415,f10092,f6703,f3695,f23661]) ).
fof(f23661,plain,
( spl0_2058
<=> ! [X11,X27,X3] :
( c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_plus(c_1,c_Finite__Set_Ocard(X27,X3),tc_nat)
| c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f23656,plain,
( spl0_2057
<=> ! [X11,X27,X3] :
( c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X27,X3),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f23659,plain,
( ! [X3,X11,X27] :
( c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_plus(c_1,c_Finite__Set_Ocard(X27,X3),tc_nat)
| c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2057 ),
inference(forward_demodulation,[],[f23657,f11235]) ).
fof(f23657,plain,
( ! [X3,X11,X27] :
( c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X27,X3),tc_nat),tc_nat) )
| ~ spl0_2057 ),
inference(avatar_component_clause,[],[f23656]) ).
fof(f23658,plain,
spl0_2057,
inference(avatar_split_clause,[],[f2927,f23656]) ).
fof(f2927,plain,
! [X3,X11,X27] :
( c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X27,X3),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f130,f1394]) ).
fof(f130,axiom,
! [X3,X11,X27] :
( c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_Finite__Set_Ocard(c_insert(X11,X27,X3),X3) = c_Suc(c_Finite__Set_Ocard(X27,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f23654,plain,
( spl0_2056
| ~ spl0_1034
| ~ spl0_1620
| ~ spl0_1703 ),
inference(avatar_split_clause,[],[f17359,f16203,f15533,f8414,f23652]) ).
fof(f23652,plain,
( spl0_2056
<=> ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f16203,plain,
( spl0_1703
<=> ! [X3,X31,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X31,X3),c_insert(X15,X27,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f17359,plain,
( ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) )
| ~ spl0_1034
| ~ spl0_1620
| ~ spl0_1703 ),
inference(forward_demodulation,[],[f17352,f8415]) ).
fof(f17352,plain,
( ! [X2,X0,X1] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X2,X1),c_UNIV,X1,X1)
| ~ c_in(X0,X2,X1) )
| ~ spl0_1620
| ~ spl0_1703 ),
inference(superposition,[],[f16204,f15534]) ).
fof(f16204,plain,
( ! [X31,X3,X27,X15] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X31,X3),c_insert(X15,X27,X3),X3,X3)
| ~ c_in(X15,X31,X3) )
| ~ spl0_1703 ),
inference(avatar_component_clause,[],[f16203]) ).
fof(f23629,plain,
( spl0_2055
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2054 ),
inference(avatar_split_clause,[],[f23625,f23622,f10415,f10092,f6703,f3695,f23627]) ).
fof(f23627,plain,
( spl0_2055
<=> ! [X41,X10,X11,X3] : c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X3) = c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_plus(c_1,X10,tc_nat),tc_nat),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f23622,plain,
( spl0_2054
<=> ! [X41,X10,X11,X3] : c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),X3) = c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f23625,plain,
( ! [X41,X10,X3,X11] : c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X3) = c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_plus(c_1,X10,tc_nat),tc_nat),X3)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_2054 ),
inference(forward_demodulation,[],[f23623,f11235]) ).
fof(f23623,plain,
( ! [X41,X3,X10,X11] : c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),X3) = c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X3)
| ~ spl0_2054 ),
inference(avatar_component_clause,[],[f23622]) ).
fof(f23624,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2831,f23622]) ).
fof(f2831,plain,
! [X41,X3,X10,X11] : c_List_Osublist(c_List_Olist_OCons(X11,X41,X3),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),X3) = c_List_Olist_OCons(X11,c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X3),
inference(definition_unfolding,[],[f619,f616,f1394,f616]) ).
fof(f619,axiom,
! [X41,X10,X3,X11] : c_List_Otake(c_Suc(X10),c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Olist_OCons(X11,c_List_Otake(X10,X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f23620,plain,
spl0_2053,
inference(avatar_split_clause,[],[f1650,f23618]) ).
fof(f1650,axiom,
! [X3,X16,X27,X17,X20] :
( ~ c_in(X16,c_Relation_OImage(X20,X27,X17,X3),X3)
| c_in(c_Pair(c_Main_OImageE__1(X27,X16,X20,X17,X3),X16,X17,X3),X20,tc_prod(X17,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f23616,plain,
spl0_2052,
inference(avatar_split_clause,[],[f1592,f23614]) ).
fof(f23614,plain,
( spl0_2052
<=> ! [X17,X31,X27,X3,X26] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OuprodE__1(X27,X31,X26,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f1592,axiom,
! [X31,X3,X26,X27,X17] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OuprodE__1(X27,X31,X26,X3,X17),X27,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f23612,plain,
spl0_2051,
inference(avatar_split_clause,[],[f1591,f23610]) ).
fof(f23610,plain,
( spl0_2051
<=> ! [X17,X31,X27,X3,X26] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OuprodE__2(X27,X31,X26,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f1591,axiom,
! [X31,X3,X26,X27,X17] :
( ~ c_in(X26,c_Datatype__Universe_Ouprod(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Main_OuprodE__2(X27,X31,X26,X3,X17),X31,tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f23608,plain,
spl0_2050,
inference(avatar_split_clause,[],[f1235,f23606]) ).
fof(f23606,plain,
( spl0_2050
<=> ! [X17,X16,X20,X3,X15] :
( ~ c_in(c_Pair(X16,X15,X17,X3),X20,tc_prod(X17,X3))
| c_in(c_Pair(X15,X16,X3,X17),c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f1235,axiom,
! [X3,X16,X17,X15,X20] :
( ~ c_in(c_Pair(X16,X15,X17,X3),X20,tc_prod(X17,X3))
| c_in(c_Pair(X15,X16,X3,X17),c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f23604,plain,
spl0_2049,
inference(avatar_split_clause,[],[f1234,f23602]) ).
fof(f23602,plain,
( spl0_2049
<=> ! [X17,X16,X20,X3,X15] :
( c_in(c_Pair(X16,X15,X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(c_Pair(X15,X16,X3,X17),c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f1234,axiom,
! [X3,X16,X17,X15,X20] :
( c_in(c_Pair(X16,X15,X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(c_Pair(X15,X16,X3,X17),c_Relation_Oconverse(X20,X17,X3),tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f23600,plain,
spl0_2048,
inference(avatar_split_clause,[],[f1182,f23598]) ).
fof(f23598,plain,
( spl0_2048
<=> ! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f1182,axiom,
! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f23596,plain,
spl0_2047,
inference(avatar_split_clause,[],[f1172,f23594]) ).
fof(f23594,plain,
( spl0_2047
<=> ! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f1172,axiom,
! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f23592,plain,
( spl0_2046
| ~ spl0_1043
| ~ spl0_1521 ),
inference(avatar_split_clause,[],[f13991,f13127,f8497,f23590]) ).
fof(f23590,plain,
( spl0_2046
<=> ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f8497,plain,
( spl0_1043
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f13991,plain,
( ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat))
| ~ spl0_1043
| ~ spl0_1521 ),
inference(resolution,[],[f13128,f8498]) ).
fof(f8498,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1043 ),
inference(avatar_component_clause,[],[f8497]) ).
fof(f23588,plain,
spl0_2045,
inference(avatar_split_clause,[],[f727,f23586]) ).
fof(f23586,plain,
( spl0_2045
<=> ! [X36,X35] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X35,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f727,axiom,
! [X36,X35] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X35,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f23584,plain,
spl0_2044,
inference(avatar_split_clause,[],[f678,f23582]) ).
fof(f23582,plain,
( spl0_2044
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f678,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f23580,plain,
spl0_2043,
inference(avatar_split_clause,[],[f123,f23578]) ).
fof(f23578,plain,
( spl0_2043
<=> ! [X11,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Finite__Set_OMin(c_insert(X11,X27,X17),X17) = c_Orderings_Omin(X11,c_Finite__Set_OMin(X27,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f123,axiom,
! [X11,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Finite__Set_OMin(c_insert(X11,X27,X17),X17) = c_Orderings_Omin(X11,c_Finite__Set_OMin(X27,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f23576,plain,
spl0_2042,
inference(avatar_split_clause,[],[f121,f23574]) ).
fof(f23574,plain,
( spl0_2042
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(X11,c_Finite__Set_OMin(X27,X3),X3)
| ~ c_less(X11,c_Main_OMin__gr__iff__1(X27,X11,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f121,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(X11,c_Finite__Set_OMin(X27,X3),X3)
| ~ c_less(X11,c_Main_OMin__gr__iff__1(X27,X11,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f23572,plain,
spl0_2041,
inference(avatar_split_clause,[],[f120,f23570]) ).
fof(f23570,plain,
( spl0_2041
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(X11,c_Finite__Set_OMin(X27,X3),X3)
| c_in(c_Main_OMin__gr__iff__1(X27,X11,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f120,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(X11,c_Finite__Set_OMin(X27,X3),X3)
| c_in(c_Main_OMin__gr__iff__1(X27,X11,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f23568,plain,
spl0_2040,
inference(avatar_split_clause,[],[f118,f23566]) ).
fof(f23566,plain,
( spl0_2040
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3)
| ~ c_lessequals(X11,c_Main_OMin__ge__iff__1(X27,X11,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f118,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3)
| ~ c_lessequals(X11,c_Main_OMin__ge__iff__1(X27,X11,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f23564,plain,
spl0_2039,
inference(avatar_split_clause,[],[f117,f23562]) ).
fof(f23562,plain,
( spl0_2039
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3)
| c_in(c_Main_OMin__ge__iff__1(X27,X11,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f117,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMin(X27,X3),X3)
| c_in(c_Main_OMin__ge__iff__1(X27,X11,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f23560,plain,
spl0_2038,
inference(avatar_split_clause,[],[f114,f23558]) ).
fof(f23558,plain,
( spl0_2038
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(c_Finite__Set_OMax(X27,X3),X11,X3)
| ~ c_less(c_Main_OMax__less__iff__1(X27,X11,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f114,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(c_Finite__Set_OMax(X27,X3),X11,X3)
| ~ c_less(c_Main_OMax__less__iff__1(X27,X11,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f23556,plain,
spl0_2037,
inference(avatar_split_clause,[],[f113,f23554]) ).
fof(f23554,plain,
( spl0_2037
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(c_Finite__Set_OMax(X27,X3),X11,X3)
| c_in(c_Main_OMax__less__iff__1(X27,X11,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f113,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_less(c_Finite__Set_OMax(X27,X3),X11,X3)
| c_in(c_Main_OMax__less__iff__1(X27,X11,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f23552,plain,
spl0_2036,
inference(avatar_split_clause,[],[f111,f23550]) ).
fof(f23550,plain,
( spl0_2036
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X27,X11,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f111,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X27,X11,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f23545,plain,
spl0_2035,
inference(avatar_split_clause,[],[f110,f23543]) ).
fof(f23543,plain,
( spl0_2035
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3)
| c_in(c_Main_OMax__le__iff__1(X27,X11,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f110,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMax(X27,X3),X11,X3)
| c_in(c_Main_OMax__le__iff__1(X27,X11,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f23541,plain,
spl0_2034,
inference(avatar_split_clause,[],[f108,f23539]) ).
fof(f23539,plain,
( spl0_2034
<=> ! [X11,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Finite__Set_OMax(c_insert(X11,X27,X17),X17) = c_Orderings_Omax(X11,c_Finite__Set_OMax(X27,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f108,axiom,
! [X11,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Finite__Set_OMax(c_insert(X11,X27,X17),X17) = c_Orderings_Omax(X11,c_Finite__Set_OMax(X27,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f23262,plain,
( spl0_2033
| ~ spl0_41
| ~ spl0_728
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9814,f9432,f6980,f3361,f23259]) ).
fof(f23259,plain,
( spl0_2033
<=> c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f6980,plain,
( spl0_728
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f9814,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint)
| ~ spl0_728
| ~ spl0_1188 ),
inference(resolution,[],[f9433,f6982]) ).
fof(f6982,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_728 ),
inference(avatar_component_clause,[],[f6980]) ).
fof(f22862,plain,
( spl0_2032
| ~ spl0_41
| ~ spl0_728
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f9763,f9416,f6980,f3361,f22859]) ).
fof(f22859,plain,
( spl0_2032
<=> c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f9763,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint)
| ~ spl0_728
| ~ spl0_1184 ),
inference(resolution,[],[f9417,f6982]) ).
fof(f22826,plain,
spl0_2031,
inference(avatar_split_clause,[],[f2936,f22824]) ).
fof(f22824,plain,
( spl0_2031
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f2936,plain,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f706,f979]) ).
fof(f706,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f22822,plain,
spl0_2030,
inference(avatar_split_clause,[],[f2935,f22820]) ).
fof(f22820,plain,
( spl0_2030
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f2935,plain,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f707,f979]) ).
fof(f707,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X77)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f22818,plain,
spl0_2029,
inference(avatar_split_clause,[],[f2908,f22816]) ).
fof(f22816,plain,
( spl0_2029
<=> ! [X25,X24,X10] :
( ~ c_lessequals(c_plus(X24,X25,tc_nat),X10,tc_nat)
| c_List_Oupt(X24,c_plus(X24,X25,tc_nat)) = c_List_Osublist(c_List_Oupt(X24,X10),c_SetInterval_OlessThan(X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f2908,plain,
! [X10,X24,X25] :
( ~ c_lessequals(c_plus(X24,X25,tc_nat),X10,tc_nat)
| c_List_Oupt(X24,c_plus(X24,X25,tc_nat)) = c_List_Osublist(c_List_Oupt(X24,X10),c_SetInterval_OlessThan(X25,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f627,f616]) ).
fof(f627,axiom,
! [X10,X24,X25] :
( ~ c_lessequals(c_plus(X24,X25,tc_nat),X10,tc_nat)
| c_List_Otake(X25,c_List_Oupt(X24,X10),tc_nat) = c_List_Oupt(X24,c_plus(X24,X25,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f22814,plain,
spl0_2028,
inference(avatar_split_clause,[],[f2798,f22812]) ).
fof(f22812,plain,
( spl0_2028
<=> ! [X3,X79] : c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Transitive__Closure_Otrancl(c_union(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),c_Relation_OId,tc_prod(X3,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f2798,plain,
! [X3,X79] : c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3) = c_Transitive__Closure_Otrancl(c_union(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),c_Relation_OId,tc_prod(X3,X3)),X3),
inference(definition_unfolding,[],[f1562,f1566,f1566]) ).
fof(f1562,axiom,
! [X3,X79] : c_Transitive__Closure_Ortrancl(X79,X3) = c_Transitive__Closure_Ortrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f22810,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1698,f22808]) ).
fof(f22808,plain,
( spl0_2027
<=> ! [X15,X20,X16,X3] :
( ~ c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X15,X16,X3,X3),c_Transitive__Closure_Otrancl(X20,X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1698,axiom,
! [X3,X16,X15,X20] :
( ~ c_in(c_Pair(X15,X16,X3,X3),X20,tc_prod(X3,X3))
| c_in(c_Pair(X15,X16,X3,X3),c_Transitive__Closure_Otrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f22806,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1651,f22804]) ).
fof(f22804,plain,
( spl0_2026
<=> ! [X15,X17,X16,X20,X27,X3] :
( ~ c_in(X15,X27,X3)
| c_in(X16,c_Relation_OImage(X20,X27,X3,X17),X17)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1651,axiom,
! [X3,X16,X27,X17,X15,X20] :
( ~ c_in(X15,X27,X3)
| c_in(X16,c_Relation_OImage(X20,X27,X3,X17),X17)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f22802,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1412,f22800]) ).
fof(f22800,plain,
( spl0_2025
<=> ! [X24,X10,X3,X25] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X10,X3)
| c_minus(c_SetInterval_OatLeastLessThan(X24,X25,X3),c_SetInterval_OatLeastLessThan(X24,X10,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X10,X25,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f1412,axiom,
! [X3,X10,X24,X25] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X24,X10,X3)
| c_minus(c_SetInterval_OatLeastLessThan(X24,X25,X3),c_SetInterval_OatLeastLessThan(X24,X10,X3),tc_set(X3)) = c_SetInterval_OatLeastLessThan(X10,X25,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f22798,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1206,f22796]) ).
fof(f22796,plain,
( spl0_2024
<=> ! [X3,X11,X16,X8] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(X11,X8,tc_nat)
| ~ c_less(c_1,X16,X3)
| c_less(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1206,axiom,
! [X3,X11,X8,X16] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(X11,X8,tc_nat)
| ~ c_less(c_1,X16,X3)
| c_less(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f22794,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1205,f22792]) ).
fof(f22792,plain,
( spl0_2023
<=> ! [X3,X11,X16,X8] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,X16,X3)
| c_less(X11,X8,tc_nat)
| ~ c_less(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1205,axiom,
! [X3,X11,X8,X16] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,X16,X3)
| c_less(X11,X8,tc_nat)
| ~ c_less(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f22790,plain,
( spl0_2022
| ~ spl0_871
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8518,f8179,f7612,f22788]) ).
fof(f22788,plain,
( spl0_2022
<=> ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f7612,plain,
( spl0_871
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f8518,plain,
( ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_871
| ~ spl0_976 ),
inference(superposition,[],[f8180,f7614]) ).
fof(f7614,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_871 ),
inference(avatar_component_clause,[],[f7612]) ).
fof(f22786,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1201,f22784]) ).
fof(f22784,plain,
( spl0_2021
<=> ! [X3,X11,X16,X8] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X11,X8,tc_nat)
| ~ c_less(c_1,X16,X3)
| c_lessequals(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f1201,axiom,
! [X3,X11,X8,X16] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X11,X8,tc_nat)
| ~ c_less(c_1,X16,X3)
| c_lessequals(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f22782,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1200,f22780]) ).
fof(f22780,plain,
( spl0_2020
<=> ! [X3,X11,X16,X8] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,X16,X3)
| c_lessequals(X11,X8,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1200,axiom,
! [X3,X11,X8,X16] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,X16,X3)
| c_lessequals(X11,X8,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X16,X11,X3),c_Nat_Opower(X16,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f22778,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1186,f22776]) ).
fof(f22776,plain,
( spl0_2019
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1186,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f22774,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1183,f22772]) ).
fof(f22772,plain,
( spl0_2018
<=> ! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_0,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1183,axiom,
! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_0,X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f22770,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1180,f22768]) ).
fof(f22768,plain,
( spl0_2017
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1180,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f22766,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1178,f22764]) ).
fof(f22764,plain,
( spl0_2016
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f1178,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X11,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f22762,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1175,f22760]) ).
fof(f22760,plain,
( spl0_2015
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X11,c_0,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f1175,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X11,c_0,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f22758,plain,
spl0_2014,
inference(avatar_split_clause,[],[f1169,f22756]) ).
fof(f22756,plain,
( spl0_2014
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X11,c_0,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f1169,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X11,c_0,X3)
| c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f22754,plain,
spl0_2013,
inference(avatar_split_clause,[],[f1018,f22752]) ).
fof(f22752,plain,
( spl0_2013
<=> ! [X37,X36,X35,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(X36,X3),c_times(c_Numeral_Onumber__of(X35,X3),X37,X3),X3) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X35),X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f1018,axiom,
! [X3,X36,X37,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(X36,X3),c_times(c_Numeral_Onumber__of(X35,X3),X37,X3),X3) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X35),X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f22750,plain,
spl0_2012,
inference(avatar_split_clause,[],[f958,f22748]) ).
fof(f22748,plain,
( spl0_2012
<=> ! [X37,X36,X35,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_plus(c_Numeral_Onumber__of(X35,X3),X37,X3),X3) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X35),X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f958,axiom,
! [X3,X36,X37,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_plus(c_Numeral_Onumber__of(X35,X3),X37,X3),X3) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X35),X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f22746,plain,
spl0_2011,
inference(avatar_split_clause,[],[f711,f22744]) ).
fof(f22744,plain,
( spl0_2011
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f711,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f22742,plain,
spl0_2010,
inference(avatar_split_clause,[],[f685,f22740]) ).
fof(f22740,plain,
( spl0_2010
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) != c_Numeral_Onumber__of(X77,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f685,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) != c_Numeral_Onumber__of(X77,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f22738,plain,
spl0_2009,
inference(avatar_split_clause,[],[f675,f22736]) ).
fof(f22736,plain,
( spl0_2009
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f675,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f22734,plain,
spl0_2008,
inference(avatar_split_clause,[],[f485,f22732]) ).
fof(f22732,plain,
( spl0_2008
<=> ! [X41,X11,X3,X8,X24] :
( ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X41,X24,X11,X3),X24,X8,X3) = c_List_Olist__update(X41,X24,X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f485,axiom,
! [X41,X3,X11,X8,X24] :
( ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X41,X24,X11,X3),X24,X8,X3) = c_List_Olist__update(X41,X24,X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f22730,plain,
spl0_2007,
inference(avatar_split_clause,[],[f484,f22728]) ).
fof(f22728,plain,
( spl0_2007
<=> ! [X41,X42,X11,X3,X8] : c_List_Olist__update(c_append(X41,c_List_Olist_OCons(X11,X42,X3),X3),c_Nat_Osize(X41,tc_List_Olist(X3)),X8,X3) = c_append(X41,c_List_Olist_OCons(X8,X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f484,axiom,
! [X41,X3,X11,X8,X42] : c_List_Olist__update(c_append(X41,c_List_Olist_OCons(X11,X42,X3),X3),c_Nat_Osize(X41,tc_List_Olist(X3)),X8,X3) = c_append(X41,c_List_Olist_OCons(X8,X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f22726,plain,
spl0_2006,
inference(avatar_split_clause,[],[f205,f22724]) ).
fof(f22724,plain,
( spl0_2006
<=> ! [X11,X8] :
( X8 = X11
| c_IntDef_OAbs__Integ(X11) != c_IntDef_OAbs__Integ(X8)
| ~ c_in(X11,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f205,axiom,
! [X11,X8] :
( X8 = X11
| c_IntDef_OAbs__Integ(X11) != c_IntDef_OAbs__Integ(X8)
| ~ c_in(X11,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f22722,plain,
spl0_2005,
inference(avatar_split_clause,[],[f144,f22720]) ).
fof(f22720,plain,
( spl0_2005
<=> ! [X27,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X8,X27,X17)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Orderings_Omax(X8,c_Finite__Set_OMin(X27,X17),X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f144,axiom,
! [X8,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X8,X27,X17)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Orderings_Omax(X8,c_Finite__Set_OMin(X27,X17),X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f22718,plain,
spl0_2004,
inference(avatar_split_clause,[],[f143,f22716]) ).
fof(f22716,plain,
( spl0_2004
<=> ! [X27,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X8,X27,X17)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Orderings_Omin(X8,c_Finite__Set_OMax(X27,X17),X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f143,axiom,
! [X8,X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X8,X27,X17)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_Orderings_Omin(X8,c_Finite__Set_OMax(X27,X17),X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f22714,plain,
spl0_2003,
inference(avatar_split_clause,[],[f72,f22712]) ).
fof(f22712,plain,
( spl0_2003
<=> ! [X9,X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_plus(X9,c_div(X25,X10,tc_nat),tc_nat) = c_div(c_plus(X25,c_times(X10,X9,tc_nat),tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f72,axiom,
! [X10,X9,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_plus(X9,c_div(X25,X10,tc_nat),tc_nat) = c_div(c_plus(X25,c_times(X10,X9,tc_nat),tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f22710,plain,
spl0_2002,
inference(avatar_split_clause,[],[f70,f22708]) ).
fof(f22708,plain,
( spl0_2002
<=> ! [X25,X9,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_plus(X25,c_times(X9,X10,tc_nat),tc_nat),X10,tc_nat) = c_plus(X9,c_div(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f70,axiom,
! [X10,X9,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_plus(X25,c_times(X9,X10,tc_nat),tc_nat),X10,tc_nat) = c_plus(X9,c_div(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f22706,plain,
( spl0_95
| ~ spl0_2001
| ~ spl0_870
| ~ spl0_967 ),
inference(avatar_split_clause,[],[f8469,f8142,f7601,f22703,f3631]) ).
fof(f22703,plain,
( spl0_2001
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f7601,plain,
( spl0_870
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f8469,plain,
( ~ c_less(c_1,c_1,tc_IntDef_Oint)
| c_0 = c_1
| ~ spl0_870
| ~ spl0_967 ),
inference(superposition,[],[f8143,f7603]) ).
fof(f7603,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7601]) ).
fof(f22089,plain,
( spl0_2000
| ~ spl0_124
| ~ spl0_1778 ),
inference(avatar_split_clause,[],[f18582,f17651,f3760,f22087]) ).
fof(f22087,plain,
( spl0_2000
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f17651,plain,
( spl0_1778
<=> ! [X15,X17,X20,X16,X3] :
( c_in(X16,c_Relation_ORange(X20,X3,X17),X17)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f18582,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_124
| ~ spl0_1778 ),
inference(resolution,[],[f17652,f3761]) ).
fof(f17652,plain,
( ! [X3,X16,X17,X15,X20] :
( ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17))
| c_in(X16,c_Relation_ORange(X20,X3,X17),X17) )
| ~ spl0_1778 ),
inference(avatar_component_clause,[],[f17651]) ).
fof(f22085,plain,
( spl0_1999
| ~ spl0_124
| ~ spl0_1775 ),
inference(avatar_split_clause,[],[f18525,f17639,f3760,f22083]) ).
fof(f22083,plain,
( spl0_1999
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f17639,plain,
( spl0_1775
<=> ! [X17,X16,X20,X3,X15] :
( c_in(X15,c_Relation_ODomain(X20,X3,X17),X3)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f18525,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_124
| ~ spl0_1775 ),
inference(resolution,[],[f17640,f3761]) ).
fof(f17640,plain,
( ! [X3,X16,X17,X15,X20] :
( ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17))
| c_in(X15,c_Relation_ODomain(X20,X3,X17),X3) )
| ~ spl0_1775 ),
inference(avatar_component_clause,[],[f17639]) ).
fof(f21816,plain,
( spl0_1998
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_1997 ),
inference(avatar_split_clause,[],[f21812,f21808,f19031,f7164,f7128,f21814]) ).
fof(f21814,plain,
( spl0_1998
<=> ! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f21808,plain,
( spl0_1997
<=> ! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,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(X25,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_1997])]) ).
fof(f21812,plain,
( ! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_1997 ),
inference(forward_demodulation,[],[f21811,f19114]) ).
fof(f21811,plain,
( ! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X25,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_764
| ~ spl0_773
| ~ spl0_1859
| ~ spl0_1997 ),
inference(forward_demodulation,[],[f21809,f19114]) ).
fof(f21809,plain,
( ! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,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(X25,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1997 ),
inference(avatar_component_clause,[],[f21808]) ).
fof(f21810,plain,
spl0_1997,
inference(avatar_split_clause,[],[f3102,f21808]) ).
fof(f3102,plain,
! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,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(X25,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3101,f1006]) ).
fof(f3101,plain,
! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,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(X25,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3100,f1004]) ).
fof(f3100,plain,
! [X25] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X25,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(X25,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3099,f1006]) ).
fof(f3099,plain,
! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,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(X25,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,[],[f3098,f1006]) ).
fof(f3098,plain,
! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,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(X25,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,[],[f3097,f1004]) ).
fof(f3097,plain,
! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,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(X25,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,[],[f825,f1006]) ).
fof(f825,axiom,
! [X25] :
( c_1 = c_Divides_Oop_Amod(X25,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(X25,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/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).
fof(f21783,plain,
( spl0_1996
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1995 ),
inference(avatar_split_clause,[],[f21779,f21776,f10415,f10092,f6703,f3695,f21781]) ).
fof(f21781,plain,
( spl0_1996
<=> ! [X9,X25,X10] : c_minus(X25,c_plus(X10,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f21776,plain,
( spl0_1995
<=> ! [X9,X25,X10] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X25,c_plus(X10,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f21779,plain,
( ! [X10,X9,X25] : c_minus(X25,c_plus(X10,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1995 ),
inference(forward_demodulation,[],[f21777,f11235]) ).
fof(f21777,plain,
( ! [X10,X9,X25] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X25,c_plus(X10,X9,tc_nat),tc_nat)
| ~ spl0_1995 ),
inference(avatar_component_clause,[],[f21776]) ).
fof(f21778,plain,
spl0_1995,
inference(avatar_split_clause,[],[f3008,f21776]) ).
fof(f3008,plain,
! [X10,X9,X25] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X25,c_plus(X10,X9,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3007,f887]) ).
fof(f887,axiom,
! [X9,X52,X24] : c_minus(c_minus(X24,X52,tc_nat),X9,tc_nat) = c_minus(X24,c_plus(X52,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3007,plain,
! [X10,X9,X25] : c_minus(c_minus(X25,X10,tc_nat),X9,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X10,X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2832,f2801]) ).
fof(f2832,plain,
! [X10,X9,X25] : c_minus(c_minus(X25,X10,tc_nat),X9,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f868,f1394,f1394]) ).
fof(f868,axiom,
! [X10,X9,X25] : c_minus(c_minus(c_Suc(X25),X10,tc_nat),c_Suc(X9),tc_nat) = c_minus(c_minus(X25,X10,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f21774,plain,
spl0_1994,
inference(avatar_split_clause,[],[f2957,f21772]) ).
fof(f21772,plain,
( spl0_1994
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f2957,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
inference(definition_unfolding,[],[f990,f979]) ).
fof(f990,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(X11)),X3),X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f21770,plain,
spl0_1993,
inference(avatar_split_clause,[],[f2956,f21768]) ).
fof(f21768,plain,
( spl0_1993
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f2956,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f998,f979]) ).
fof(f998,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f21766,plain,
spl0_1992,
inference(avatar_split_clause,[],[f2955,f21764]) ).
fof(f21764,plain,
( spl0_1992
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f2955,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
inference(definition_unfolding,[],[f999,f979]) ).
fof(f999,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(X8)),X3),X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f21762,plain,
spl0_1991,
inference(avatar_split_clause,[],[f2954,f21760]) ).
fof(f21760,plain,
( spl0_1991
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f2954,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
inference(definition_unfolding,[],[f989,f979]) ).
fof(f989,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(X11)),X3),X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_Numeral_Onumber__of(X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f21758,plain,
spl0_1990,
inference(avatar_split_clause,[],[f2934,f21756]) ).
fof(f21756,plain,
( spl0_1990
<=> ! [X31,X27,X80,X3] :
( ~ c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,X27,tc_set(X3))
| c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f2934,plain,
! [X31,X3,X80,X27] :
( ~ c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,X27,tc_set(X3))
| c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ),
inference(definition_unfolding,[],[f1461,f1223]) ).
fof(f1461,axiom,
! [X31,X3,X80,X27] :
( ~ c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,X27,tc_set(X3))
| c_lessequals(X80,c_inter(X27,X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f21754,plain,
spl0_1989,
inference(avatar_split_clause,[],[f2905,f21752]) ).
fof(f21752,plain,
( spl0_1989
<=> ! [X15,X27,X3,X31] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f2905,plain,
! [X31,X3,X27,X15] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1528,f1223,f1223]) ).
fof(f1528,axiom,
! [X31,X3,X27,X15] :
( c_emptyset = c_inter(X27,X31,X3)
| c_emptyset != c_inter(c_insert(X15,X27,X3),X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
fof(f21750,plain,
spl0_1988,
inference(avatar_split_clause,[],[f2903,f21748]) ).
fof(f21748,plain,
( spl0_1988
<=> ! [X31,X16,X27,X3] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X27,X3),c_insert(X16,X31,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f2903,plain,
! [X31,X3,X16,X27] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X27,X3),c_insert(X16,X31,X3),X3,X3) ),
inference(definition_unfolding,[],[f1515,f1223,f1223]) ).
fof(f1515,axiom,
! [X31,X3,X16,X27] :
( c_emptyset = c_inter(X27,X31,X3)
| c_emptyset != c_inter(X27,c_insert(X16,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
fof(f21685,plain,
( spl0_1987
| ~ spl0_109
| ~ spl0_667
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1694
| ~ spl0_1986 ),
inference(avatar_split_clause,[],[f21681,f21677,f16113,f10415,f10092,f7128,f7108,f6703,f3695,f21683]) ).
fof(f21683,plain,
( spl0_1987
<=> ! [X52,X24] :
( c_List_Oupt(X24,c_plus(c_1,X52,tc_nat)) = c_append(c_List_Oupt(X24,X52),c_List_Oreplicate(c_1,X52,tc_nat),tc_nat)
| ~ c_lessequals(X24,X52,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f21677,plain,
( spl0_1986
<=> ! [X52,X24] :
( ~ c_lessequals(X24,X52,tc_nat)
| c_append(c_List_Oupt(X24,X52),c_List_Olist_OCons(X52,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f21681,plain,
( ! [X52,X24] :
( c_List_Oupt(X24,c_plus(c_1,X52,tc_nat)) = c_append(c_List_Oupt(X24,X52),c_List_Oreplicate(c_1,X52,tc_nat),tc_nat)
| ~ c_lessequals(X24,X52,tc_nat) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1694
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f21680,f16139]) ).
fof(f21680,plain,
( ! [X52,X24] :
( c_append(c_List_Oupt(X24,X52),c_List_Olist_OCons(X52,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X24,c_plus(c_1,X52,tc_nat))
| ~ c_lessequals(X24,X52,tc_nat) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f21678,f11235]) ).
fof(f21678,plain,
( ! [X52,X24] :
( ~ c_lessequals(X24,X52,tc_nat)
| c_append(c_List_Oupt(X24,X52),c_List_Olist_OCons(X52,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) )
| ~ spl0_1986 ),
inference(avatar_component_clause,[],[f21677]) ).
fof(f21679,plain,
spl0_1986,
inference(avatar_split_clause,[],[f2870,f21677]) ).
fof(f2870,plain,
! [X52,X24] :
( ~ c_lessequals(X24,X52,tc_nat)
| c_append(c_List_Oupt(X24,X52),c_List_Olist_OCons(X52,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f632,f1394]) ).
fof(f632,axiom,
! [X52,X24] :
( ~ c_lessequals(X24,X52,tc_nat)
| c_List_Oupt(X24,c_Suc(X52)) = c_append(c_List_Oupt(X24,X52),c_List_Olist_OCons(X52,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f21675,plain,
spl0_1985,
inference(avatar_split_clause,[],[f2834,f21673]) ).
fof(f21673,plain,
( spl0_1985
<=> ! [X27,X3,X31] : c_union(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),X3) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f2834,plain,
! [X31,X3,X27] : c_union(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),X3) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)),
inference(definition_unfolding,[],[f1425,f1223]) ).
fof(f1425,axiom,
! [X31,X3,X27] : c_uminus(c_inter(X27,X31,X3),tc_set(X3)) = c_union(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f21671,plain,
spl0_1984,
inference(avatar_split_clause,[],[f2833,f21669]) ).
fof(f21669,plain,
( spl0_1984
<=> ! [X27,X3,X31] : c_uminus(c_union(X27,X31,X3),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),c_uminus(X31,tc_set(X3)),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f2833,plain,
! [X31,X3,X27] : c_uminus(c_union(X27,X31,X3),tc_set(X3)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),c_uminus(X31,tc_set(X3)),X3,X3),
inference(definition_unfolding,[],[f1427,f1223]) ).
fof(f1427,axiom,
! [X31,X3,X27] : c_uminus(c_union(X27,X31,X3),tc_set(X3)) = c_inter(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f21667,plain,
spl0_1983,
inference(avatar_split_clause,[],[f2827,f21665]) ).
fof(f21665,plain,
( spl0_1983
<=> ! [X41,X10,X3,X25] : c_List_Osublist(c_List_Osublist(X41,c_SetInterval_OlessThan(X25,tc_nat),X3),c_SetInterval_OlessThan(X10,tc_nat),X3) = c_List_Osublist(X41,c_SetInterval_OlessThan(c_Orderings_Omin(X10,X25,tc_nat),tc_nat),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f2827,plain,
! [X41,X3,X10,X25] : c_List_Osublist(c_List_Osublist(X41,c_SetInterval_OlessThan(X25,tc_nat),X3),c_SetInterval_OlessThan(X10,tc_nat),X3) = c_List_Osublist(X41,c_SetInterval_OlessThan(c_Orderings_Omin(X10,X25,tc_nat),tc_nat),X3),
inference(definition_unfolding,[],[f626,f616,f616,f616]) ).
fof(f626,axiom,
! [X41,X10,X3,X25] : c_List_Otake(X10,c_List_Otake(X25,X41,X3),X3) = c_List_Otake(c_Orderings_Omin(X10,X25,tc_nat),X41,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f21644,plain,
( spl0_1982
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21640,f21635,f10415,f10092,f6703,f3695,f21642]) ).
fof(f21635,plain,
( spl0_1981
<=> ! [X25,X10] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X25,X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f21640,plain,
( ! [X10,X25] : c_plus(c_1,c_Orderings_Omin(X25,X10,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21639,f11235]) ).
fof(f21639,plain,
( ! [X10,X25] : c_plus(c_1,c_Orderings_Omin(X25,X10,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21638,f11235]) ).
fof(f21638,plain,
( ! [X10,X25] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X25,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21636,f11235]) ).
fof(f21636,plain,
( ! [X10,X25] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X25,X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1981 ),
inference(avatar_component_clause,[],[f21635]) ).
fof(f21637,plain,
spl0_1981,
inference(avatar_split_clause,[],[f2803,f21635]) ).
fof(f2803,plain,
! [X10,X25] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X25,X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f905,f1394,f1394,f1394]) ).
fof(f905,axiom,
! [X10,X25] : c_Orderings_Omin(c_Suc(X25),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Omin(X25,X10,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f21614,plain,
( spl0_1980
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1979 ),
inference(avatar_split_clause,[],[f21610,f21605,f10415,f10092,f6703,f3695,f21612]) ).
fof(f21612,plain,
( spl0_1980
<=> ! [X25,X10] : c_plus(c_1,c_Orderings_Omax(X25,X10,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f21605,plain,
( spl0_1979
<=> ! [X25,X10] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X25,X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f21610,plain,
( ! [X10,X25] : c_plus(c_1,c_Orderings_Omax(X25,X10,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21609,f11235]) ).
fof(f21609,plain,
( ! [X10,X25] : c_plus(c_1,c_Orderings_Omax(X25,X10,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21608,f11235]) ).
fof(f21608,plain,
( ! [X10,X25] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X25,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21606,f11235]) ).
fof(f21606,plain,
( ! [X10,X25] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X25,X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1979 ),
inference(avatar_component_clause,[],[f21605]) ).
fof(f21607,plain,
spl0_1979,
inference(avatar_split_clause,[],[f2802,f21605]) ).
fof(f2802,plain,
! [X10,X25] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X25,X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f902,f1394,f1394,f1394]) ).
fof(f902,axiom,
! [X10,X25] : c_Orderings_Omax(c_Suc(X25),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Omax(X25,X10,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f21603,plain,
spl0_1978,
inference(avatar_split_clause,[],[f1656,f21601]) ).
fof(f21601,plain,
( spl0_1978
<=> ! [X27,X3,X26] :
( ~ c_in(X26,c_Relation_Odiag(X27,X3),tc_prod(X3,X3))
| c_Pair(c_Main_OdiagE__1(X27,X26,X3),c_Main_OdiagE__1(X27,X26,X3),X3,X3) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f1656,axiom,
! [X3,X26,X27] :
( ~ c_in(X26,c_Relation_Odiag(X27,X3),tc_prod(X3,X3))
| c_Pair(c_Main_OdiagE__1(X27,X26,X3),c_Main_OdiagE__1(X27,X26,X3),X3,X3) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f21599,plain,
spl0_1977,
inference(avatar_split_clause,[],[f1652,f21597]) ).
fof(f21597,plain,
( spl0_1977
<=> ! [X17,X20,X16,X3] :
( ~ c_in(X16,c_Relation_ORange(X20,X17,X3),X3)
| c_in(c_Pair(c_Main_ORangeE__1(X16,X20,X3,X17),X16,X17,X3),X20,tc_prod(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f1652,axiom,
! [X3,X16,X17,X20] :
( ~ c_in(X16,c_Relation_ORange(X20,X17,X3),X3)
| c_in(c_Pair(c_Main_ORangeE__1(X16,X20,X3,X17),X16,X17,X3),X20,tc_prod(X17,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f21595,plain,
spl0_1976,
inference(avatar_split_clause,[],[f1646,f21593]) ).
fof(f21593,plain,
( spl0_1976
<=> ! [X17,X20,X3,X15] :
( ~ c_in(X15,c_Relation_ODomain(X20,X3,X17),X3)
| c_in(c_Pair(X15,c_Main_ODomainE__1(X15,X20,X3,X17),X3,X17),X20,tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f1646,axiom,
! [X3,X17,X15,X20] :
( ~ c_in(X15,c_Relation_ODomain(X20,X3,X17),X3)
| c_in(c_Pair(X15,c_Main_ODomainE__1(X15,X20,X3,X17),X3,X17),X20,tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f21591,plain,
spl0_1975,
inference(avatar_split_clause,[],[f1637,f21589]) ).
fof(f21589,plain,
( spl0_1975
<=> ! [X15,X27,X74,X3] :
( ~ c_in(X15,X27,X3)
| ~ c_in(X74,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_List_Olist_OCons(X15,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f1637,axiom,
! [X3,X27,X15,X74] :
( ~ c_in(X15,X27,X3)
| ~ c_in(X74,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_List_Olist_OCons(X15,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f21587,plain,
spl0_1974,
inference(avatar_split_clause,[],[f1599,f21585]) ).
fof(f21585,plain,
( spl0_1974
<=> ! [X17,X31,X3,X27,X19] :
( ~ c_in(X19,X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OIn1(X19,X3,X17),c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f1599,axiom,
! [X31,X3,X19,X27,X17] :
( ~ c_in(X19,X31,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OIn1(X19,X3,X17),c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f21583,plain,
spl0_1973,
inference(avatar_split_clause,[],[f1598,f21581]) ).
fof(f21581,plain,
( spl0_1973
<=> ! [X18,X17,X31,X27,X3] :
( ~ c_in(X18,X27,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OIn0(X18,X3,X17),c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f1598,axiom,
! [X31,X3,X18,X27,X17] :
( ~ c_in(X18,X27,tc_set(tc_Datatype__Universe_Onode(X3,X17)))
| c_in(c_Datatype__Universe_OIn0(X18,X3,X17),c_Datatype__Universe_Ousum(X27,X31,X3,X17),tc_set(tc_Datatype__Universe_Onode(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f21579,plain,
spl0_1972,
inference(avatar_split_clause,[],[f1416,f21577]) ).
fof(f21577,plain,
( spl0_1972
<=> ! [X24,X10,X3,X25,X52] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X25,X24,X3)
| ~ c_lessequals(X52,X10,X3)
| c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f1416,axiom,
! [X3,X10,X52,X24,X25] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X25,X24,X3)
| ~ c_lessequals(X52,X10,X3)
| c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f21575,plain,
spl0_1971,
inference(avatar_split_clause,[],[f1414,f21573]) ).
fof(f21573,plain,
( spl0_1971
<=> ! [X24,X10,X3,X25,X52] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X52,X24,X3)
| c_lessequals(X52,X10,X3)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f1414,axiom,
! [X3,X10,X52,X24,X25] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X52,X24,X3)
| c_lessequals(X52,X10,X3)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f21571,plain,
( spl0_1970
| ~ spl0_110
| ~ spl0_1783 ),
inference(avatar_split_clause,[],[f21479,f17695,f3700,f21568]) ).
fof(f21568,plain,
( spl0_1970
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f17695,plain,
( spl0_1783
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f21479,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1783 ),
inference(superposition,[],[f17696,f3702]) ).
fof(f17696,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1783 ),
inference(avatar_component_clause,[],[f17695]) ).
fof(f21566,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1413,f21564]) ).
fof(f21564,plain,
( spl0_1969
<=> ! [X24,X10,X3,X25,X52] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X52,X24,X3)
| c_lessequals(X25,X24,X3)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f1413,axiom,
! [X3,X10,X52,X24,X25] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X52,X24,X3)
| c_lessequals(X25,X24,X3)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f21562,plain,
spl0_1968,
inference(avatar_split_clause,[],[f1226,f21560]) ).
fof(f21560,plain,
( spl0_1968
<=> ! [X15,X17,X20,X16,X3] :
( ~ c_in(c_Pair(X15,X16,X17,X3),X20,tc_prod(X17,X3))
| c_in(X16,c_Relation_OImage(X20,c_insert(X15,c_emptyset,X17),X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f1226,axiom,
! [X3,X16,X17,X15,X20] :
( ~ c_in(c_Pair(X15,X16,X17,X3),X20,tc_prod(X17,X3))
| c_in(X16,c_Relation_OImage(X20,c_insert(X15,c_emptyset,X17),X17,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f21558,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1225,f21556]) ).
fof(f21556,plain,
( spl0_1967
<=> ! [X15,X17,X20,X16,X3] :
( c_in(c_Pair(X15,X16,X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(X16,c_Relation_OImage(X20,c_insert(X15,c_emptyset,X17),X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f1225,axiom,
! [X3,X16,X17,X15,X20] :
( c_in(c_Pair(X15,X16,X17,X3),X20,tc_prod(X17,X3))
| ~ c_in(X16,c_Relation_OImage(X20,c_insert(X15,c_emptyset,X17),X17,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f21554,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1185,f21552]) ).
fof(f21552,plain,
( spl0_1966
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f1185,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f21550,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1168,f21548]) ).
fof(f21548,plain,
( spl0_1965
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f1168,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f21546,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1024,f21544]) ).
fof(f21544,plain,
( spl0_1964
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_plus(c_HOL_Oabs(X15,X3),c_HOL_Oabs(X16,X3),X3) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X15,X3),c_HOL_Oabs(X16,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f1024,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_plus(c_HOL_Oabs(X15,X3),c_HOL_Oabs(X16,X3),X3) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X15,X3),c_HOL_Oabs(X16,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f21542,plain,
spl0_1963,
inference(avatar_split_clause,[],[f971,f21540]) ).
fof(f21540,plain,
( spl0_1963
<=> ! [X11,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_HOL_Oabs(c_Numeral_Onumber__of(X11,X3),X3) = c_uminus(c_Numeral_Onumber__of(X11,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f971,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_HOL_Oabs(c_Numeral_Onumber__of(X11,X3),X3) = c_uminus(c_Numeral_Onumber__of(X11,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f21538,plain,
spl0_1962,
inference(avatar_split_clause,[],[f660,f21536]) ).
fof(f21536,plain,
( spl0_1962
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_lessequals(X10,X25,tc_nat)
| c_NatArith_Oof__nat(c_minus(X25,X10,tc_nat),X3) = c_minus(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f660,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_lessequals(X10,X25,tc_nat)
| c_NatArith_Oof__nat(c_minus(X25,X10,tc_nat),X3) = c_minus(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f21534,plain,
spl0_1961,
inference(avatar_split_clause,[],[f522,f21532]) ).
fof(f21532,plain,
( spl0_1961
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X8,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f522,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X8,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f21530,plain,
spl0_1960,
inference(avatar_split_clause,[],[f521,f21528]) ).
fof(f21528,plain,
( spl0_1960
<=> ! [X28,X29,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X8,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble7,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f521,axiom,
! [X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X8,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble7,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f21526,plain,
( spl0_1959
| ~ spl0_109
| ~ spl0_1783 ),
inference(avatar_split_clause,[],[f21478,f17695,f3695,f21523]) ).
fof(f21523,plain,
( spl0_1959
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f21478,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1783 ),
inference(superposition,[],[f17696,f3697]) ).
fof(f21521,plain,
spl0_1958,
inference(avatar_split_clause,[],[f520,f21519]) ).
fof(f21519,plain,
( spl0_1958
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X8,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble6,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f520,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X8,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble6,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f21517,plain,
spl0_1957,
inference(avatar_split_clause,[],[f519,f21515]) ).
fof(f21515,plain,
( spl0_1957
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X8,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble5,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f519,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X8,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble5,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f21513,plain,
spl0_1956,
inference(avatar_split_clause,[],[f518,f21511]) ).
fof(f21511,plain,
( spl0_1956
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X8,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble4,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f518,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X8,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble4,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f21509,plain,
spl0_1955,
inference(avatar_split_clause,[],[f517,f21507]) ).
fof(f21507,plain,
( spl0_1955
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X8,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f517,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X8,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f21505,plain,
spl0_1954,
inference(avatar_split_clause,[],[f516,f21503]) ).
fof(f21503,plain,
( spl0_1954
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X8,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble2,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f516,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X8,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble2,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f21501,plain,
spl0_1953,
inference(avatar_split_clause,[],[f515,f21499]) ).
fof(f21499,plain,
( spl0_1953
<=> ! [X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X8,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f515,axiom,
! [X65,X72,X70,X29,X73,X71,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X8,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f21497,plain,
spl0_1952,
inference(avatar_split_clause,[],[f514,f21495]) ).
fof(f21495,plain,
( spl0_1952
<=> ! [X28,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X8,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f514,axiom,
! [X65,X28,X70,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X8,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f21493,plain,
spl0_1951,
inference(avatar_split_clause,[],[f513,f21491]) ).
fof(f21491,plain,
( spl0_1951
<=> ! [X28,X29,X65,X3,X70,X73,X71,X8,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X8,c_List_Onibble_ONibbleF,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f513,axiom,
! [X65,X28,X70,X29,X73,X71,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X8,c_List_Onibble_ONibbleF,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f21489,plain,
spl0_1950,
inference(avatar_split_clause,[],[f512,f21487]) ).
fof(f21487,plain,
( spl0_1950
<=> ! [X28,X29,X65,X3,X70,X73,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X8,X72,c_List_Onibble_ONibbleE,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f512,axiom,
! [X65,X28,X70,X29,X73,X72,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X8,X72,c_List_Onibble_ONibbleE,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f21485,plain,
spl0_1949,
inference(avatar_split_clause,[],[f511,f21483]) ).
fof(f21483,plain,
( spl0_1949
<=> ! [X28,X29,X65,X3,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X8,X71,X72,c_List_Onibble_ONibbleD,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f511,axiom,
! [X65,X28,X72,X29,X73,X71,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X8,X71,X72,c_List_Onibble_ONibbleD,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f21475,plain,
spl0_1948,
inference(avatar_split_clause,[],[f510,f21473]) ).
fof(f21473,plain,
( spl0_1948
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X8,X70,X71,X72,c_List_Onibble_ONibbleC,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f510,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X68,X8,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X8,X70,X71,X72,c_List_Onibble_ONibbleC,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f21471,plain,
spl0_1947,
inference(avatar_split_clause,[],[f509,f21469]) ).
fof(f21469,plain,
( spl0_1947
<=> ! [X28,X29,X65,X3,X70,X73,X71,X8,X72,X69,X62,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X8,X69,X70,X71,X72,c_List_Onibble_ONibbleB,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f509,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X8,X69,X70,X71,X72,c_List_Onibble_ONibbleB,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f21467,plain,
spl0_1946,
inference(avatar_split_clause,[],[f508,f21465]) ).
fof(f21465,plain,
( spl0_1946
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X8,X68,X69,X70,X71,X72,c_List_Onibble_ONibbleA,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f508,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X8,X68,X69,X70,X71,X72,c_List_Onibble_ONibbleA,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f21463,plain,
spl0_1945,
inference(avatar_split_clause,[],[f507,f21461]) ).
fof(f21461,plain,
( spl0_1945
<=> ! [X28,X65,X3,X70,X29,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X8,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble9,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f507,axiom,
! [X65,X28,X70,X29,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X29,X28,X60,X61,X62,X63,X64,X65,X66,X8,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble9,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f21459,plain,
spl0_1944,
inference(avatar_split_clause,[],[f506,f21457]) ).
fof(f21457,plain,
( spl0_1944
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X8,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f506,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X8,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f21455,plain,
spl0_1943,
inference(avatar_split_clause,[],[f505,f21453]) ).
fof(f21453,plain,
( spl0_1943
<=> ! [X28,X29,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X8,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble7,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f505,axiom,
! [X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X8,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble7,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f21451,plain,
spl0_1942,
inference(avatar_split_clause,[],[f504,f21449]) ).
fof(f21449,plain,
( spl0_1942
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X8,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble6,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f504,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X8,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble6,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f21447,plain,
spl0_1941,
inference(avatar_split_clause,[],[f503,f21445]) ).
fof(f21445,plain,
( spl0_1941
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X8,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble5,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f503,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X8,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble5,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f21443,plain,
spl0_1940,
inference(avatar_split_clause,[],[f502,f21441]) ).
fof(f21441,plain,
( spl0_1940
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X8,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble4,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f502,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X8,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble4,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f21439,plain,
spl0_1939,
inference(avatar_split_clause,[],[f501,f21437]) ).
fof(f21437,plain,
( spl0_1939
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X8,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f501,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X8,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f21433,plain,
spl0_1938,
inference(avatar_split_clause,[],[f500,f21431]) ).
fof(f21431,plain,
( spl0_1938
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X8,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble2,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f500,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X8,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble2,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f21429,plain,
spl0_1937,
inference(avatar_split_clause,[],[f499,f21427]) ).
fof(f21427,plain,
( spl0_1937
<=> ! [X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X8,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f499,axiom,
! [X65,X72,X70,X29,X73,X71,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X8,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f21425,plain,
spl0_1936,
inference(avatar_split_clause,[],[f498,f21423]) ).
fof(f21423,plain,
( spl0_1936
<=> ! [X28,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X8,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f498,axiom,
! [X65,X28,X70,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X8,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f21421,plain,
spl0_1935,
inference(avatar_split_clause,[],[f497,f21419]) ).
fof(f21419,plain,
( spl0_1935
<=> ! [X28,X29,X65,X3,X70,X73,X71,X8,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X8,c_List_Onibble_ONibbleF,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f497,axiom,
! [X65,X28,X70,X29,X73,X71,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X71,X8,c_List_Onibble_ONibbleF,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f21417,plain,
spl0_1934,
inference(avatar_split_clause,[],[f496,f21415]) ).
fof(f21415,plain,
( spl0_1934
<=> ! [X28,X29,X65,X3,X70,X73,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X8,X72,c_List_Onibble_ONibbleE,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f496,axiom,
! [X65,X28,X70,X29,X73,X72,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X70,X8,X72,c_List_Onibble_ONibbleE,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f21413,plain,
spl0_1933,
inference(avatar_split_clause,[],[f495,f21411]) ).
fof(f21411,plain,
( spl0_1933
<=> ! [X28,X29,X65,X3,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X8,X71,X72,c_List_Onibble_ONibbleD,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f495,axiom,
! [X65,X28,X72,X29,X73,X71,X3,X68,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X69,X8,X71,X72,c_List_Onibble_ONibbleD,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f21409,plain,
spl0_1932,
inference(avatar_split_clause,[],[f494,f21407]) ).
fof(f21407,plain,
( spl0_1932
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X8,X70,X71,X72,c_List_Onibble_ONibbleC,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f494,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X68,X8,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X68,X8,X70,X71,X72,c_List_Onibble_ONibbleC,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f21405,plain,
spl0_1931,
inference(avatar_split_clause,[],[f493,f21403]) ).
fof(f21403,plain,
( spl0_1931
<=> ! [X28,X29,X65,X3,X70,X73,X71,X8,X72,X69,X62,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X8,X69,X70,X71,X72,c_List_Onibble_ONibbleB,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f493,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X67,X8,X69,X70,X71,X72,c_List_Onibble_ONibbleB,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f21401,plain,
spl0_1930,
inference(avatar_split_clause,[],[f492,f21399]) ).
fof(f21399,plain,
( spl0_1930
<=> ! [X28,X29,X65,X3,X70,X73,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X8,X68,X69,X70,X71,X72,c_List_Onibble_ONibbleA,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f492,axiom,
! [X65,X28,X70,X29,X73,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X73,X8,X68,X69,X70,X71,X72,c_List_Onibble_ONibbleA,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f21397,plain,
spl0_1929,
inference(avatar_split_clause,[],[f491,f21395]) ).
fof(f21395,plain,
( spl0_1929
<=> ! [X28,X65,X3,X70,X29,X71,X68,X72,X69,X62,X60,X8,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X8,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble9,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f491,axiom,
! [X65,X28,X70,X29,X71,X72,X3,X8,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X29,X28,X60,X61,X62,X63,X64,X65,X66,X8,X67,X68,X69,X70,X71,X72,c_List_Onibble_ONibble9,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f21391,plain,
spl0_1928,
inference(avatar_split_clause,[],[f479,f21389]) ).
fof(f21389,plain,
( spl0_1928
<=> ! [X53,X13,X58,X15] :
( ~ c_in(X15,c_List_Oset(X58,X13),X13)
| c_List_Olist__inter(c_List_Olist_OCons(X15,X53,X13),X58,X13) = c_List_Olist_OCons(X15,c_List_Olist__inter(X53,X58,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f479,axiom,
! [X58,X15,X53,X13] :
( ~ c_in(X15,c_List_Oset(X58,X13),X13)
| c_List_Olist__inter(c_List_Olist_OCons(X15,X53,X13),X58,X13) = c_List_Olist_OCons(X15,c_List_Olist__inter(X53,X58,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f21387,plain,
spl0_1927,
inference(avatar_split_clause,[],[f464,f21385]) ).
fof(f21385,plain,
( spl0_1927
<=> ! [X41,X42,X17,X3] : c_Nat_Osize(c_List_Ozip(X41,X42,X3,X17),tc_List_Olist(tc_prod(X3,X17))) = c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),c_Nat_Osize(X42,tc_List_Olist(X17)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f464,axiom,
! [X41,X3,X17,X42] : c_Nat_Osize(c_List_Ozip(X41,X42,X3,X17),tc_List_Olist(tc_prod(X3,X17))) = c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),c_Nat_Osize(X42,tc_List_Olist(X17)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f21383,plain,
spl0_1926,
inference(avatar_split_clause,[],[f373,f21381]) ).
fof(f21381,plain,
( spl0_1926
<=> ! [X42,X41,X46,X3,X45] :
( X45 = X46
| c_Nat_Osize(X45,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f373,axiom,
! [X3,X41,X46,X45,X42] :
( X45 = X46
| c_Nat_Osize(X45,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f21379,plain,
spl0_1925,
inference(avatar_split_clause,[],[f372,f21377]) ).
fof(f21377,plain,
( spl0_1925
<=> ! [X41,X42,X3,X45,X46] :
( X41 = X42
| c_Nat_Osize(X45,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f372,axiom,
! [X41,X3,X46,X45,X42] :
( X41 = X42
| c_Nat_Osize(X45,tc_List_Olist(X3)) != c_Nat_Osize(X46,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f21375,plain,
spl0_1924,
inference(avatar_split_clause,[],[f371,f21373]) ).
fof(f21373,plain,
( spl0_1924
<=> ! [X42,X41,X46,X3,X45] :
( X45 = X46
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f371,axiom,
! [X41,X3,X46,X45,X42] :
( X45 = X46
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f21371,plain,
spl0_1923,
inference(avatar_split_clause,[],[f370,f21369]) ).
fof(f21369,plain,
( spl0_1923
<=> ! [X41,X42,X3,X45,X46] :
( X41 = X42
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f370,axiom,
! [X41,X3,X46,X45,X42] :
( X41 = X42
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(X42,tc_List_Olist(X3))
| c_append(X41,X45,X3) != c_append(X42,X46,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f21367,plain,
spl0_1922,
inference(avatar_split_clause,[],[f318,f21365]) ).
fof(f21365,plain,
( spl0_1922
<=> ! [X36,X35] : c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f318,axiom,
! [X36,X35] : c_div(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_Numeral_Onumber__of(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
fof(f21363,plain,
spl0_1921,
inference(avatar_split_clause,[],[f133,f21361]) ).
fof(f21361,plain,
( spl0_1921
<=> ! [X3,X31,X27,X15] :
( ~ c_in(c_minus(X27,X31,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_minus(X27,c_insert(X15,X31,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f133,axiom,
! [X31,X3,X27,X15] :
( ~ c_in(c_minus(X27,X31,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_minus(X27,c_insert(X15,X31,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f21359,plain,
spl0_1920,
inference(avatar_split_clause,[],[f132,f21357]) ).
fof(f21357,plain,
( spl0_1920
<=> ! [X3,X31,X27,X15] :
( c_in(c_minus(X27,X31,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_minus(X27,c_insert(X15,X31,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f132,axiom,
! [X31,X3,X27,X15] :
( c_in(c_minus(X27,X31,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_minus(X27,c_insert(X15,X31,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f21249,plain,
( spl0_1919
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_1902 ),
inference(avatar_split_clause,[],[f20720,f20717,f11729,f3421,f21247]) ).
fof(f21247,plain,
( spl0_1919
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f20717,plain,
( spl0_1902
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f20720,plain,
( ! [X36,X77] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_1902 ),
inference(forward_demodulation,[],[f20718,f12793]) ).
fof(f20718,plain,
( ! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_1902 ),
inference(avatar_component_clause,[],[f20717]) ).
fof(f21245,plain,
( spl0_1918
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_1901 ),
inference(avatar_split_clause,[],[f20715,f20712,f11729,f3421,f21243]) ).
fof(f21243,plain,
( spl0_1918
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f20712,plain,
( spl0_1901
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f20715,plain,
( ! [X36,X77] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_53
| ~ spl0_1444
| ~ spl0_1901 ),
inference(forward_demodulation,[],[f20713,f12793]) ).
fof(f20713,plain,
( ! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) )
| ~ spl0_1901 ),
inference(avatar_component_clause,[],[f20712]) ).
fof(f20884,plain,
( spl0_1917
| ~ spl0_1538
| ~ spl0_1916 ),
inference(avatar_split_clause,[],[f20880,f20877,f13937,f20882]) ).
fof(f20882,plain,
( spl0_1917
<=> ! [X11,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f13937,plain,
( spl0_1538
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f20877,plain,
( spl0_1916
<=> ! [X11,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f20880,plain,
( ! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) )
| ~ spl0_1538
| ~ spl0_1916 ),
inference(forward_demodulation,[],[f20878,f13939]) ).
fof(f13939,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1538 ),
inference(avatar_component_clause,[],[f13937]) ).
fof(f20878,plain,
( ! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) )
| ~ spl0_1916 ),
inference(avatar_component_clause,[],[f20877]) ).
fof(f20879,plain,
spl0_1916,
inference(avatar_split_clause,[],[f3155,f20877]) ).
fof(f3155,plain,
! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ),
inference(forward_demodulation,[],[f2952,f1006]) ).
fof(f2952,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f169,f979]) ).
fof(f169,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f20875,plain,
spl0_1915,
inference(avatar_split_clause,[],[f3153,f20873]) ).
fof(f20873,plain,
( spl0_1915
<=> ! [X8,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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f3153,plain,
! [X3,X8] :
( ~ 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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2950,f1006]) ).
fof(f2950,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| ~ 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,X8)),X3),X3) ),
inference(definition_unfolding,[],[f165,f979]) ).
fof(f165,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| ~ 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(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f20871,plain,
spl0_1914,
inference(avatar_split_clause,[],[f3151,f20869]) ).
fof(f20869,plain,
( spl0_1914
<=> ! [X11,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,X11)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f3151,plain,
! [X3,X11] :
( 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,X11)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3) ),
inference(forward_demodulation,[],[f2948,f1006]) ).
fof(f2948,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| 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,X11)),X3),X3) ),
inference(definition_unfolding,[],[f177,f979]) ).
fof(f177,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| 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(X11)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f20813,plain,
( spl0_1913
| ~ spl0_1538
| ~ spl0_1912 ),
inference(avatar_split_clause,[],[f20809,f20806,f13937,f20811]) ).
fof(f20811,plain,
( spl0_1913
<=> ! [X8,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f20806,plain,
( spl0_1912
<=> ! [X8,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f20809,plain,
( ! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) )
| ~ spl0_1538
| ~ spl0_1912 ),
inference(forward_demodulation,[],[f20807,f13939]) ).
fof(f20807,plain,
( ! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) )
| ~ spl0_1912 ),
inference(avatar_component_clause,[],[f20806]) ).
fof(f20808,plain,
spl0_1912,
inference(avatar_split_clause,[],[f3148,f20806]) ).
fof(f3148,plain,
! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2946,f1006]) ).
fof(f2946,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f173,f979]) ).
fof(f173,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f20787,plain,
( spl0_1911
| ~ spl0_1538
| ~ spl0_1910 ),
inference(avatar_split_clause,[],[f20783,f20780,f13937,f20785]) ).
fof(f20785,plain,
( spl0_1911
<=> ! [X11,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f20780,plain,
( spl0_1910
<=> ! [X11,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f20783,plain,
( ! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) )
| ~ spl0_1538
| ~ spl0_1910 ),
inference(forward_demodulation,[],[f20781,f13939]) ).
fof(f20781,plain,
( ! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) )
| ~ spl0_1910 ),
inference(avatar_component_clause,[],[f20780]) ).
fof(f20782,plain,
spl0_1910,
inference(avatar_split_clause,[],[f3145,f20780]) ).
fof(f3145,plain,
! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3) ),
inference(forward_demodulation,[],[f2944,f1006]) ).
fof(f2944,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f168,f979]) ).
fof(f168,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f20778,plain,
spl0_1909,
inference(avatar_split_clause,[],[f3143,f20776]) ).
fof(f20776,plain,
( spl0_1909
<=> ! [X8,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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f3143,plain,
! [X3,X8] :
( 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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2942,f1006]) ).
fof(f2942,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| 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,X8)),X3),X3) ),
inference(definition_unfolding,[],[f164,f979]) ).
fof(f164,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| 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(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f20774,plain,
spl0_1908,
inference(avatar_split_clause,[],[f3141,f20772]) ).
fof(f20772,plain,
( spl0_1908
<=> ! [X11,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,X11)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f3141,plain,
! [X3,X11] :
( ~ 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,X11)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3) ),
inference(forward_demodulation,[],[f2940,f1006]) ).
fof(f2940,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| ~ 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,X11)),X3),X3) ),
inference(definition_unfolding,[],[f176,f979]) ).
fof(f176,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_1,X3)
| ~ 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(X11)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f20761,plain,
( spl0_1907
| ~ spl0_1538
| ~ spl0_1906 ),
inference(avatar_split_clause,[],[f20757,f20754,f13937,f20759]) ).
fof(f20759,plain,
( spl0_1907
<=> ! [X8,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f20754,plain,
( spl0_1906
<=> ! [X8,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f20757,plain,
( ! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) )
| ~ spl0_1538
| ~ spl0_1906 ),
inference(forward_demodulation,[],[f20755,f13939]) ).
fof(f20755,plain,
( ! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) )
| ~ spl0_1906 ),
inference(avatar_component_clause,[],[f20754]) ).
fof(f20756,plain,
spl0_1906,
inference(avatar_split_clause,[],[f3138,f20754]) ).
fof(f3138,plain,
! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2938,f1006]) ).
fof(f2938,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f172,f979]) ).
fof(f172,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f20752,plain,
( spl0_1905
| ~ spl0_907
| ~ spl0_1022
| ~ spl0_1721 ),
inference(avatar_split_clause,[],[f20662,f16846,f8365,f7783,f20749]) ).
fof(f20749,plain,
( spl0_1905
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f7783,plain,
( spl0_907
<=> ! [X35] : c_IntDef_Onat(c_Numeral_Onumber__of(X35,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X35,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f8365,plain,
( spl0_1022
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f20662,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_907
| ~ spl0_1022
| ~ spl0_1721 ),
inference(forward_demodulation,[],[f20621,f8367]) ).
fof(f8367,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f8365]) ).
fof(f20621,plain,
( c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_907
| ~ spl0_1721 ),
inference(superposition,[],[f7784,f16848]) ).
fof(f7784,plain,
( ! [X35] : c_IntDef_Onat(c_Numeral_Onumber__of(X35,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X35,tc_nat)
| ~ spl0_907 ),
inference(avatar_component_clause,[],[f7783]) ).
fof(f20730,plain,
( spl0_1904
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1903 ),
inference(avatar_split_clause,[],[f20726,f20722,f10431,f3421,f20728]) ).
fof(f20728,plain,
( spl0_1904
<=> ! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X11,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f20722,plain,
( spl0_1903
<=> ! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,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(X11,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_1903])]) ).
fof(f20726,plain,
( ! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X11,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1903 ),
inference(forward_demodulation,[],[f20725,f11307]) ).
fof(f20725,plain,
( ! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1903 ),
inference(forward_demodulation,[],[f20723,f11307]) ).
fof(f20723,plain,
( ! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,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(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1903 ),
inference(avatar_component_clause,[],[f20722]) ).
fof(f20724,plain,
spl0_1903,
inference(avatar_split_clause,[],[f3096,f20722]) ).
fof(f3096,plain,
! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,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(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3095,f1006]) ).
fof(f3095,plain,
! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,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(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3094,f1004]) ).
fof(f3094,plain,
! [X11] :
( c_0 = c_Divides_Oop_Amod(X11,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(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3093,f1006]) ).
fof(f3093,plain,
! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,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(X11,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,[],[f3092,f1006]) ).
fof(f3092,plain,
! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,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(X11,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,[],[f3091,f1004]) ).
fof(f3091,plain,
! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,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(X11,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,[],[f1158,f1006]) ).
fof(f1158,axiom,
! [X11] :
( c_1 = c_Divides_Oop_Amod(X11,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(X11,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).
fof(f20719,plain,
spl0_1902,
inference(avatar_split_clause,[],[f2933,f20717]) ).
fof(f2933,plain,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f705,f979]) ).
fof(f705,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X77),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f20714,plain,
spl0_1901,
inference(avatar_split_clause,[],[f2932,f20712]) ).
fof(f2932,plain,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X77),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f708,f979]) ).
fof(f708,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X77),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f20710,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1610,f20708]) ).
fof(f20708,plain,
( spl0_1900
<=> ! [X27,X3] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
| ~ c_in(c_Main_Ofinite__Union__1(X27,X3),c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Union(X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f1610,axiom,
! [X3,X27] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
| ~ c_in(c_Main_Ofinite__Union__1(X27,X3),c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Union(X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f20706,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1609,f20704]) ).
fof(f20704,plain,
( spl0_1899
<=> ! [X27,X3] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
| c_in(c_Main_Ofinite__Union__1(X27,X3),X27,tc_set(X3))
| c_in(c_Union(X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f1609,axiom,
! [X3,X27] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
| c_in(c_Main_Ofinite__Union__1(X27,X3),X27,tc_set(X3))
| c_in(c_Union(X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f20702,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1202,f20700]) ).
fof(f20700,plain,
( spl0_1898
<=> ! [X10,X3,X25,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| ~ c_less(c_1,X15,X3)
| c_Nat_Opower(X15,X10,X3) != c_Nat_Opower(X15,X25,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f1202,axiom,
! [X3,X10,X15,X25] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| ~ c_less(c_1,X15,X3)
| c_Nat_Opower(X15,X10,X3) != c_Nat_Opower(X15,X25,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f20698,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1177,f20696]) ).
fof(f20696,plain,
( spl0_1897
<=> ! [X11,X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven(X10,tc_nat)
| c_Nat_Opower(c_uminus(X11,X3),X10,X3) = c_uminus(c_Nat_Opower(X11,X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f1177,axiom,
! [X3,X10,X11] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven(X10,tc_nat)
| c_Nat_Opower(c_uminus(X11,X3),X10,X3) = c_uminus(c_Nat_Opower(X11,X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f20694,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1170,f20692]) ).
fof(f20692,plain,
( spl0_1896
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| c_lessequals(X11,c_0,X3)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f1170,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X11
| c_lessequals(X11,c_0,X3)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f20619,plain,
spl0_1895,
inference(avatar_split_clause,[],[f823,f20617]) ).
fof(f20617,plain,
( spl0_1895
<=> ! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17)
| c_less(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f823,axiom,
! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17)
| c_less(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f20615,plain,
spl0_1894,
inference(avatar_split_clause,[],[f822,f20613]) ).
fof(f20613,plain,
( spl0_1894
<=> ! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f822,axiom,
! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17)
| c_less(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f20611,plain,
spl0_1893,
inference(avatar_split_clause,[],[f819,f20609]) ).
fof(f20609,plain,
( spl0_1893
<=> ! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17)
| c_lessequals(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f819,axiom,
! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17)
| c_lessequals(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f20607,plain,
spl0_1892,
inference(avatar_split_clause,[],[f818,f20605]) ).
fof(f20605,plain,
( spl0_1892
<=> ! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f818,axiom,
! [X36,X17,X15] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_uminus(X15,X17),c_Numeral_Onumber__of(X36,X17),X17)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f20603,plain,
spl0_1891,
inference(avatar_split_clause,[],[f812,f20601]) ).
fof(f20601,plain,
( spl0_1891
<=> ! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f812,axiom,
! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17)
| c_less(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f20599,plain,
spl0_1890,
inference(avatar_split_clause,[],[f811,f20597]) ).
fof(f20597,plain,
( spl0_1890
<=> ! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17)
| c_less(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f811,axiom,
! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_less(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17)
| c_less(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f20595,plain,
spl0_1889,
inference(avatar_split_clause,[],[f796,f20593]) ).
fof(f20593,plain,
( spl0_1889
<=> ! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f796,axiom,
! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17)
| c_lessequals(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f20591,plain,
spl0_1888,
inference(avatar_split_clause,[],[f795,f20589]) ).
fof(f20589,plain,
( spl0_1888
<=> ! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17)
| c_lessequals(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f795,axiom,
! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ c_lessequals(c_Numeral_Onumber__of(X36,X17),c_uminus(X16,X17),X17)
| c_lessequals(X16,c_uminus(c_Numeral_Onumber__of(X36,X17),X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f20587,plain,
spl0_1887,
inference(avatar_split_clause,[],[f726,f20585]) ).
fof(f20585,plain,
( spl0_1887
<=> ! [X36,X35] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X35,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f726,axiom,
! [X36,X35] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X35,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f20583,plain,
spl0_1886,
inference(avatar_split_clause,[],[f605,f20581]) ).
fof(f20581,plain,
( spl0_1886
<=> ! [X41,X11,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Oset(c_List_Oremove1(X11,X41,X3),X3) = c_minus(c_List_Oset(X41,X3),c_insert(X11,c_emptyset,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f605,axiom,
! [X41,X3,X11] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Oset(c_List_Oremove1(X11,X41,X3),X3) = c_minus(c_List_Oset(X41,X3),c_insert(X11,c_emptyset,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f20578,plain,
spl0_1885,
inference(avatar_split_clause,[],[f124,f20576]) ).
fof(f20576,plain,
( spl0_1885
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMin(X27,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f124,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(c_Finite__Set_OMin(X27,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f20574,plain,
spl0_1884,
inference(avatar_split_clause,[],[f106,f20572]) ).
fof(f20572,plain,
( spl0_1884
<=> ! [X11,X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMax(X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f106,axiom,
! [X3,X11,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X11,X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_lessequals(X11,c_Finite__Set_OMax(X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f20207,plain,
( spl0_1883
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1869 ),
inference(avatar_split_clause,[],[f20052,f20049,f16113,f7128,f7108,f20205]) ).
fof(f20205,plain,
( spl0_1883
<=> ! [X41,X42,X3,X8] :
( c_append(c_List_Orev(X42,X3),c_List_Oreplicate(c_1,X8,X3),X3) = X41
| c_List_Olist_OCons(X8,X42,X3) != c_List_Orev(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f20049,plain,
( spl0_1869
<=> ! [X41,X42,X3,X8] :
( c_List_Olist_OCons(X8,X42,X3) != c_List_Orev(X41,X3)
| c_append(c_List_Orev(X42,X3),c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) = X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f20052,plain,
( ! [X3,X41,X8,X42] :
( c_append(c_List_Orev(X42,X3),c_List_Oreplicate(c_1,X8,X3),X3) = X41
| c_List_Olist_OCons(X8,X42,X3) != c_List_Orev(X41,X3) )
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1869 ),
inference(forward_demodulation,[],[f20050,f16139]) ).
fof(f20050,plain,
( ! [X3,X41,X8,X42] :
( c_List_Olist_OCons(X8,X42,X3) != c_List_Orev(X41,X3)
| c_append(c_List_Orev(X42,X3),c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) = X41 )
| ~ spl0_1869 ),
inference(avatar_component_clause,[],[f20049]) ).
fof(f20175,plain,
( spl0_1882
| ~ spl0_1721
| ~ spl0_1866 ),
inference(avatar_split_clause,[],[f20039,f20036,f16846,f20173]) ).
fof(f20173,plain,
( spl0_1882
<=> ! [X16] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X16,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f20036,plain,
( spl0_1866
<=> ! [X16] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X16,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f20039,plain,
( ! [X16] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X16,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1721
| ~ spl0_1866 ),
inference(forward_demodulation,[],[f20037,f16848]) ).
fof(f20037,plain,
( ! [X16] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X16,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1866 ),
inference(avatar_component_clause,[],[f20036]) ).
fof(f20111,plain,
spl0_1881,
inference(avatar_split_clause,[],[f3071,f20109]) ).
fof(f20109,plain,
( spl0_1881
<=> ! [X77] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f3071,plain,
! [X77] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2896,f2749]) ).
fof(f2749,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f866,f1394]) ).
fof(f866,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2896,plain,
! [X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,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(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f722,f1394]) ).
fof(f722,axiom,
! [X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f20107,plain,
spl0_1880,
inference(avatar_split_clause,[],[f2902,f20105]) ).
fof(f20105,plain,
( spl0_1880
<=> ! [X20,X40,X3] :
( ~ c_in(X40,X20,tc_prod(X3,X3))
| c_in(X40,c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f2902,plain,
! [X40,X3,X20] :
( ~ c_in(X40,X20,tc_prod(X3,X3))
| c_in(X40,c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
inference(definition_unfolding,[],[f1696,f1566]) ).
fof(f1696,axiom,
! [X40,X3,X20] :
( ~ c_in(X40,X20,tc_prod(X3,X3))
| c_in(X40,c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f20103,plain,
spl0_1879,
inference(avatar_split_clause,[],[f2900,f20101]) ).
fof(f20101,plain,
( spl0_1879
<=> ! [X41,X3,X42] :
( ~ c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X41,X3),X3),c_List_Oset(X42,X3),X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f2900,plain,
! [X41,X3,X42] :
( ~ c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X41,X3),X3),c_List_Oset(X42,X3),X3,X3) ),
inference(definition_unfolding,[],[f407,f1223]) ).
fof(f407,axiom,
! [X41,X3,X42] :
( ~ c_List_Odistinct(c_append(X41,X42,X3),X3)
| c_emptyset = c_inter(c_List_Oset(X41,X3),c_List_Oset(X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f20099,plain,
spl0_1878,
inference(avatar_split_clause,[],[f2851,f20097]) ).
fof(f20097,plain,
( spl0_1878
<=> ! [X37,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_uminus(c_Numeral_Onumber__of(X35,X3),X3),X37,X3) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X35),X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f2851,plain,
! [X3,X37,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_uminus(c_Numeral_Onumber__of(X35,X3),X3),X37,X3) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X35),X3),X37,X3) ),
inference(definition_unfolding,[],[f1015,f979]) ).
fof(f1015,axiom,
! [X3,X37,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_uminus(c_Numeral_Onumber__of(X35,X3),X3),X37,X3) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X35),X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f20095,plain,
spl0_1877,
inference(avatar_split_clause,[],[f2825,f20093]) ).
fof(f20093,plain,
( spl0_1877
<=> ! [X41,X11,X42,X13] : c_append(c_List_Orev(c_List_Olist_OCons(X11,X41,X13),X13),X42,X13) = c_append(c_List_Orev(X41,X13),c_List_Olist_OCons(X11,X42,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f2825,plain,
! [X41,X11,X42,X13] : c_append(c_List_Orev(c_List_Olist_OCons(X11,X41,X13),X13),X42,X13) = c_append(c_List_Orev(X41,X13),c_List_Olist_OCons(X11,X42,X13),X13),
inference(definition_unfolding,[],[f437,f435,f435]) ).
fof(f435,axiom,
! [X41,X3,X11] : c_List_Oitrev(X41,X11,X3) = c_append(c_List_Orev(X41,X3),X11,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f437,axiom,
! [X41,X11,X42,X13] : c_List_Oitrev(c_List_Olist_OCons(X11,X41,X13),X42,X13) = c_List_Oitrev(X41,c_List_Olist_OCons(X11,X42,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f20091,plain,
spl0_1876,
inference(avatar_split_clause,[],[f1634,f20089]) ).
fof(f20089,plain,
( spl0_1876
<=> ! [X20,X41,X3] :
( c_List_Olist_ONil = X41
| ~ c_in(c_Pair(X41,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f1634,axiom,
! [X41,X3,X20] :
( c_List_Olist_ONil = X41
| ~ c_in(c_Pair(X41,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f20087,plain,
spl0_1875,
inference(avatar_split_clause,[],[f1633,f20085]) ).
fof(f20085,plain,
( spl0_1875
<=> ! [X20,X41,X3] :
( c_List_Olist_ONil = X41
| ~ c_in(c_Pair(c_List_Olist_ONil,X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f1633,axiom,
! [X41,X3,X20] :
( c_List_Olist_ONil = X41
| ~ c_in(c_Pair(c_List_Olist_ONil,X41,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f20083,plain,
spl0_1874,
inference(avatar_split_clause,[],[f972,f20081]) ).
fof(f20081,plain,
( spl0_1874
<=> ! [X11,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_Numeral_Onumber__of(X11,X3) = c_HOL_Oabs(c_Numeral_Onumber__of(X11,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f972,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_Numeral_Onumber__of(X11,X3) = c_HOL_Oabs(c_Numeral_Onumber__of(X11,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f20068,plain,
spl0_1873,
inference(avatar_split_clause,[],[f714,f20066]) ).
fof(f20066,plain,
( spl0_1873
<=> ! [X77,X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X77),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f714,axiom,
! [X36,X77] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X77),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f20064,plain,
spl0_1872,
inference(avatar_split_clause,[],[f650,f20062]) ).
fof(f20062,plain,
( spl0_1872
<=> ! [X52,X9,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(X24,c_minus(X52,X9,tc_nat),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),X52,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f650,axiom,
! [X9,X52,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_minus(X24,c_minus(X52,X9,tc_nat),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),X52,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f20060,plain,
spl0_1871,
inference(avatar_split_clause,[],[f646,f20058]) ).
fof(f20058,plain,
( spl0_1871
<=> ! [X52,X9,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_plus(X24,c_minus(X52,X9,tc_nat),tc_nat) = c_minus(c_plus(X24,X52,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f646,axiom,
! [X9,X52,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_plus(X24,c_minus(X52,X9,tc_nat),tc_nat) = c_minus(c_plus(X24,X52,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f20056,plain,
spl0_1870,
inference(avatar_split_clause,[],[f645,f20054]) ).
fof(f20054,plain,
( spl0_1870
<=> ! [X52,X9,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_plus(c_minus(X52,X9,tc_nat),X24,tc_nat) = c_minus(c_plus(X52,X24,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f645,axiom,
! [X9,X52,X24] :
( ~ c_lessequals(X9,X52,tc_nat)
| c_plus(c_minus(X52,X9,tc_nat),X24,tc_nat) = c_minus(c_plus(X52,X24,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f20051,plain,
spl0_1869,
inference(avatar_split_clause,[],[f576,f20049]) ).
fof(f576,axiom,
! [X3,X41,X8,X42] :
( c_List_Olist_OCons(X8,X42,X3) != c_List_Orev(X41,X3)
| c_append(c_List_Orev(X42,X3),c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) = X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f20047,plain,
spl0_1868,
inference(avatar_split_clause,[],[f564,f20045]) ).
fof(f20045,plain,
( spl0_1868
<=> ! [X13,X41,X11] :
( c_in(X11,c_List_Oset(X41,X13),X13)
| c_List_Oremdups(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Olist_OCons(X11,c_List_Oremdups(X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f564,axiom,
! [X41,X11,X13] :
( c_in(X11,c_List_Oset(X41,X13),X13)
| c_List_Oremdups(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Olist_OCons(X11,c_List_Oremdups(X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f20043,plain,
spl0_1867,
inference(avatar_split_clause,[],[f467,f20041]) ).
fof(f20041,plain,
( spl0_1867
<=> ! [X54,X20,X30,X3] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X30,X54,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f467,axiom,
! [X3,X54,X30,X20] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X30,X54,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f20038,plain,
spl0_1866,
inference(avatar_split_clause,[],[f303,f20036]) ).
fof(f303,axiom,
! [X16] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X16,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f20034,plain,
spl0_1865,
inference(avatar_split_clause,[],[f69,f20032]) ).
fof(f20032,plain,
( spl0_1865
<=> ! [X15,X16,X26] :
( ~ c_less(c_0,X26,tc_nat)
| c_div(X15,X16,tc_nat) = c_div(c_times(X15,X26,tc_nat),c_times(X16,X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f69,axiom,
! [X26,X16,X15] :
( ~ c_less(c_0,X26,tc_nat)
| c_div(X15,X16,tc_nat) = c_div(c_times(X15,X26,tc_nat),c_times(X16,X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f20030,plain,
spl0_1864,
inference(avatar_split_clause,[],[f68,f20028]) ).
fof(f20028,plain,
( spl0_1864
<=> ! [X15,X16,X26] :
( ~ c_less(c_0,X26,tc_nat)
| c_div(c_times(X26,X15,tc_nat),c_times(X26,X16,tc_nat),tc_nat) = c_div(X15,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f68,axiom,
! [X26,X16,X15] :
( ~ c_less(c_0,X26,tc_nat)
| c_div(c_times(X26,X15,tc_nat),c_times(X26,X16,tc_nat),tc_nat) = c_div(X15,X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f19741,plain,
( spl0_1863
| ~ spl0_110
| ~ spl0_1717 ),
inference(avatar_split_clause,[],[f19333,f16305,f3700,f19738]) ).
fof(f19738,plain,
( spl0_1863
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f16305,plain,
( spl0_1717
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f19333,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1717 ),
inference(superposition,[],[f16306,f3702]) ).
fof(f16306,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1717 ),
inference(avatar_component_clause,[],[f16305]) ).
fof(f19578,plain,
( spl0_1862
| ~ spl0_109
| ~ spl0_1717 ),
inference(avatar_split_clause,[],[f19332,f16305,f3695,f19575]) ).
fof(f19575,plain,
( spl0_1862
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f19332,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1717 ),
inference(superposition,[],[f16306,f3697]) ).
fof(f19360,plain,
( spl0_1861
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1833 ),
inference(avatar_split_clause,[],[f18922,f18918,f16113,f7128,f7108,f19358]) ).
fof(f19358,plain,
( spl0_1861
<=> ! [X41,X42,X11,X3,X8] :
( c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3) != c_append(X41,c_List_Oreplicate(c_1,X11,X3),X3)
| X8 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f18918,plain,
( spl0_1833
<=> ! [X42,X41,X11,X3,X8] :
( X8 = X11
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f18922,plain,
( ! [X3,X41,X11,X8,X42] :
( c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3) != c_append(X41,c_List_Oreplicate(c_1,X11,X3),X3)
| X8 = X11 )
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1833 ),
inference(forward_demodulation,[],[f18921,f16139]) ).
fof(f18921,plain,
( ! [X41,X3,X11,X8,X42] :
( c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3)
| X8 = X11 )
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1833 ),
inference(forward_demodulation,[],[f18919,f16139]) ).
fof(f18919,plain,
( ! [X41,X3,X11,X8,X42] :
( X8 = X11
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) )
| ~ spl0_1833 ),
inference(avatar_component_clause,[],[f18918]) ).
fof(f19356,plain,
( spl0_1860
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1832 ),
inference(avatar_split_clause,[],[f18916,f18912,f16113,f7128,f7108,f19354]) ).
fof(f19354,plain,
( spl0_1860
<=> ! [X41,X42,X11,X3,X8] :
( c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3) != c_append(X41,c_List_Oreplicate(c_1,X11,X3),X3)
| X41 = X42 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f18912,plain,
( spl0_1832
<=> ! [X41,X42,X11,X3,X8] :
( X41 = X42
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f18916,plain,
( ! [X3,X41,X11,X8,X42] :
( c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3) != c_append(X41,c_List_Oreplicate(c_1,X11,X3),X3)
| X41 = X42 )
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1832 ),
inference(forward_demodulation,[],[f18915,f16139]) ).
fof(f18915,plain,
( ! [X41,X3,X11,X8,X42] :
( c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Oreplicate(c_1,X8,X3),X3)
| X41 = X42 )
| ~ spl0_759
| ~ spl0_764
| ~ spl0_1694
| ~ spl0_1832 ),
inference(forward_demodulation,[],[f18913,f16139]) ).
fof(f18913,plain,
( ! [X41,X3,X11,X8,X42] :
( X41 = X42
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) )
| ~ spl0_1832 ),
inference(avatar_component_clause,[],[f18912]) ).
fof(f19033,plain,
( spl0_1859
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1858 ),
inference(avatar_split_clause,[],[f19029,f19025,f10415,f10092,f6703,f3695,f19031]) ).
fof(f19025,plain,
( spl0_1858
<=> ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X10,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_1858])]) ).
fof(f19029,plain,
( ! [X10] : c_plus(X10,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,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1858 ),
inference(forward_demodulation,[],[f19028,f11235]) ).
fof(f19028,plain,
( ! [X10] : c_plus(X10,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,X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1858 ),
inference(forward_demodulation,[],[f19026,f11235]) ).
fof(f19026,plain,
( ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X10,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1858 ),
inference(avatar_component_clause,[],[f19025]) ).
fof(f19027,plain,
spl0_1858,
inference(avatar_split_clause,[],[f2996,f19025]) ).
fof(f19023,plain,
spl0_1857,
inference(avatar_split_clause,[],[f2926,f19021]) ).
fof(f19021,plain,
( spl0_1857
<=> ! [X3,X31,X27,X26] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,X27,X3)
| c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f2926,plain,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,X27,X3)
| c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ),
inference(definition_unfolding,[],[f1458,f1223]) ).
fof(f1458,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,X27,X3)
| c_in(X26,c_inter(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f19019,plain,
spl0_1856,
inference(avatar_split_clause,[],[f2921,f19017]) ).
fof(f19017,plain,
( spl0_1856
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f2921,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f992,f979]) ).
fof(f992,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f19015,plain,
spl0_1855,
inference(avatar_split_clause,[],[f2920,f19013]) ).
fof(f19013,plain,
( spl0_1855
<=> ! [X11,X8,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f2920,plain,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f991,f979]) ).
fof(f991,axiom,
! [X3,X11,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(X8,X3) != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f19011,plain,
spl0_1854,
inference(avatar_split_clause,[],[f2875,f19009]) ).
fof(f19009,plain,
( spl0_1854
<=> ! [X41,X10,X3,X24] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(X41,X24,X3) = c_List_Onth(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X24,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f2875,plain,
! [X41,X10,X3,X24] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(X41,X24,X3) = c_List_Onth(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),X24,X3) ),
inference(definition_unfolding,[],[f553,f616]) ).
fof(f553,axiom,
! [X41,X10,X3,X24] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(c_List_Otake(X10,X41,X3),X24,X3) = c_List_Onth(X41,X24,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f19007,plain,
spl0_1853,
inference(avatar_split_clause,[],[f2848,f19005]) ).
fof(f19005,plain,
( spl0_1853
<=> ! [X36,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f2848,plain,
! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3) ),
inference(definition_unfolding,[],[f970,f979]) ).
fof(f970,axiom,
! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(X35)),X3) = c_minus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f19003,plain,
spl0_1852,
inference(avatar_split_clause,[],[f1524,f19001]) ).
fof(f19001,plain,
( spl0_1852
<=> ! [X31,X11,X27,X3] :
( ~ c_in(X11,X31,X3)
| c_minus(X27,X31,tc_set(X3)) = c_minus(c_insert(X11,X27,X3),X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f1524,axiom,
! [X31,X3,X11,X27] :
( ~ c_in(X11,X31,X3)
| c_minus(X27,X31,tc_set(X3)) = c_minus(c_insert(X11,X27,X3),X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f18999,plain,
spl0_1851,
inference(avatar_split_clause,[],[f1497,f18997]) ).
fof(f18997,plain,
( spl0_1851
<=> ! [X31,X27,X80,X3] :
( ~ c_lessequals(X31,X80,tc_set(X3))
| ~ c_lessequals(X27,X80,tc_set(X3))
| c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f1497,axiom,
! [X31,X3,X80,X27] :
( ~ c_lessequals(X31,X80,tc_set(X3))
| ~ c_lessequals(X27,X80,tc_set(X3))
| c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f18995,plain,
spl0_1850,
inference(avatar_split_clause,[],[f1447,f18993]) ).
fof(f18993,plain,
( spl0_1850
<=> ! [X31,X11,X27,X3] :
( c_in(X11,X27,X3)
| c_minus(X27,X31,tc_set(X3)) = c_minus(X27,c_insert(X11,X31,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f1447,axiom,
! [X31,X3,X11,X27] :
( c_in(X11,X27,X3)
| c_minus(X27,X31,tc_set(X3)) = c_minus(X27,c_insert(X11,X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f18991,plain,
spl0_1849,
inference(avatar_split_clause,[],[f1187,f18989]) ).
fof(f18989,plain,
( spl0_1849
<=> ! [X11,X35] :
( c_less(c_0,X11,tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f1187,axiom,
! [X11,X35] :
( c_less(c_0,X11,tc_nat)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f18987,plain,
spl0_1848,
inference(avatar_split_clause,[],[f1179,f18985]) ).
fof(f18985,plain,
( spl0_1848
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f1179,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f18983,plain,
spl0_1847,
inference(avatar_split_clause,[],[f1176,f18981]) ).
fof(f18981,plain,
( spl0_1847
<=> ! [X11,X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven(X10,tc_nat)
| c_Nat_Opower(c_uminus(X11,X3),X10,X3) = c_Nat_Opower(X11,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f1176,axiom,
! [X3,X10,X11] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven(X10,tc_nat)
| c_Nat_Opower(c_uminus(X11,X3),X10,X3) = c_Nat_Opower(X11,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f18979,plain,
spl0_1846,
inference(avatar_split_clause,[],[f1173,f18977]) ).
fof(f18977,plain,
( spl0_1846
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f1173,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X35,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f18975,plain,
spl0_1845,
inference(avatar_split_clause,[],[f927,f18973]) ).
fof(f18973,plain,
( spl0_1845
<=> ! [X25,X9,X10] :
( ~ c_less(X25,X10,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f927,axiom,
! [X10,X9,X25] :
( ~ c_less(X25,X10,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f18967,plain,
spl0_1844,
inference(avatar_split_clause,[],[f924,f18965]) ).
fof(f18965,plain,
( spl0_1844
<=> ! [X25,X9,X10] :
( ~ c_less(X25,X10,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f924,axiom,
! [X10,X9,X25] :
( ~ c_less(X25,X10,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f18963,plain,
spl0_1843,
inference(avatar_split_clause,[],[f919,f18961]) ).
fof(f18961,plain,
( spl0_1843
<=> ! [X9,X25,X10] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f919,axiom,
! [X10,X9,X25] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f18959,plain,
spl0_1842,
inference(avatar_split_clause,[],[f916,f18957]) ).
fof(f18957,plain,
( spl0_1842
<=> ! [X9,X25,X10] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f916,axiom,
! [X10,X9,X25] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f18955,plain,
spl0_1841,
inference(avatar_split_clause,[],[f779,f18953]) ).
fof(f18953,plain,
( spl0_1841
<=> ! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Oab__group__add(X17)
| c_uminus(X16,X17) != c_Numeral_Onumber__of(X36,X17)
| c_uminus(c_Numeral_Onumber__of(X36,X17),X17) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f779,axiom,
! [X36,X16,X17] :
( ~ class_Numeral_Onumber(X17)
| ~ class_OrderedGroup_Oab__group__add(X17)
| c_uminus(X16,X17) != c_Numeral_Onumber__of(X36,X17)
| c_uminus(c_Numeral_Onumber__of(X36,X17),X17) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f18951,plain,
spl0_1840,
inference(avatar_split_clause,[],[f680,f18949]) ).
fof(f18949,plain,
( spl0_1840
<=> ! [X11,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f680,axiom,
! [X11,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f18947,plain,
spl0_1839,
inference(avatar_split_clause,[],[f679,f18945]) ).
fof(f18945,plain,
( spl0_1839
<=> ! [X11,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f679,axiom,
! [X11,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f18943,plain,
spl0_1838,
inference(avatar_split_clause,[],[f571,f18941]) ).
fof(f18941,plain,
( spl0_1838
<=> ! [X41,X11,X13,X8] :
( X8 = X11
| c_List_Oremove1(X11,c_List_Olist_OCons(X8,X41,X13),X13) = c_List_Olist_OCons(X8,c_List_Oremove1(X11,X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f571,axiom,
! [X41,X11,X8,X13] :
( X8 = X11
| c_List_Oremove1(X11,c_List_Olist_OCons(X8,X41,X13),X13) = c_List_Olist_OCons(X8,c_List_Oremove1(X11,X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f18939,plain,
spl0_1837,
inference(avatar_split_clause,[],[f554,f18937]) ).
fof(f18937,plain,
( spl0_1837
<=> ! [X52,X9,X24] :
( ~ c_less(c_plus(X24,X9,tc_nat),X52,tc_nat)
| c_plus(X24,X9,tc_nat) = c_List_Onth(c_List_Oupt(X24,X52),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f554,axiom,
! [X9,X52,X24] :
( ~ c_less(c_plus(X24,X9,tc_nat),X52,tc_nat)
| c_plus(X24,X9,tc_nat) = c_List_Onth(c_List_Oupt(X24,X52),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f18935,plain,
spl0_1836,
inference(avatar_split_clause,[],[f547,f18933]) ).
fof(f18933,plain,
( spl0_1836
<=> ! [X42,X41,X10,X3] : c_List_Onth(c_append(X41,X42,X3),c_plus(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat),X3) = c_List_Onth(X42,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f547,axiom,
! [X41,X3,X10,X42] : c_List_Onth(c_append(X41,X42,X3),c_plus(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat),X3) = c_List_Onth(X42,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f18931,plain,
spl0_1835,
inference(avatar_split_clause,[],[f480,f18929]) ).
fof(f18929,plain,
( spl0_1835
<=> ! [X53,X13,X58,X15] :
( c_in(X15,c_List_Oset(X58,X13),X13)
| c_List_Olist__inter(c_List_Olist_OCons(X15,X53,X13),X58,X13) = c_List_Olist__inter(X53,X58,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f480,axiom,
! [X58,X15,X53,X13] :
( c_in(X15,c_List_Oset(X58,X13),X13)
| c_List_Olist__inter(c_List_Olist_OCons(X15,X53,X13),X58,X13) = c_List_Olist__inter(X53,X58,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f18926,plain,
spl0_1834,
inference(avatar_split_clause,[],[f449,f18924]) ).
fof(f18924,plain,
( spl0_1834
<=> ! [X41,X3,X42] : c_Nat_Osize(c_append(X41,X42,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_Nat_Osize(X42,tc_List_Olist(X3)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f449,axiom,
! [X41,X3,X42] : c_Nat_Osize(c_append(X41,X42,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_Nat_Osize(X42,tc_List_Olist(X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f18920,plain,
spl0_1833,
inference(avatar_split_clause,[],[f367,f18918]) ).
fof(f367,axiom,
! [X41,X3,X11,X8,X42] :
( X8 = X11
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f18914,plain,
spl0_1832,
inference(avatar_split_clause,[],[f366,f18912]) ).
fof(f366,axiom,
! [X41,X3,X11,X8,X42] :
( X41 = X42
| c_append(X41,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) != c_append(X42,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f18910,plain,
spl0_1831,
inference(avatar_split_clause,[],[f331,f18908]) ).
fof(f331,axiom,
! [X11,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f18906,plain,
spl0_1830,
inference(avatar_split_clause,[],[f330,f18904]) ).
fof(f18904,plain,
( spl0_1830
<=> ! [X11,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f330,axiom,
! [X11,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f18902,plain,
spl0_1829,
inference(avatar_split_clause,[],[f323,f18900]) ).
fof(f18900,plain,
( spl0_1829
<=> ! [X16,X15] :
( c_0 = X15
| c_plus(c_div(X16,X15,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f323,axiom,
! [X16,X15] :
( c_0 = X15
| c_plus(c_div(X16,X15,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f18898,plain,
spl0_1828,
inference(avatar_split_clause,[],[f322,f18896]) ).
fof(f18896,plain,
( spl0_1828
<=> ! [X16,X15] :
( c_0 = X15
| c_div(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_plus(c_div(X16,X15,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f322,axiom,
! [X16,X15] :
( c_0 = X15
| c_div(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_plus(c_div(X16,X15,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f18894,plain,
spl0_1827,
inference(avatar_split_clause,[],[f142,f18892]) ).
fof(f18892,plain,
( spl0_1827
<=> ! [X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_lessequals(c_Finite__Set_OMin(X27,X17),c_Finite__Set_OMax(X27,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f142,axiom,
! [X27,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X17))
| c_lessequals(c_Finite__Set_OMin(X27,X17),c_Finite__Set_OMax(X27,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f18890,plain,
spl0_1826,
inference(avatar_split_clause,[],[f138,f18888]) ).
fof(f18888,plain,
( spl0_1826
<=> ! [X34,X3,X33] :
( ~ c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f138,axiom,
! [X3,X34,X33] :
( ~ c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f18875,plain,
( ~ spl0_1825
| ~ spl0_109
| ~ spl0_1673 ),
inference(avatar_split_clause,[],[f18636,f15760,f3695,f18872]) ).
fof(f18872,plain,
( spl0_1825
<=> c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f15760,plain,
( spl0_1673
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f18636,plain,
( ~ c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1673 ),
inference(superposition,[],[f15761,f3697]) ).
fof(f15761,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1673 ),
inference(avatar_component_clause,[],[f15760]) ).
fof(f18403,plain,
( ~ spl0_1824
| ~ spl0_109
| ~ spl0_1662 ),
inference(avatar_split_clause,[],[f18244,f15716,f3695,f18400]) ).
fof(f18400,plain,
( spl0_1824
<=> c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f15716,plain,
( spl0_1662
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f18244,plain,
( ~ c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_1662 ),
inference(superposition,[],[f15717,f3697]) ).
fof(f15717,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1662 ),
inference(avatar_component_clause,[],[f15716]) ).
fof(f18014,plain,
( spl0_1823
| ~ spl0_115
| ~ spl0_766
| ~ spl0_1467 ),
inference(avatar_split_clause,[],[f13309,f12900,f7136,f3722,f18011]) ).
fof(f18011,plain,
( spl0_1823
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f12900,plain,
( spl0_1467
<=> ! [X52,X24] :
( ~ c_less(X24,X52,tc_nat)
| c_List_Olast(c_List_Oupt(X24,X52),tc_nat) = c_minus(X52,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f13309,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_115
| ~ spl0_766
| ~ spl0_1467 ),
inference(forward_demodulation,[],[f13292,f7137]) ).
fof(f13292,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_115
| ~ spl0_1467 ),
inference(resolution,[],[f12901,f3724]) ).
fof(f12901,plain,
( ! [X52,X24] :
( ~ c_less(X24,X52,tc_nat)
| c_List_Olast(c_List_Oupt(X24,X52),tc_nat) = c_minus(X52,c_1,tc_nat) )
| ~ spl0_1467 ),
inference(avatar_component_clause,[],[f12900]) ).
fof(f18004,plain,
spl0_1822,
inference(avatar_split_clause,[],[f3154,f18002]) ).
fof(f18002,plain,
( spl0_1822
<=> ! [X8,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f3154,plain,
! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2951,f964]) ).
fof(f964,axiom,
! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f2951,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f163,f979]) ).
fof(f163,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f18000,plain,
spl0_1821,
inference(avatar_split_clause,[],[f3152,f17998]) ).
fof(f17998,plain,
( spl0_1821
<=> ! [X11,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f3152,plain,
! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f2949,f964]) ).
fof(f2949,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3) ),
inference(definition_unfolding,[],[f175,f979]) ).
fof(f175,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X11)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f17996,plain,
spl0_1820,
inference(avatar_split_clause,[],[f3144,f17994]) ).
fof(f17994,plain,
( spl0_1820
<=> ! [X8,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f3144,plain,
! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2943,f964]) ).
fof(f2943,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f162,f979]) ).
fof(f162,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f17992,plain,
spl0_1819,
inference(avatar_split_clause,[],[f3142,f17990]) ).
fof(f17990,plain,
( spl0_1819
<=> ! [X11,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f3142,plain,
! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f2941,f964]) ).
fof(f2941,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X3),X3) ),
inference(definition_unfolding,[],[f174,f979]) ).
fof(f174,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X11)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f17988,plain,
spl0_1818,
inference(avatar_split_clause,[],[f3110,f17986]) ).
fof(f17986,plain,
( spl0_1818
<=> ! [X8,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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f3110,plain,
! [X3,X8] :
( ~ 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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X8,X3) ),
inference(forward_demodulation,[],[f2917,f1006]) ).
fof(f2917,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X8,X3)
| ~ 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,X8)),X3),X3) ),
inference(definition_unfolding,[],[f186,f979]) ).
fof(f186,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X8,X3)
| ~ 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(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f17979,plain,
( spl0_1817
| ~ spl0_1538
| ~ spl0_1816 ),
inference(avatar_split_clause,[],[f17975,f17972,f13937,f17977]) ).
fof(f17977,plain,
( spl0_1817
<=> ! [X11,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f17972,plain,
( spl0_1816
<=> ! [X11,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f17975,plain,
( ! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3) )
| ~ spl0_1538
| ~ spl0_1816 ),
inference(forward_demodulation,[],[f17973,f13939]) ).
fof(f17973,plain,
( ! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3) )
| ~ spl0_1816 ),
inference(avatar_component_clause,[],[f17972]) ).
fof(f17974,plain,
spl0_1816,
inference(avatar_split_clause,[],[f3109,f17972]) ).
fof(f3109,plain,
! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2916,f1006]) ).
fof(f2916,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f190,f979]) ).
fof(f190,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f17970,plain,
spl0_1815,
inference(avatar_split_clause,[],[f3104,f17968]) ).
fof(f17968,plain,
( spl0_1815
<=> ! [X8,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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f3104,plain,
! [X3,X8] :
( 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,X8)),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X8,X3) ),
inference(forward_demodulation,[],[f2913,f1006]) ).
fof(f2913,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X8,X3)
| 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,X8)),X3),X3) ),
inference(definition_unfolding,[],[f185,f979]) ).
fof(f185,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X8,X3)
| 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(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f17957,plain,
( spl0_1814
| ~ spl0_1538
| ~ spl0_1813 ),
inference(avatar_split_clause,[],[f17953,f17950,f13937,f17955]) ).
fof(f17955,plain,
( spl0_1814
<=> ! [X11,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f17950,plain,
( spl0_1813
<=> ! [X11,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f17953,plain,
( ! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OMin),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3) )
| ~ spl0_1538
| ~ spl0_1813 ),
inference(forward_demodulation,[],[f17951,f13939]) ).
fof(f17951,plain,
( ! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3) )
| ~ spl0_1813 ),
inference(avatar_component_clause,[],[f17950]) ).
fof(f17952,plain,
spl0_1813,
inference(avatar_split_clause,[],[f3103,f17950]) ).
fof(f3103,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2912,f1006]) ).
fof(f2912,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
inference(definition_unfolding,[],[f189,f979]) ).
fof(f189,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f17946,plain,
( spl0_1812
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1811 ),
inference(avatar_split_clause,[],[f17942,f17939,f10431,f3421,f17944]) ).
fof(f17944,plain,
( spl0_1812
<=> ! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f17939,plain,
( spl0_1811
<=> ! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f17942,plain,
( ! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1811 ),
inference(forward_demodulation,[],[f17940,f11307]) ).
fof(f17940,plain,
( ! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1811 ),
inference(avatar_component_clause,[],[f17939]) ).
fof(f17941,plain,
spl0_1811,
inference(avatar_split_clause,[],[f3074,f17939]) ).
fof(f3074,plain,
! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3073,f1006]) ).
fof(f3073,plain,
! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3072,f1004]) ).
fof(f3072,plain,
! [X36] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1123,f1006]) ).
fof(f1123,axiom,
! [X36] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f17935,plain,
( spl0_1809
| spl0_1810
| ~ spl0_720
| ~ spl0_1460 ),
inference(avatar_split_clause,[],[f13206,f12872,f6938,f17933,f17930]) ).
fof(f17930,plain,
( spl0_1809
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f13206,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_720
| ~ spl0_1460 ),
inference(resolution,[],[f12873,f6939]) ).
fof(f17928,plain,
( spl0_1808
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1807 ),
inference(avatar_split_clause,[],[f17924,f17921,f10431,f3421,f17926]) ).
fof(f17926,plain,
( spl0_1808
<=> ! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f17921,plain,
( spl0_1807
<=> ! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f17924,plain,
( ! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_53
| ~ spl0_1344
| ~ spl0_1807 ),
inference(forward_demodulation,[],[f17922,f11307]) ).
fof(f17922,plain,
( ! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1807 ),
inference(avatar_component_clause,[],[f17921]) ).
fof(f17923,plain,
spl0_1807,
inference(avatar_split_clause,[],[f3070,f17921]) ).
fof(f3070,plain,
! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3069,f1006]) ).
fof(f3069,plain,
! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3068,f1004]) ).
fof(f3068,plain,
! [X36] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1122,f1006]) ).
fof(f1122,axiom,
! [X36] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,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/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f17918,plain,
( spl0_1806
| ~ spl0_1538
| ~ spl0_1805 ),
inference(avatar_split_clause,[],[f17914,f17911,f13937,f17916]) ).
fof(f17916,plain,
( spl0_1806
<=> ! [X36,X3] :
( c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_OMin),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f17911,plain,
( spl0_1805
<=> ! [X36,X3] :
( c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f17914,plain,
( ! [X3,X36] :
( c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_OMin),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_1538
| ~ spl0_1805 ),
inference(forward_demodulation,[],[f17912,f13939]) ).
fof(f17912,plain,
( ! [X3,X36] :
( c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_1805 ),
inference(avatar_component_clause,[],[f17911]) ).
fof(f17913,plain,
spl0_1805,
inference(avatar_split_clause,[],[f3039,f17911]) ).
fof(f3039,plain,
! [X3,X36] :
( c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f2850,f1006]) ).
fof(f2850,plain,
! [X3,X36] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3) ),
inference(definition_unfolding,[],[f182,f979]) ).
fof(f182,axiom,
! [X3,X36] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f17909,plain,
spl0_1804,
inference(avatar_split_clause,[],[f3038,f17907]) ).
fof(f17907,plain,
( spl0_1804
<=> ! [X3,X35] :
( c_minus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f3038,plain,
! [X3,X35] :
( c_minus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X35)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f2849,f1006]) ).
fof(f2849,plain,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = 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,X35)),X3) ),
inference(definition_unfolding,[],[f181,f979]) ).
fof(f181,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_minus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X35)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f17905,plain,
spl0_1803,
inference(avatar_split_clause,[],[f3000,f17903]) ).
fof(f17903,plain,
( spl0_1803
<=> ! [X10] : c_plus(X10,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),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f3000,plain,
! [X10] : c_plus(X10,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),X10,tc_nat),
inference(forward_demodulation,[],[f2999,f1006]) ).
fof(f2999,plain,
! [X10] : c_plus(X10,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),X10,tc_nat),
inference(forward_demodulation,[],[f2998,f1004]) ).
fof(f2998,plain,
! [X10] : c_plus(X10,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),X10,tc_nat),
inference(forward_demodulation,[],[f2997,f1006]) ).
fof(f2997,plain,
! [X10] : 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),X10,tc_nat) = c_plus(X10,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2821,f2996]) ).
fof(f2821,plain,
! [X10] : 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),X10,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f731,f1394,f1394]) ).
fof(f731,axiom,
! [X10] : 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),X10,tc_nat) = c_Suc(c_Suc(X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f17883,plain,
( spl0_1802
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1801 ),
inference(avatar_split_clause,[],[f17879,f17876,f10415,f10092,f6703,f3695,f17881]) ).
fof(f17881,plain,
( spl0_1802
<=> ! [X36] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f17876,plain,
( spl0_1801
<=> ! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f17879,plain,
( ! [X36] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1801 ),
inference(forward_demodulation,[],[f17877,f11235]) ).
fof(f17877,plain,
( ! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1801 ),
inference(avatar_component_clause,[],[f17876]) ).
fof(f17878,plain,
spl0_1801,
inference(avatar_split_clause,[],[f2895,f17876]) ).
fof(f2895,plain,
! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f673,f1394]) ).
fof(f673,axiom,
! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X36,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X36),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f17874,plain,
( spl0_1800
| ~ spl0_807
| ~ spl0_1452 ),
inference(avatar_split_clause,[],[f12844,f11791,f7307,f17872]) ).
fof(f17872,plain,
( spl0_1800
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f11791,plain,
( spl0_1452
<=> ! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f12844,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_807
| ~ spl0_1452 ),
inference(superposition,[],[f7308,f11792]) ).
fof(f11792,plain,
( ! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X8
| ~ spl0_1452 ),
inference(avatar_component_clause,[],[f11791]) ).
fof(f17870,plain,
spl0_1799,
inference(avatar_split_clause,[],[f2826,f17868]) ).
fof(f2826,plain,
! [X3,X11,X9,X24] : c_List_Oreplicate(c_Orderings_Omin(X24,X9,tc_nat),X11,X3) = c_List_Osublist(c_List_Oreplicate(X9,X11,X3),c_SetInterval_OlessThan(X24,tc_nat),X3),
inference(definition_unfolding,[],[f625,f616]) ).
fof(f625,axiom,
! [X3,X11,X9,X24] : c_List_Otake(X24,c_List_Oreplicate(X9,X11,X3),X3) = c_List_Oreplicate(c_Orderings_Omin(X24,X9,tc_nat),X11,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f17866,plain,
spl0_1798,
inference(avatar_split_clause,[],[f2824,f17864]) ).
fof(f2824,plain,
! [X41,X3,X10] : c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) = c_Nat_Osize(c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3),tc_List_Olist(X3)),
inference(definition_unfolding,[],[f461,f616]) ).
fof(f461,axiom,
! [X41,X10,X3] : c_Nat_Osize(c_List_Otake(X10,X41,X3),tc_List_Olist(X3)) = c_Orderings_Omin(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f17862,plain,
spl0_1797,
inference(avatar_split_clause,[],[f2820,f17860]) ).
fof(f2820,plain,
! [X31,X3,X15] : c_Inter(c_insert(X15,X31,tc_set(X3)),X3) = c_Relation_OImage(c_Relation_Odiag(X15,X3),c_Inter(X31,X3),X3,X3),
inference(definition_unfolding,[],[f1473,f1223]) ).
fof(f1473,axiom,
! [X31,X3,X15] : c_Inter(c_insert(X15,X31,tc_set(X3)),X3) = c_inter(X15,c_Inter(X31,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f17857,plain,
( spl0_1796
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1795 ),
inference(avatar_split_clause,[],[f17853,f17850,f10415,f10092,f6703,f3695,f17855]) ).
fof(f17855,plain,
( spl0_1796
<=> ! [X17,X9,X3,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f17850,plain,
( spl0_1795
<=> ! [X17,X9,X3,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f17853,plain,
( ! [X3,X9,X17,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1795 ),
inference(forward_demodulation,[],[f17851,f11235]) ).
fof(f17851,plain,
( ! [X3,X9,X17,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17)
| ~ spl0_1795 ),
inference(avatar_component_clause,[],[f17850]) ).
fof(f17852,plain,
spl0_1795,
inference(avatar_split_clause,[],[f2819,f17850]) ).
fof(f2819,plain,
! [X3,X9,X17,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17),
inference(definition_unfolding,[],[f57,f1394]) ).
fof(f57,axiom,
! [X3,X9,X17,X24] : c_Datatype__Universe_ONumb(X24,X3,X17) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_ONumb(X24,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f17847,plain,
( spl0_1794
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1793 ),
inference(avatar_split_clause,[],[f17843,f17840,f10415,f10092,f6703,f3695,f17845]) ).
fof(f17845,plain,
( spl0_1794
<=> ! [X15,X17,X9,X3] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f17840,plain,
( spl0_1793
<=> ! [X15,X17,X9,X3] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f17843,plain,
( ! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1793 ),
inference(forward_demodulation,[],[f17841,f11235]) ).
fof(f17841,plain,
( ! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17)
| ~ spl0_1793 ),
inference(avatar_component_clause,[],[f17840]) ).
fof(f17842,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2818,f17840]) ).
fof(f2818,plain,
! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17),
inference(definition_unfolding,[],[f56,f1394]) ).
fof(f56,axiom,
! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OLeaf(X15,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f17837,plain,
( spl0_1792
| ~ spl0_1136
| ~ spl0_1410 ),
inference(avatar_split_clause,[],[f12524,f11569,f9223,f17835]) ).
fof(f17835,plain,
( spl0_1792
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f9223,plain,
( spl0_1136
<=> ! [X16,X17,X3,X15] : c_0 = c_Nat_Osize(c_Pair(X15,X16,X3,X17),tc_prod(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f12524,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1136
| ~ spl0_1410 ),
inference(superposition,[],[f9224,f11570]) ).
fof(f9224,plain,
( ! [X3,X16,X17,X15] : c_0 = c_Nat_Osize(c_Pair(X15,X16,X3,X17),tc_prod(X3,X17))
| ~ spl0_1136 ),
inference(avatar_component_clause,[],[f9223]) ).
fof(f17833,plain,
( spl0_1791
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1790 ),
inference(avatar_split_clause,[],[f17829,f17826,f10415,f10092,f6703,f3695,f17831]) ).
fof(f17831,plain,
( spl0_1791
<=> ! [X15,X17,X9,X3] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f17826,plain,
( spl0_1790
<=> ! [X15,X17,X9,X3] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f17829,plain,
( ! [X3,X9,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1790 ),
inference(forward_demodulation,[],[f17827,f11235]) ).
fof(f17827,plain,
( ! [X3,X9,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17)
| ~ spl0_1790 ),
inference(avatar_component_clause,[],[f17826]) ).
fof(f17828,plain,
spl0_1790,
inference(avatar_split_clause,[],[f2817,f17826]) ).
fof(f2817,plain,
! [X3,X9,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17),
inference(definition_unfolding,[],[f53,f1394]) ).
fof(f53,axiom,
! [X3,X9,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OAtom(X15,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f17824,plain,
spl0_1789,
inference(avatar_split_clause,[],[f2806,f17822]) ).
fof(f17822,plain,
( spl0_1789
<=> ! [X20,X3,X15] : c_in(c_Pair(X15,X15,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f2806,plain,
! [X3,X15,X20] : c_in(c_Pair(X15,X15,X3,X3),c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),tc_prod(X3,X3)),
inference(definition_unfolding,[],[f1697,f1566]) ).
fof(f1697,axiom,
! [X3,X15,X20] : c_in(c_Pair(X15,X15,X3,X3),c_Transitive__Closure_Ortrancl(X20,X3),tc_prod(X3,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f17820,plain,
spl0_1788,
inference(avatar_split_clause,[],[f2804,f17818]) ).
fof(f17818,plain,
( spl0_1788
<=> ! [X20,X3] : c_union(c_Transitive__Closure_Otrancl(X20,X3),c_Relation_OId,tc_prod(X3,X3)) = c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f2804,plain,
! [X3,X20] : c_union(c_Transitive__Closure_Otrancl(X20,X3),c_Relation_OId,tc_prod(X3,X3)) = c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),
inference(definition_unfolding,[],[f1558,f1566]) ).
fof(f1558,axiom,
! [X3,X20] : c_union(c_Transitive__Closure_Otrancl(X20,X3),c_Relation_OId,tc_prod(X3,X3)) = c_Transitive__Closure_Ortrancl(X20,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f17797,plain,
( spl0_1787
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1786 ),
inference(avatar_split_clause,[],[f17793,f17790,f10415,f10092,f6703,f3695,f17795]) ).
fof(f17790,plain,
( spl0_1786
<=> ! [X25,X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f17793,plain,
( ! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1786 ),
inference(forward_demodulation,[],[f17791,f11235]) ).
fof(f17791,plain,
( ! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1786 ),
inference(avatar_component_clause,[],[f17790]) ).
fof(f17792,plain,
spl0_1786,
inference(avatar_split_clause,[],[f2797,f17790]) ).
fof(f2797,plain,
! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f877,f1394,f1394]) ).
fof(f877,axiom,
! [X10,X25] : c_plus(X25,c_Suc(X10),tc_nat) = c_Suc(c_plus(X25,X10,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f17707,plain,
( spl0_1785
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1784 ),
inference(avatar_split_clause,[],[f17703,f17699,f10415,f10092,f6703,f3695,f17705]) ).
fof(f17705,plain,
( spl0_1785
<=> ! [X25,X10] : c_plus(c_plus(c_1,X25,tc_nat),X10,tc_nat) = c_plus(c_1,c_plus(X25,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f17699,plain,
( spl0_1784
<=> ! [X25,X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f17703,plain,
( ! [X10,X25] : c_plus(c_plus(c_1,X25,tc_nat),X10,tc_nat) = c_plus(c_1,c_plus(X25,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1784 ),
inference(forward_demodulation,[],[f17702,f11235]) ).
fof(f17702,plain,
( ! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X25,tc_nat),X10,tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1784 ),
inference(forward_demodulation,[],[f17700,f11235]) ).
fof(f17700,plain,
( ! [X10,X25] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X25,X10,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat)
| ~ spl0_1784 ),
inference(avatar_component_clause,[],[f17699]) ).
fof(f17701,plain,
spl0_1784,
inference(avatar_split_clause,[],[f2796,f17699]) ).
fof(f17697,plain,
( spl0_1783
| ~ spl0_110
| ~ spl0_1128
| ~ spl0_1207 ),
inference(avatar_split_clause,[],[f9902,f9513,f9126,f3700,f17695]) ).
fof(f9126,plain,
( spl0_1128
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f9902,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1128
| ~ spl0_1207 ),
inference(forward_demodulation,[],[f9899,f9127]) ).
fof(f9127,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f9126]) ).
fof(f9899,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_110
| ~ spl0_1207 ),
inference(superposition,[],[f9514,f3702]) ).
fof(f17671,plain,
( spl0_1782
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1781 ),
inference(avatar_split_clause,[],[f17667,f17663,f10415,f10092,f6703,f3695,f17669]) ).
fof(f17669,plain,
( spl0_1782
<=> ! [X25,X10] : c_minus(X25,X10,tc_nat) = c_minus(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f17663,plain,
( spl0_1781
<=> ! [X25,X10] : c_minus(X25,X10,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f17667,plain,
( ! [X10,X25] : c_minus(X25,X10,tc_nat) = c_minus(c_plus(c_1,X25,tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f17666,f11235]) ).
fof(f17666,plain,
( ! [X10,X25] : c_minus(X25,X10,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f17664,f11235]) ).
fof(f17664,plain,
( ! [X10,X25] : c_minus(X25,X10,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1781 ),
inference(avatar_component_clause,[],[f17663]) ).
fof(f17665,plain,
spl0_1781,
inference(avatar_split_clause,[],[f2795,f17663]) ).
fof(f2795,plain,
! [X10,X25] : c_minus(X25,X10,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f885,f1394,f1394]) ).
fof(f885,axiom,
! [X10,X25] : c_minus(X25,X10,tc_nat) = c_minus(c_Suc(X25),c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f17661,plain,
spl0_1780,
inference(avatar_split_clause,[],[f1691,f17659]) ).
fof(f17659,plain,
( spl0_1780
<=> ! [X17,X31,X16,X27,X3] :
( ~ c_in(X16,X31,X3)
| c_in(c_Sum__Type_OInr(X16,X3,X17),c_Sum__Type_OPlus(X27,X31,X17,X3),tc_sum(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f1691,axiom,
! [X31,X3,X16,X27,X17] :
( ~ c_in(X16,X31,X3)
| c_in(c_Sum__Type_OInr(X16,X3,X17),c_Sum__Type_OPlus(X27,X31,X17,X3),tc_sum(X17,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f17657,plain,
spl0_1779,
inference(avatar_split_clause,[],[f1690,f17655]) ).
fof(f17655,plain,
( spl0_1779
<=> ! [X15,X17,X31,X27,X3] :
( ~ c_in(X15,X27,X3)
| c_in(c_Sum__Type_OInl(X15,X3,X17),c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f1690,axiom,
! [X31,X3,X27,X17,X15] :
( ~ c_in(X15,X27,X3)
| c_in(c_Sum__Type_OInl(X15,X3,X17),c_Sum__Type_OPlus(X27,X31,X3,X17),tc_sum(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f17653,plain,
spl0_1778,
inference(avatar_split_clause,[],[f1653,f17651]) ).
fof(f1653,axiom,
! [X3,X16,X17,X15,X20] :
( c_in(X16,c_Relation_ORange(X20,X3,X17),X17)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f17649,plain,
spl0_1777,
inference(avatar_split_clause,[],[f1649,f17647]) ).
fof(f17647,plain,
( spl0_1777
<=> ! [X17,X16,X20,X27,X3] :
( ~ c_in(X16,c_Relation_OImage(X20,X27,X17,X3),X3)
| c_in(c_Main_OImageE__1(X27,X16,X20,X17,X3),X27,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f1649,axiom,
! [X3,X16,X27,X17,X20] :
( ~ c_in(X16,c_Relation_OImage(X20,X27,X17,X3),X3)
| c_in(c_Main_OImageE__1(X27,X16,X20,X17,X3),X27,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f17645,plain,
spl0_1776,
inference(avatar_split_clause,[],[f1648,f17643]) ).
fof(f17643,plain,
( spl0_1776
<=> ! [X40,X3] :
( ~ c_in(X40,c_Relation_OId,tc_prod(X3,X3))
| c_Pair(c_Main_OIdE__1(X40,X3),c_Main_OIdE__1(X40,X3),X3,X3) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f1648,axiom,
! [X40,X3] :
( ~ c_in(X40,c_Relation_OId,tc_prod(X3,X3))
| c_Pair(c_Main_OIdE__1(X40,X3),c_Main_OIdE__1(X40,X3),X3,X3) = X40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f17641,plain,
spl0_1775,
inference(avatar_split_clause,[],[f1647,f17639]) ).
fof(f1647,axiom,
! [X3,X16,X17,X15,X20] :
( c_in(X15,c_Relation_ODomain(X20,X3,X17),X3)
| ~ c_in(c_Pair(X15,X16,X3,X17),X20,tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f17637,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1635,f17635]) ).
fof(f17635,plain,
( spl0_1774
<=> ! [X11,X27,X3,X74] :
( c_in(X74,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_List_Olist_OCons(X11,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1635,axiom,
! [X3,X11,X27,X74] :
( c_in(X74,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_List_Olist_OCons(X11,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f17633,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1623,f17631]) ).
fof(f17631,plain,
( spl0_1773
<=> ! [X41,X30,X27,X3] :
( c_in(X30,X27,X3)
| ~ c_in(X30,c_List_Oset(X41,X3),X3)
| ~ c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1623,axiom,
! [X3,X41,X27,X30] :
( c_in(X30,X27,X3)
| ~ c_in(X30,c_List_Oset(X41,X3),X3)
| ~ c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f17629,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1547,f17627]) ).
fof(f17627,plain,
( spl0_1772
<=> ! [X27,X11,X3] :
( ~ c_lessequals(X27,c_insert(X11,c_emptyset,X3),tc_set(X3))
| c_insert(X11,X27,X3) = c_insert(X11,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1547,axiom,
! [X3,X11,X27] :
( ~ c_lessequals(X27,c_insert(X11,c_emptyset,X3),tc_set(X3))
| c_insert(X11,X27,X3) = c_insert(X11,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
fof(f17625,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1546,f17623]) ).
fof(f17623,plain,
( spl0_1771
<=> ! [X16,X27,X3,X15] :
( c_lessequals(X27,c_insert(X16,c_emptyset,X3),tc_set(X3))
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1546,axiom,
! [X3,X16,X27,X15] :
( c_lessequals(X27,c_insert(X16,c_emptyset,X3),tc_set(X3))
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
fof(f17621,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1540,f17619]) ).
fof(f17619,plain,
( spl0_1770
<=> ! [X31,X11,X27,X3] :
( ~ c_in(X11,X31,X3)
| ~ c_lessequals(X27,X31,tc_set(X3))
| c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1540,axiom,
! [X31,X3,X11,X27] :
( ~ c_in(X11,X31,X3)
| ~ c_lessequals(X27,X31,tc_set(X3))
| c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f17617,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1423,f17615]) ).
fof(f17615,plain,
( spl0_1769
<=> ! [X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_insert(X9,c_emptyset,X3) = c_minus(c_insert(X9,c_emptyset,X3),c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f1423,axiom,
! [X3,X9] :
( ~ class_Orderings_Oorder(X3)
| c_insert(X9,c_emptyset,X3) = c_minus(c_insert(X9,c_emptyset,X3),c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f17613,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1415,f17611]) ).
fof(f17611,plain,
( spl0_1768
<=> ! [X24,X10,X3,X25,X52] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X52,X24,X3)
| c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1415,axiom,
! [X3,X10,X52,X24,X25] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X52,X24,X3)
| c_lessequals(c_SetInterval_OatLeastLessThan(X24,X52,X3),c_SetInterval_OatLeastLessThan(X25,X10,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f17609,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1406,f17607]) ).
fof(f17607,plain,
( spl0_1767
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X74,X24,X3)
| ~ c_less(X24,X38,X3)
| c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f1406,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X74,X24,X3)
| ~ c_less(X24,X38,X3)
| c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f17605,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1403,f17603]) ).
fof(f17603,plain,
( spl0_1766
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X38,X3)
| ~ c_less(X74,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1403,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X38,X3)
| ~ c_less(X74,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f17601,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1376,f17599]) ).
fof(f17599,plain,
( spl0_1765
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X74,X24,X3)
| ~ c_less(X24,X38,X3)
| c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1376,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X74,X24,X3)
| ~ c_less(X24,X38,X3)
| c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f17597,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1371,f17595]) ).
fof(f17595,plain,
( spl0_1764
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X74,X24,X3)
| ~ c_lessequals(X24,X38,X3)
| c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1371,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X74,X24,X3)
| ~ c_lessequals(X24,X38,X3)
| c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f17593,plain,
( spl0_1762
| ~ spl0_1763
| ~ spl0_122
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9731,f9408,f3752,f17590,f17587]) ).
fof(f17587,plain,
( spl0_1762
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f17590,plain,
( spl0_1763
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f9731,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_122
| ~ spl0_1182 ),
inference(resolution,[],[f9409,f3753]) ).
fof(f17585,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1174,f17583]) ).
fof(f17583,plain,
( spl0_1761
<=> ! [X11,X3,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X11,c_0,X3)
| ~ c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1174,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X11,c_0,X3)
| ~ c_less(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f17581,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1157,f17579]) ).
fof(f17579,plain,
( spl0_1760
<=> ! [X11,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| c_Parity_Oeven(X11,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f1157,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| c_Parity_Oeven(X11,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f17577,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1155,f17575]) ).
fof(f17575,plain,
( spl0_1759
<=> ! [X11,X3] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven(X11,tc_nat)
| c_uminus(c_1,X3) = c_Nat_Opower(c_uminus(c_1,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1155,axiom,
! [X3,X11] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven(X11,tc_nat)
| c_uminus(c_1,X3) = c_Nat_Opower(c_uminus(c_1,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f17573,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1116,f17571]) ).
fof(f17571,plain,
( spl0_1758
<=> ! [X37,X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| ~ c_lessequals(X11,X37,X17)
| ~ c_lessequals(X8,X37,X17)
| c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1116,axiom,
! [X11,X37,X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ c_lessequals(X11,X37,X17)
| ~ c_lessequals(X8,X37,X17)
| c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f17569,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1111,f17567]) ).
fof(f17567,plain,
( spl0_1757
<=> ! [X37,X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| ~ c_lessequals(X11,X8,X17)
| ~ c_lessequals(X11,X37,X17)
| c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1111,axiom,
! [X11,X8,X37,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ c_lessequals(X11,X8,X17)
| ~ c_lessequals(X11,X37,X17)
| c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f17565,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1108,f17563]) ).
fof(f17563,plain,
( spl0_1756
<=> ! [X37,X11,X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_less(X37,X11,X3)
| ~ c_less(X37,X8,X3)
| c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f1108,axiom,
! [X3,X11,X37,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_less(X37,X11,X3)
| ~ c_less(X37,X8,X3)
| c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f17561,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1105,f17559]) ).
fof(f17559,plain,
( spl0_1755
<=> ! [X37,X11,X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_less(X11,X37,X3)
| ~ c_less(X8,X37,X3)
| c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1105,axiom,
! [X3,X11,X37,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_less(X11,X37,X3)
| ~ c_less(X8,X37,X3)
| c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f17557,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1087,f17555]) ).
fof(f17555,plain,
( spl0_1754
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_uminus(c_LOrder_Omeet(X15,X16,X3),X3) = c_LOrder_Ojoin(c_uminus(X15,X3),c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1087,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_uminus(c_LOrder_Omeet(X15,X16,X3),X3) = c_LOrder_Ojoin(c_uminus(X15,X3),c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f17553,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1078,f17551]) ).
fof(f17551,plain,
( spl0_1753
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_uminus(c_LOrder_Ojoin(X15,X16,X3),X3) = c_LOrder_Omeet(c_uminus(X15,X3),c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f1078,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_uminus(c_LOrder_Ojoin(X15,X16,X3),X3) = c_LOrder_Omeet(c_uminus(X15,X3),c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f17549,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1064,f17547]) ).
fof(f1064,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_plus(X15,X16,X3),X3) = c_plus(c_uminus(X15,X3),c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f17545,plain,
( spl0_1751
| ~ spl0_697
| ~ spl0_723
| ~ spl0_865
| ~ spl0_1177 ),
inference(avatar_split_clause,[],[f9718,f9388,f7540,f6950,f6841,f17542]) ).
fof(f17542,plain,
( spl0_1751
<=> 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_1751])]) ).
fof(f6841,plain,
( spl0_697
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f6950,plain,
( spl0_723
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f9718,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_697
| ~ spl0_723
| ~ spl0_865
| ~ spl0_1177 ),
inference(forward_demodulation,[],[f9717,f6843]) ).
fof(f6843,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_697 ),
inference(avatar_component_clause,[],[f6841]) ).
fof(f9717,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_723
| ~ spl0_865
| ~ spl0_1177 ),
inference(forward_demodulation,[],[f9713,f7542]) ).
fof(f9713,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_723
| ~ spl0_1177 ),
inference(superposition,[],[f9389,f6952]) ).
fof(f6952,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_723 ),
inference(avatar_component_clause,[],[f6950]) ).
fof(f17540,plain,
spl0_1750,
inference(avatar_split_clause,[],[f693,f17538]) ).
fof(f17538,plain,
( spl0_1750
<=> ! [X77,X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f693,axiom,
! [X36,X77] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f17536,plain,
spl0_1749,
inference(avatar_split_clause,[],[f686,f17534]) ).
fof(f17534,plain,
( spl0_1749
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f686,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_nat) = c_Numeral_Onumber__of(X77,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f17532,plain,
spl0_1748,
inference(avatar_split_clause,[],[f674,f17530]) ).
fof(f17530,plain,
( spl0_1748
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X77,tc_nat) = c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f674,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X77,tc_nat) = c_plus(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f17528,plain,
spl0_1747,
inference(avatar_split_clause,[],[f671,f17526]) ).
fof(f17526,plain,
( spl0_1747
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_NatArith_Oof__nat(c_times(X25,X10,tc_nat),X3) = c_times(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f671,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_NatArith_Oof__nat(c_times(X25,X10,tc_nat),X3) = c_times(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f17524,plain,
spl0_1746,
inference(avatar_split_clause,[],[f659,f17522]) ).
fof(f17522,plain,
( spl0_1746
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_NatArith_Oof__nat(c_plus(X25,X10,tc_nat),X3) = c_plus(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f659,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_NatArith_Oof__nat(c_plus(X25,X10,tc_nat),X3) = c_plus(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f17520,plain,
spl0_1745,
inference(avatar_split_clause,[],[f631,f17518]) ).
fof(f17518,plain,
( spl0_1745
<=> ! [X11,X3,X10] :
( c_0 = X10
| c_List_Otl(c_List_Oreplicate(X10,X11,X3),X3) = c_List_Oreplicate(c_minus(X10,c_1,tc_nat),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f631,axiom,
! [X3,X10,X11] :
( c_0 = X10
| c_List_Otl(c_List_Oreplicate(X10,X11,X3),X3) = c_List_Oreplicate(c_minus(X10,c_1,tc_nat),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f17516,plain,
spl0_1744,
inference(avatar_split_clause,[],[f549,f17514]) ).
fof(f17514,plain,
( spl0_1744
<=> ! [X41,X3,X8,X24] :
( ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Olist__update(X41,X24,X8,X3),X24,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f549,axiom,
! [X41,X3,X8,X24] :
( ~ c_less(X24,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Onth(c_List_Olist__update(X41,X24,X8,X3),X24,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f17512,plain,
spl0_1743,
inference(avatar_split_clause,[],[f483,f17510]) ).
fof(f17510,plain,
( spl0_1743
<=> ! [X24,X8,X3] :
( ~ c_less(X24,c_Nat_Osize(X8,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(X8,X24,c_List_Onth(X8,X24,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f483,axiom,
! [X3,X8,X24] :
( ~ c_less(X24,c_Nat_Osize(X8,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(X8,X24,c_List_Onth(X8,X24,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f17508,plain,
spl0_1742,
inference(avatar_split_clause,[],[f442,f17506]) ).
fof(f17506,plain,
( spl0_1742
<=> ! [X41,X3,X10] :
( ~ c_less(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Olast(X41,X3) = c_List_Olast(c_List_Odrop(X10,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f442,axiom,
! [X41,X10,X3] :
( ~ c_less(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_List_Olast(X41,X3) = c_List_Olast(c_List_Odrop(X10,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f17504,plain,
spl0_1741,
inference(avatar_split_clause,[],[f375,f17502]) ).
fof(f17502,plain,
( spl0_1741
<=> ! [X41,X27,X3,X42] :
( c_in(X42,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f375,axiom,
! [X3,X41,X27,X42] :
( c_in(X42,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f17500,plain,
( spl0_1740
| ~ spl0_115
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9625,f9308,f3722,f17497]) ).
fof(f17497,plain,
( spl0_1740
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f9625,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_115
| ~ spl0_1157 ),
inference(resolution,[],[f9309,f3724]) ).
fof(f17495,plain,
spl0_1739,
inference(avatar_split_clause,[],[f374,f17493]) ).
fof(f17493,plain,
( spl0_1739
<=> ! [X41,X42,X27,X3] :
( c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f374,axiom,
! [X41,X3,X27,X42] :
( c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| ~ c_in(c_append(X41,X42,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f17491,plain,
spl0_1738,
inference(avatar_split_clause,[],[f267,f17489]) ).
fof(f17489,plain,
( spl0_1738
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_times(X35,X37,tc_IntDef_Oint),X3) = c_times(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f267,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_times(X35,X37,tc_IntDef_Oint),X3) = c_times(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f17487,plain,
spl0_1737,
inference(avatar_split_clause,[],[f253,f17485]) ).
fof(f17485,plain,
( spl0_1737
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_minus(X35,X37,tc_IntDef_Oint),X3) = c_minus(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f253,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_minus(X35,X37,tc_IntDef_Oint),X3) = c_minus(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f17483,plain,
spl0_1736,
inference(avatar_split_clause,[],[f252,f17481]) ).
fof(f17481,plain,
( spl0_1736
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_plus(X35,X37,tc_IntDef_Oint),X3) = c_plus(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f252,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_plus(X35,X37,tc_IntDef_Oint),X3) = c_plus(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f17479,plain,
spl0_1735,
inference(avatar_split_clause,[],[f216,f17477]) ).
fof(f17477,plain,
( spl0_1735
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_in(X15,c_IntDef_ONats,X3)
| ~ c_in(X16,c_IntDef_ONats,X3)
| c_in(c_times(X15,X16,X3),c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f216,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_in(X15,c_IntDef_ONats,X3)
| ~ c_in(X16,c_IntDef_ONats,X3)
| c_in(c_times(X15,X16,X3),c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f17475,plain,
spl0_1734,
inference(avatar_split_clause,[],[f215,f17473]) ).
fof(f17473,plain,
( spl0_1734
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_in(X15,c_IntDef_ONats,X3)
| ~ c_in(X16,c_IntDef_ONats,X3)
| c_in(c_plus(X15,X16,X3),c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f215,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_in(X15,c_IntDef_ONats,X3)
| ~ c_in(X16,c_IntDef_ONats,X3)
| c_in(c_plus(X15,X16,X3),c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f17471,plain,
spl0_1733,
inference(avatar_split_clause,[],[f212,f17469]) ).
fof(f17469,plain,
( spl0_1733
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_times(X15,X16,X3),c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f212,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_times(X15,X16,X3),c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f17467,plain,
spl0_1732,
inference(avatar_split_clause,[],[f210,f17465]) ).
fof(f17465,plain,
( spl0_1732
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_minus(X15,X16,X3),c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f210,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_minus(X15,X16,X3),c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f17463,plain,
spl0_1731,
inference(avatar_split_clause,[],[f209,f17461]) ).
fof(f17461,plain,
( spl0_1731
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_plus(X15,X16,X3),c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f209,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| ~ c_in(X16,c_IntDef_OInts,X3)
| c_in(c_plus(X15,X16,X3),c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f17459,plain,
spl0_1730,
inference(avatar_split_clause,[],[f156,f17457]) ).
fof(f17457,plain,
( spl0_1730
<=> ! [X9,X25,X10] :
( ~ c_Divides_Oop_Advd(X9,X10,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X25,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f156,axiom,
! [X10,X9,X25] :
( ~ c_Divides_Oop_Advd(X9,X10,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X25,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f17455,plain,
( spl0_1729
| ~ spl0_774
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f9122,f8838,f7168,f17453]) ).
fof(f17453,plain,
( spl0_1729
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f7168,plain,
( spl0_774
<=> ! [X8] : c_minus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f8838,plain,
( spl0_1090
<=> ! [X25,X10] :
( c_lessequals(X25,X10,tc_nat)
| c_0 != c_minus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f9122,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_774
| ~ spl0_1090 ),
inference(superposition,[],[f8839,f7169]) ).
fof(f7169,plain,
( ! [X8] : c_minus(X8,c_0,tc_nat) = X8
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7168]) ).
fof(f8839,plain,
( ! [X10,X25] :
( c_0 != c_minus(X25,X10,tc_nat)
| c_lessequals(X25,X10,tc_nat) )
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f8838]) ).
fof(f17451,plain,
spl0_1728,
inference(avatar_split_clause,[],[f140,f17449]) ).
fof(f17449,plain,
( spl0_1728
<=> ! [X20,X17,X3] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X17,X3)))
| c_in(c_Relation_Oconverse(X20,X17,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f140,axiom,
! [X3,X17,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X17,X3)))
| c_in(c_Relation_Oconverse(X20,X17,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f17447,plain,
spl0_1727,
inference(avatar_split_clause,[],[f139,f17445]) ).
fof(f17445,plain,
( spl0_1727
<=> ! [X20,X17,X3] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X17,X3)))
| ~ c_in(c_Relation_Oconverse(X20,X17,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f139,axiom,
! [X3,X17,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X17,X3)))
| ~ c_in(c_Relation_Oconverse(X20,X17,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f17443,plain,
spl0_1726,
inference(avatar_split_clause,[],[f9,f17441]) ).
fof(f17441,plain,
( spl0_1726
<=> ! [X2,X4,X7,X0,X3,X1] : c_Tarski_Opotype_Omore__update(X7,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X4,X3) = c_Tarski_Opotype_Opotype__ext(X0,X1,X7,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X7,X4] : c_Tarski_Opotype_Omore__update(X7,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X4,X3) = c_Tarski_Opotype_Opotype__ext(X0,X1,X7,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__3_0) ).
fof(f17439,plain,
spl0_1725,
inference(avatar_split_clause,[],[f8,f17437]) ).
fof(f17437,plain,
( spl0_1725
<=> ! [X3,X4,X0,X6,X2,X1] : c_Tarski_Opotype_Oorder__update(X6,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X3,X4) = c_Tarski_Opotype_Opotype__ext(X0,X6,X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X6,X4] : c_Tarski_Opotype_Oorder__update(X6,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X3,X4) = c_Tarski_Opotype_Opotype__ext(X0,X6,X2,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__2_0) ).
fof(f17435,plain,
spl0_1724,
inference(avatar_split_clause,[],[f7,f17433]) ).
fof(f17433,plain,
( spl0_1724
<=> ! [X5,X4,X0,X3,X2,X1] : c_Tarski_Opotype_Opset__update(X5,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X3,X4) = c_Tarski_Opotype_Opotype__ext(X5,X1,X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] : c_Tarski_Opotype_Opset__update(X5,c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4),X3,X4) = c_Tarski_Opotype_Opotype__ext(X5,X1,X2,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__1_0) ).
fof(f17363,plain,
( spl0_1723
| ~ spl0_853
| ~ spl0_1019 ),
inference(avatar_split_clause,[],[f8604,f8353,f7491,f17361]) ).
fof(f17361,plain,
( spl0_1723
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f8604,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_853
| ~ spl0_1019 ),
inference(superposition,[],[f7492,f8354]) ).
fof(f17173,plain,
( spl0_1722
| ~ spl0_10
| ~ spl0_1009 ),
inference(avatar_split_clause,[],[f8595,f8313,f3206,f17171]) ).
fof(f17171,plain,
( spl0_1722
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f8313,plain,
( spl0_1009
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_uminus(X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f8595,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_1009 ),
inference(resolution,[],[f8314,f3208]) ).
fof(f8314,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_uminus(X8,X3),X3) = X8 )
| ~ spl0_1009 ),
inference(avatar_component_clause,[],[f8313]) ).
fof(f16849,plain,
( spl0_1721
| ~ spl0_53
| ~ spl0_1005 ),
inference(avatar_split_clause,[],[f8587,f8297,f3421,f16846]) ).
fof(f16743,plain,
( spl0_1720
| ~ spl0_853
| ~ spl0_994 ),
inference(avatar_split_clause,[],[f8555,f8252,f7491,f16741]) ).
fof(f16741,plain,
( spl0_1720
<=> ! [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_1720])]) ).
fof(f8555,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_853
| ~ spl0_994 ),
inference(superposition,[],[f7492,f8253]) ).
fof(f16569,plain,
( spl0_1719
| ~ spl0_110
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8108,f7920,f3700,f16567]) ).
fof(f16567,plain,
( spl0_1719
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f7920,plain,
( spl0_941
<=> ! [X25,X10] : c_lessequals(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f8108,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_941 ),
inference(superposition,[],[f7921,f3702]) ).
fof(f7921,plain,
( ! [X10,X25] : c_lessequals(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint)
| ~ spl0_941 ),
inference(avatar_component_clause,[],[f7920]) ).
fof(f16449,plain,
( spl0_1718
| ~ spl0_109
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8107,f7920,f3695,f16447]) ).
fof(f16447,plain,
( spl0_1718
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f8107,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_941 ),
inference(superposition,[],[f7921,f3697]) ).
fof(f16307,plain,
( spl0_1717
| ~ spl0_109
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8105,f7920,f3695,f16305]) ).
fof(f8105,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_941 ),
inference(superposition,[],[f7921,f3697]) ).
fof(f16303,plain,
( spl0_1714
| spl0_1716 ),
inference(avatar_split_clause,[],[f3159,f16301,f16280]) ).
fof(f16280,plain,
( spl0_1714
<=> ! [X35] : c_0 != c_Numeral_Onumber__of(X35,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f16301,plain,
( spl0_1716
<=> ! [X11,X3] :
( ~ class_Power_Orecpower(X3)
| c_less(c_0,c_Nat_Opower(X11,c_0,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f3159,plain,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 != c_Numeral_Onumber__of(X35,tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_0,X3),X3) ),
inference(inner_rewriting,[],[f1184]) ).
fof(f1184,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 != c_Numeral_Onumber__of(X35,tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f16289,plain,
( ~ spl0_695
| ~ spl0_1714 ),
inference(avatar_contradiction_clause,[],[f16288]) ).
fof(f16288,plain,
( $false
| ~ spl0_695
| ~ spl0_1714 ),
inference(trivial_inequality_removal,[],[f16286]) ).
fof(f16286,plain,
( c_0 != c_0
| ~ spl0_695
| ~ spl0_1714 ),
inference(superposition,[],[f16281,f6833]) ).
fof(f6833,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_695 ),
inference(avatar_component_clause,[],[f6831]) ).
fof(f6831,plain,
( spl0_695
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f16281,plain,
( ! [X35] : c_0 != c_Numeral_Onumber__of(X35,tc_nat)
| ~ spl0_1714 ),
inference(avatar_component_clause,[],[f16280]) ).
fof(f16285,plain,
( spl0_1714
| spl0_1715 ),
inference(avatar_split_clause,[],[f3158,f16283,f16280]) ).
fof(f16283,plain,
( spl0_1715
<=> ! [X11,X3] :
( ~ class_Power_Orecpower(X3)
| ~ c_lessequals(c_Nat_Opower(X11,c_0,X3),c_0,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f3158,plain,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 != c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_0,X3),c_0,X3) ),
inference(inner_rewriting,[],[f1167]) ).
fof(f1167,axiom,
! [X3,X11,X35] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 != c_Numeral_Onumber__of(X35,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f16252,plain,
( spl0_1713
| ~ spl0_109
| ~ spl0_667
| ~ spl0_764
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1601
| ~ spl0_1712 ),
inference(avatar_split_clause,[],[f16248,f16244,f14433,f10415,f10092,f7128,f6703,f3695,f16250]) ).
fof(f16250,plain,
( spl0_1713
<=> ! [X8] :
( c_plus(c_1,c_minus(X8,c_1,tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f16244,plain,
( spl0_1712
<=> ! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f16248,plain,
( ! [X8] :
( c_plus(c_1,c_minus(X8,c_1,tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_764
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1601
| ~ spl0_1712 ),
inference(forward_demodulation,[],[f16247,f14436]) ).
fof(f14436,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_764
| ~ spl0_1601 ),
inference(superposition,[],[f14434,f7129]) ).
fof(f16247,plain,
( ! [X8] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1712 ),
inference(forward_demodulation,[],[f16245,f11235]) ).
fof(f16245,plain,
( ! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_1712 ),
inference(avatar_component_clause,[],[f16244]) ).
fof(f16246,plain,
spl0_1712,
inference(avatar_split_clause,[],[f3049,f16244]) ).
fof(f3049,plain,
! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ),
inference(forward_demodulation,[],[f2867,f2800]) ).
fof(f2867,plain,
! [X8] :
( ~ c_less(c_0,X8,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X8 ),
inference(definition_unfolding,[],[f874,f1394,f1394]) ).
fof(f874,axiom,
! [X8] :
( ~ c_less(c_0,X8,tc_nat)
| c_Suc(c_minus(X8,c_Suc(c_0),tc_nat)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f16242,plain,
spl0_1711,
inference(avatar_split_clause,[],[f2898,f16240]) ).
fof(f16240,plain,
( spl0_1711
<=> ! [X31,X27,X80,X3] :
( c_lessequals(X80,X27,tc_set(X3))
| ~ c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f2898,plain,
! [X31,X3,X80,X27] :
( c_lessequals(X80,X27,tc_set(X3))
| ~ c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ),
inference(definition_unfolding,[],[f1459,f1223]) ).
fof(f1459,axiom,
! [X31,X3,X80,X27] :
( c_lessequals(X80,X27,tc_set(X3))
| ~ c_lessequals(X80,c_inter(X27,X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f16238,plain,
spl0_1710,
inference(avatar_split_clause,[],[f2897,f16236]) ).
fof(f16236,plain,
( spl0_1710
<=> ! [X31,X27,X80,X3] :
( c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f2897,plain,
! [X31,X3,X80,X27] :
( c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),tc_set(X3)) ),
inference(definition_unfolding,[],[f1460,f1223]) ).
fof(f1460,axiom,
! [X31,X3,X80,X27] :
( c_lessequals(X80,X31,tc_set(X3))
| ~ c_lessequals(X80,c_inter(X27,X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f16234,plain,
( spl0_1709
| ~ spl0_938
| ~ spl0_939 ),
inference(avatar_split_clause,[],[f8101,f7912,f7907,f16231]) ).
fof(f16231,plain,
( spl0_1709
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f8101,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_938
| ~ spl0_939 ),
inference(superposition,[],[f7913,f7909]) ).
fof(f16229,plain,
spl0_1708,
inference(avatar_split_clause,[],[f2893,f16227]) ).
fof(f16227,plain,
( spl0_1708
<=> ! [X34,X3,X33] :
( ~ c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Relation_OImage(c_Relation_Odiag(X33,X3),X34,X3,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f2893,plain,
! [X3,X34,X33] :
( ~ c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Relation_OImage(c_Relation_Odiag(X33,X3),X34,X3,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
inference(definition_unfolding,[],[f1607,f1223]) ).
fof(f1607,axiom,
! [X3,X34,X33] :
( ~ c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_inter(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f16225,plain,
spl0_1707,
inference(avatar_split_clause,[],[f2892,f16223]) ).
fof(f16223,plain,
( spl0_1707
<=> ! [X34,X3,X33] :
( ~ c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Relation_OImage(c_Relation_Odiag(X33,X3),X34,X3,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f2892,plain,
! [X3,X34,X33] :
( ~ c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Relation_OImage(c_Relation_Odiag(X33,X3),X34,X3,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
inference(definition_unfolding,[],[f1608,f1223]) ).
fof(f1608,axiom,
! [X3,X34,X33] :
( ~ c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_inter(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f16219,plain,
spl0_1706,
inference(avatar_split_clause,[],[f2886,f16217]) ).
fof(f16217,plain,
( spl0_1706
<=> ! [X25,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f2886,plain,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f871,f1394,f1394]) ).
fof(f871,axiom,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_Suc(X25),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f16213,plain,
spl0_1705,
inference(avatar_split_clause,[],[f2882,f16211]) ).
fof(f16211,plain,
( spl0_1705
<=> ! [X25,X10] :
( c_lessequals(X10,X25,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f2882,plain,
! [X10,X25] :
( c_lessequals(X10,X25,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f869,f1394,f1394]) ).
fof(f869,axiom,
! [X10,X25] :
( c_lessequals(X10,X25,tc_nat)
| ~ c_lessequals(c_Suc(X10),c_Suc(X25),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f16209,plain,
spl0_1704,
inference(avatar_split_clause,[],[f2878,f16207]) ).
fof(f16207,plain,
( spl0_1704
<=> ! [X3,X31,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f2878,plain,
! [X31,X3,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X15,X27,X3),X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1530,f1223]) ).
fof(f1530,axiom,
! [X31,X3,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_inter(c_insert(X15,X27,X3),X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
fof(f16205,plain,
spl0_1703,
inference(avatar_split_clause,[],[f2876,f16203]) ).
fof(f2876,plain,
! [X31,X3,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X31,X3),c_insert(X15,X27,X3),X3,X3) ),
inference(definition_unfolding,[],[f1511,f1223]) ).
fof(f1511,axiom,
! [X31,X3,X27,X15] :
( ~ c_in(X15,X31,X3)
| c_emptyset != c_inter(X31,c_insert(X15,X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
fof(f16199,plain,
spl0_1702,
inference(avatar_split_clause,[],[f2874,f16197]) ).
fof(f16197,plain,
( spl0_1702
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f2874,plain,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f872,f1394,f1394]) ).
fof(f872,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_Suc(X25),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f16193,plain,
spl0_1701,
inference(avatar_split_clause,[],[f2869,f16191]) ).
fof(f16191,plain,
( spl0_1701
<=> ! [X25,X10] :
( ~ c_lessequals(X10,X25,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f2869,plain,
! [X10,X25] :
( ~ c_lessequals(X10,X25,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f870,f1394,f1394]) ).
fof(f870,axiom,
! [X10,X25] :
( ~ c_lessequals(X10,X25,tc_nat)
| c_lessequals(c_Suc(X10),c_Suc(X25),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f16185,plain,
( spl0_1700
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1699 ),
inference(avatar_split_clause,[],[f16181,f16178,f10415,f10092,f6703,f3695,f16183]) ).
fof(f16183,plain,
( spl0_1700
<=> ! [X13,X25] :
( c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) = c_NatArith_Oof__nat(c_plus(c_1,X25,tc_nat),X13)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f16178,plain,
( spl0_1699
<=> ! [X13,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13)
| c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f16181,plain,
( ! [X25,X13] :
( c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) = c_NatArith_Oof__nat(c_plus(c_1,X25,tc_nat),X13)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1699 ),
inference(forward_demodulation,[],[f16179,f11235]) ).
fof(f16179,plain,
( ! [X25,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13)
| c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X13) )
| ~ spl0_1699 ),
inference(avatar_component_clause,[],[f16178]) ).
fof(f16180,plain,
spl0_1699,
inference(avatar_split_clause,[],[f2854,f16178]) ).
fof(f2854,plain,
! [X25,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13)
| c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X13) ),
inference(definition_unfolding,[],[f652,f1394]) ).
fof(f652,axiom,
! [X25,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X13)
| c_NatArith_Oof__nat(c_Suc(X25),X13) = c_plus(c_NatArith_Oof__nat(X25,X13),c_1,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f16172,plain,
( spl0_1698
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1697 ),
inference(avatar_split_clause,[],[f16168,f16165,f10415,f10092,f6703,f3695,f16170]) ).
fof(f16170,plain,
( spl0_1698
<=> ! [X41,X10,X11,X3] : c_List_Onth(X41,X10,X3) = c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_plus(c_1,X10,tc_nat),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f16165,plain,
( spl0_1697
<=> ! [X41,X10,X11,X3] : c_List_Onth(X41,X10,X3) = c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f16168,plain,
( ! [X41,X10,X3,X11] : c_List_Onth(X41,X10,X3) = c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_plus(c_1,X10,tc_nat),X3)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1697 ),
inference(forward_demodulation,[],[f16166,f11235]) ).
fof(f16166,plain,
( ! [X41,X10,X3,X11] : c_List_Onth(X41,X10,X3) = c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3)
| ~ spl0_1697 ),
inference(avatar_component_clause,[],[f16165]) ).
fof(f16167,plain,
spl0_1697,
inference(avatar_split_clause,[],[f2814,f16165]) ).
fof(f2814,plain,
! [X41,X10,X3,X11] : c_List_Onth(X41,X10,X3) = c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3),
inference(definition_unfolding,[],[f543,f1394]) ).
fof(f543,axiom,
! [X41,X3,X10,X11] : c_List_Onth(c_List_Olist_OCons(X11,X41,X3),c_Suc(X10),X3) = c_List_Onth(X41,X10,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f16150,plain,
( spl0_1696
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1695 ),
inference(avatar_split_clause,[],[f16146,f16143,f10415,f10092,f6703,f3695,f16148]) ).
fof(f16143,plain,
( spl0_1695
<=> ! [X41,X10,X11,X3] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_List_Olist_OCons(X11,X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f16146,plain,
( ! [X41,X10,X3,X11] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_plus(c_1,X10,tc_nat),c_List_Olist_OCons(X11,X41,X3),X3)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1695 ),
inference(forward_demodulation,[],[f16144,f11235]) ).
fof(f16144,plain,
( ! [X41,X10,X3,X11] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_List_Olist_OCons(X11,X41,X3),X3)
| ~ spl0_1695 ),
inference(avatar_component_clause,[],[f16143]) ).
fof(f16145,plain,
spl0_1695,
inference(avatar_split_clause,[],[f2813,f16143]) ).
fof(f2813,plain,
! [X41,X10,X3,X11] : c_List_Odrop(X10,X41,X3) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),c_List_Olist_OCons(X11,X41,X3),X3),
inference(definition_unfolding,[],[f422,f1394]) ).
fof(f422,axiom,
! [X41,X10,X3,X11] : c_List_Odrop(c_Suc(X10),c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Odrop(X10,X41,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f16115,plain,
( spl0_1694
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1693 ),
inference(avatar_split_clause,[],[f16111,f16108,f10415,f10092,f6703,f3695,f16113]) ).
fof(f16108,plain,
( spl0_1693
<=> ! [X13,X11,X10] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X11,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f16111,plain,
( ! [X10,X11,X13] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_plus(c_1,X10,tc_nat),X11,X13)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1693 ),
inference(forward_demodulation,[],[f16109,f11235]) ).
fof(f16109,plain,
( ! [X10,X11,X13] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X11,X13)
| ~ spl0_1693 ),
inference(avatar_component_clause,[],[f16108]) ).
fof(f16110,plain,
spl0_1693,
inference(avatar_split_clause,[],[f2812,f16108]) ).
fof(f2812,plain,
! [X10,X11,X13] : c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X11,X13),
inference(definition_unfolding,[],[f573,f1394]) ).
fof(f573,axiom,
! [X10,X11,X13] : c_List_Oreplicate(c_Suc(X10),X11,X13) = c_List_Olist_OCons(X11,c_List_Oreplicate(X10,X11,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f16106,plain,
( spl0_1691
| ~ spl0_1692
| ~ spl0_828
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8065,f7827,f7391,f16103,f16100]) ).
fof(f16100,plain,
( spl0_1691
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f16103,plain,
( spl0_1692
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f8065,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_828
| ~ spl0_918 ),
inference(resolution,[],[f7828,f7392]) ).
fof(f16003,plain,
( spl0_1690
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1689 ),
inference(avatar_split_clause,[],[f15999,f15996,f10415,f10092,f6703,f3695,f16001]) ).
fof(f15996,plain,
( spl0_1689
<=> ! [X25,X10] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f15999,plain,
( ! [X10,X25] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_plus(c_1,X25,tc_nat),X10,tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1689 ),
inference(forward_demodulation,[],[f15997,f11235]) ).
fof(f15997,plain,
( ! [X10,X25] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat)
| ~ spl0_1689 ),
inference(avatar_component_clause,[],[f15996]) ).
fof(f15998,plain,
spl0_1689,
inference(avatar_split_clause,[],[f2811,f15996]) ).
fof(f2811,plain,
! [X10,X25] : c_plus(X10,c_times(X25,X10,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),X10,tc_nat),
inference(definition_unfolding,[],[f949,f1394]) ).
fof(f949,axiom,
! [X10,X25] : c_times(c_Suc(X25),X10,tc_nat) = c_plus(X10,c_times(X25,X10,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f15903,plain,
( spl0_1688
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1687 ),
inference(avatar_split_clause,[],[f15899,f15896,f10415,f10092,f6703,f3695,f15901]) ).
fof(f15896,plain,
( spl0_1687
<=> ! [X25,X10] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f15899,plain,
( ! [X10,X25] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1687 ),
inference(forward_demodulation,[],[f15897,f11235]) ).
fof(f15897,plain,
( ! [X10,X25] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1687 ),
inference(avatar_component_clause,[],[f15896]) ).
fof(f15898,plain,
spl0_1687,
inference(avatar_split_clause,[],[f2810,f15896]) ).
fof(f2810,plain,
! [X10,X25] : c_plus(X25,c_times(X25,X10,tc_nat),tc_nat) = c_times(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f907,f1394]) ).
fof(f907,axiom,
! [X10,X25] : c_times(X25,c_Suc(X10),tc_nat) = c_plus(X25,c_times(X25,X10,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f15840,plain,
( spl0_1686
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1685 ),
inference(avatar_split_clause,[],[f15836,f15833,f10415,f10092,f6703,f3695,f15838]) ).
fof(f15833,plain,
( spl0_1685
<=> ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f15836,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1685 ),
inference(forward_demodulation,[],[f15834,f11235]) ).
fof(f15834,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat)
| ~ spl0_1685 ),
inference(avatar_component_clause,[],[f15833]) ).
fof(f15835,plain,
spl0_1685,
inference(avatar_split_clause,[],[f2809,f15833]) ).
fof(f2809,plain,
! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1195,f1394]) ).
fof(f1195,axiom,
! [X40,X10] : c_Nat_Opower(X40,c_Suc(X10),tc_nat) = c_times(X40,c_Nat_Opower(X40,X10,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f15807,plain,
( spl0_1684
| ~ spl0_109
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f8014,f7689,f3695,f15805]) ).
fof(f15805,plain,
( spl0_1684
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f7689,plain,
( spl0_884
<=> ! [X25,X10] : ~ c_less(c_IntDef_Oint(X10),c_uminus(c_IntDef_Oint(X25),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f8014,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_884 ),
inference(superposition,[],[f7690,f3697]) ).
fof(f7690,plain,
( ! [X10,X25] : ~ c_less(c_IntDef_Oint(X10),c_uminus(c_IntDef_Oint(X25),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7689]) ).
fof(f15803,plain,
( spl0_1683
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1682 ),
inference(avatar_split_clause,[],[f15799,f15796,f10415,f10092,f6703,f3695,f15801]) ).
fof(f15796,plain,
( spl0_1682
<=> ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f15799,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_plus(c_1,X10,tc_nat),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1682 ),
inference(forward_demodulation,[],[f15797,f11235]) ).
fof(f15797,plain,
( ! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1682 ),
inference(avatar_component_clause,[],[f15796]) ).
fof(f15798,plain,
spl0_1682,
inference(avatar_split_clause,[],[f2808,f15796]) ).
fof(f2808,plain,
! [X40,X10] : c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X40,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f315,f1394]) ).
fof(f315,axiom,
! [X40,X10] : c_Nat_Opower(X40,c_Suc(X10),tc_IntDef_Oint) = c_times(X40,c_Nat_Opower(X40,X10,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f15794,plain,
spl0_1681,
inference(avatar_split_clause,[],[f2807,f15792]) ).
fof(f15792,plain,
( spl0_1681
<=> ! [X27,X3,X31] : c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) = c_minus(X27,c_uminus(X31,tc_set(X3)),tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f2807,plain,
! [X31,X3,X27] : c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) = c_minus(X27,c_uminus(X31,tc_set(X3)),tc_set(X3)),
inference(definition_unfolding,[],[f1436,f1223]) ).
fof(f1436,axiom,
! [X31,X3,X27] : c_inter(X27,X31,X3) = c_minus(X27,c_uminus(X31,tc_set(X3)),tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f15790,plain,
spl0_1680,
inference(avatar_split_clause,[],[f2738,f15788]) ).
fof(f2738,axiom,
! [X3,X93] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Orefl(c_Tarski_Opotype_Opset(X93,X3,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
fof(f15786,plain,
spl0_1679,
inference(avatar_split_clause,[],[f1658,f15784]) ).
fof(f1658,axiom,
! [X3,X27,X15] :
( ~ c_in(X15,X27,X3)
| c_in(c_Pair(X15,X15,X3,X3),c_Relation_Odiag(X27,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f15782,plain,
spl0_1678,
inference(avatar_split_clause,[],[f1624,f15780]) ).
fof(f1624,axiom,
! [X41,X3,X27] :
( c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3))
| c_in(c_Main_Oin__listsI__1(X27,X41,X3),c_List_Oset(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f15778,plain,
spl0_1677,
inference(avatar_split_clause,[],[f1525,f15776]) ).
fof(f15776,plain,
( spl0_1677
<=> ! [X27,X3,X15] : c_insert(X15,X27,X3) = c_insert(X15,c_minus(X27,c_insert(X15,c_emptyset,X3),tc_set(X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f1525,axiom,
! [X3,X27,X15] : c_insert(X15,X27,X3) = c_insert(X15,c_minus(X27,c_insert(X15,c_emptyset,X3),tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f15774,plain,
spl0_1676,
inference(avatar_split_clause,[],[f1500,f15772]) ).
fof(f15772,plain,
( spl0_1676
<=> ! [X27,X3,X31] : c_Union(c_union(X27,X31,tc_set(X3)),X3) = c_union(c_Union(X27,X3),c_Union(X31,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f1500,axiom,
! [X31,X3,X27] : c_Union(c_union(X27,X31,tc_set(X3)),X3) = c_union(c_Union(X27,X3),c_Union(X31,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f15770,plain,
spl0_1675,
inference(avatar_split_clause,[],[f1446,f15768]) ).
fof(f15768,plain,
( spl0_1675
<=> ! [X31,X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f1446,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f15766,plain,
spl0_1674,
inference(avatar_split_clause,[],[f1435,f15764]) ).
fof(f15764,plain,
( spl0_1674
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| c_lessequals(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f1435,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| c_lessequals(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f15762,plain,
( spl0_1673
| ~ spl0_110
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f8013,f7689,f3700,f15760]) ).
fof(f8013,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_884 ),
inference(superposition,[],[f7690,f3702]) ).
fof(f15758,plain,
spl0_1672,
inference(avatar_split_clause,[],[f1434,f15756]) ).
fof(f15756,plain,
( spl0_1672
<=> ! [X27,X3,X31] :
( c_lessequals(X31,X27,tc_set(X3))
| ~ c_lessequals(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f1434,axiom,
! [X31,X3,X27] :
( c_lessequals(X31,X27,tc_set(X3))
| ~ c_lessequals(c_uminus(X27,tc_set(X3)),c_uminus(X31,tc_set(X3)),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f15754,plain,
spl0_1671,
inference(avatar_split_clause,[],[f1424,f15752]) ).
fof(f1424,axiom,
! [X31,X3,X27] : c_uminus(c_minus(X27,X31,tc_set(X3)),tc_set(X3)) = c_union(c_uminus(X27,tc_set(X3)),X31,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f15750,plain,
spl0_1670,
inference(avatar_split_clause,[],[f1210,f15748]) ).
fof(f15748,plain,
( spl0_1670
<=> ! [X10,X3,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X15
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f1210,axiom,
! [X3,X10,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X15
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f15746,plain,
spl0_1669,
inference(avatar_split_clause,[],[f1209,f15744]) ).
fof(f15744,plain,
( spl0_1669
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X3),X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f1209,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X3),X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f15742,plain,
spl0_1668,
inference(avatar_split_clause,[],[f1044,f15740]) ).
fof(f15740,plain,
( spl0_1668
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f1044,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f15738,plain,
spl0_1667,
inference(avatar_split_clause,[],[f1043,f15736]) ).
fof(f1043,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f15734,plain,
spl0_1666,
inference(avatar_split_clause,[],[f1042,f15732]) ).
fof(f1042,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f15730,plain,
spl0_1665,
inference(avatar_split_clause,[],[f1041,f15728]) ).
fof(f15728,plain,
( spl0_1665
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f1041,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f15726,plain,
spl0_1664,
inference(avatar_split_clause,[],[f1039,f15724]) ).
fof(f15724,plain,
( spl0_1664
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f1039,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f15722,plain,
spl0_1663,
inference(avatar_split_clause,[],[f1038,f15720]) ).
fof(f1038,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_plus(X15,X26,X3),c_plus(X16,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f15718,plain,
( spl0_1662
| ~ spl0_109
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f8012,f7689,f3695,f15716]) ).
fof(f8012,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_884 ),
inference(superposition,[],[f7690,f3697]) ).
fof(f15714,plain,
spl0_1661,
inference(avatar_split_clause,[],[f1037,f15712]) ).
fof(f1037,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f15710,plain,
spl0_1660,
inference(avatar_split_clause,[],[f1036,f15708]) ).
fof(f15708,plain,
( spl0_1660
<=> ! [X15,X3,X16,X26] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f1036,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_plus(X26,X15,X3),c_plus(X26,X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f15706,plain,
spl0_1659,
inference(avatar_split_clause,[],[f996,f15704]) ).
fof(f15704,plain,
( spl0_1659
<=> ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X35,X3),X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f996,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X35,X3),X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f15702,plain,
spl0_1658,
inference(avatar_split_clause,[],[f995,f15700]) ).
fof(f15700,plain,
( spl0_1658
<=> ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X35,X3),X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f995,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X35,X3),X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f15698,plain,
spl0_1657,
inference(avatar_split_clause,[],[f988,f15696]) ).
fof(f15696,plain,
( spl0_1657
<=> ! [X11,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X35,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X35,X11),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f988,axiom,
! [X3,X11,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X35,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X35,X11),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f15694,plain,
spl0_1656,
inference(avatar_split_clause,[],[f987,f15692]) ).
fof(f15692,plain,
( spl0_1656
<=> ! [X11,X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X35,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X35,X11),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f987,axiom,
! [X3,X11,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X35,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X35,X11),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f15690,plain,
spl0_1655,
inference(avatar_split_clause,[],[f969,f15688]) ).
fof(f969,axiom,
! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X36,X35),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f15686,plain,
spl0_1654,
inference(avatar_split_clause,[],[f966,f15684]) ).
fof(f966,axiom,
! [X3,X36,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,X35),X3) = c_plus(c_Numeral_Onumber__of(X36,X3),c_Numeral_Onumber__of(X35,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f15682,plain,
spl0_1653,
inference(avatar_split_clause,[],[f821,f15680]) ).
fof(f15680,plain,
( spl0_1653
<=> ! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_uminus(c_1,X17),X15,X17)
| c_less(c_uminus(X15,X17),c_1,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f821,axiom,
! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_uminus(c_1,X17),X15,X17)
| c_less(c_uminus(X15,X17),c_1,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f15678,plain,
spl0_1652,
inference(avatar_split_clause,[],[f820,f15676]) ).
fof(f15676,plain,
( spl0_1652
<=> ! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_uminus(X15,X17),c_1,X17)
| c_less(c_uminus(c_1,X17),X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f820,axiom,
! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_uminus(X15,X17),c_1,X17)
| c_less(c_uminus(c_1,X17),X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f15674,plain,
( spl0_1651
| ~ spl0_109
| ~ spl0_880 ),
inference(avatar_split_clause,[],[f7998,f7672,f3695,f15672]) ).
fof(f15672,plain,
( spl0_1651
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f7672,plain,
( spl0_880
<=> ! [X25,X10] :
( X10 = X25
| c_IntDef_Oint(X25) != c_IntDef_Oint(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f7998,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_109
| ~ spl0_880 ),
inference(superposition,[],[f7673,f3697]) ).
fof(f7673,plain,
( ! [X10,X25] :
( c_IntDef_Oint(X25) != c_IntDef_Oint(X10)
| X10 = X25 )
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f7672]) ).
fof(f15670,plain,
spl0_1650,
inference(avatar_split_clause,[],[f817,f15668]) ).
fof(f15668,plain,
( spl0_1650
<=> ! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_uminus(c_1,X17),X15,X17)
| c_lessequals(c_uminus(X15,X17),c_1,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f817,axiom,
! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_uminus(c_1,X17),X15,X17)
| c_lessequals(c_uminus(X15,X17),c_1,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f15666,plain,
spl0_1649,
inference(avatar_split_clause,[],[f816,f15664]) ).
fof(f15664,plain,
( spl0_1649
<=> ! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_uminus(X15,X17),c_1,X17)
| c_lessequals(c_uminus(c_1,X17),X15,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f816,axiom,
! [X17,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_uminus(X15,X17),c_1,X17)
| c_lessequals(c_uminus(c_1,X17),X15,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f15662,plain,
spl0_1648,
inference(avatar_split_clause,[],[f810,f15660]) ).
fof(f15660,plain,
( spl0_1648
<=> ! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(X16,c_uminus(c_1,X17),X17)
| c_less(c_1,c_uminus(X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f810,axiom,
! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(X16,c_uminus(c_1,X17),X17)
| c_less(c_1,c_uminus(X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f15658,plain,
spl0_1647,
inference(avatar_split_clause,[],[f809,f15656]) ).
fof(f15656,plain,
( spl0_1647
<=> ! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_1,c_uminus(X16,X17),X17)
| c_less(X16,c_uminus(c_1,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f809,axiom,
! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_less(c_1,c_uminus(X16,X17),X17)
| c_less(X16,c_uminus(c_1,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f15654,plain,
spl0_1646,
inference(avatar_split_clause,[],[f794,f15652]) ).
fof(f15652,plain,
( spl0_1646
<=> ! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(X16,c_uminus(c_1,X17),X17)
| c_lessequals(c_1,c_uminus(X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f794,axiom,
! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(X16,c_uminus(c_1,X17),X17)
| c_lessequals(c_1,c_uminus(X16,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f15650,plain,
spl0_1645,
inference(avatar_split_clause,[],[f793,f15648]) ).
fof(f15648,plain,
( spl0_1645
<=> ! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_1,c_uminus(X16,X17),X17)
| c_lessequals(X16,c_uminus(c_1,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f793,axiom,
! [X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X17)
| ~ class_HOL_Oone(X17)
| ~ c_lessequals(c_1,c_uminus(X16,X17),X17)
| c_lessequals(X16,c_uminus(c_1,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f15646,plain,
spl0_1644,
inference(avatar_split_clause,[],[f719,f15644]) ).
fof(f15644,plain,
( spl0_1644
<=> ! [X36,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,X3) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X36,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f719,axiom,
! [X3,X36] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,X3) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X36,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f15642,plain,
spl0_1643,
inference(avatar_split_clause,[],[f630,f15640]) ).
fof(f15640,plain,
( spl0_1643
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Otl(c_append(X41,X42,X3),X3) = c_append(c_List_Otl(X41,X3),X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f630,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Otl(c_append(X41,X42,X3),X3) = c_append(c_List_Otl(X41,X3),X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f15638,plain,
spl0_1642,
inference(avatar_split_clause,[],[f614,f15636]) ).
fof(f15636,plain,
( spl0_1642
<=> ! [X11,X27,X3] :
( ~ c_in(c_0,X27,tc_nat)
| c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Osublist(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f614,axiom,
! [X3,X11,X27] :
( ~ c_in(c_0,X27,tc_nat)
| c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Osublist(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f15633,plain,
spl0_1641,
inference(avatar_split_clause,[],[f577,f15631]) ).
fof(f15631,plain,
( spl0_1641
<=> ! [X8,X3,X42] : c_List_Olist_OCons(X8,X42,X3) = c_List_Orev(c_append(c_List_Orev(X42,X3),c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f577,axiom,
! [X3,X8,X42] : c_List_Olist_OCons(X8,X42,X3) = c_List_Orev(c_append(c_List_Orev(X42,X3),c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f15629,plain,
spl0_1640,
inference(avatar_split_clause,[],[f574,f15627]) ).
fof(f574,axiom,
! [X41,X11,X13] : c_List_Orev(c_List_Olist_OCons(X11,X41,X13),X13) = c_append(c_List_Orev(X41,X13),c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f15625,plain,
spl0_1639,
inference(avatar_split_clause,[],[f563,f15623]) ).
fof(f15623,plain,
( spl0_1639
<=> ! [X13,X41,X11] :
( ~ c_in(X11,c_List_Oset(X41,X13),X13)
| c_List_Oremdups(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Oremdups(X41,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f563,axiom,
! [X41,X11,X13] :
( ~ c_in(X11,c_List_Oset(X41,X13),X13)
| c_List_Oremdups(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Oremdups(X41,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f15621,plain,
spl0_1638,
inference(avatar_split_clause,[],[f551,f15619]) ).
fof(f15619,plain,
( spl0_1638
<=> ! [X41,X3,X10] :
( ~ c_less(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_in(c_List_Onth(X41,X10,X3),c_List_Oset(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f551,axiom,
! [X41,X10,X3] :
( ~ c_less(X10,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat)
| c_in(c_List_Onth(X41,X10,X3),c_List_Oset(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f15617,plain,
spl0_1637,
inference(avatar_split_clause,[],[f550,f15615]) ).
fof(f15615,plain,
( spl0_1637
<=> ! [X41,X11,X3,X52,X24] :
( X24 = X52
| c_List_Onth(c_List_Olist__update(X41,X24,X11,X3),X52,X3) = c_List_Onth(X41,X52,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f550,axiom,
! [X41,X3,X11,X52,X24] :
( X24 = X52
| c_List_Onth(c_List_Olist__update(X41,X24,X11,X3),X52,X3) = c_List_Onth(X41,X52,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f15613,plain,
spl0_1636,
inference(avatar_split_clause,[],[f468,f15611]) ).
fof(f15611,plain,
( spl0_1636
<=> ! [X20,X11,X3] : ~ c_in(c_Pair(X11,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f468,axiom,
! [X3,X11,X20] : ~ c_in(c_Pair(X11,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olexord(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f15609,plain,
spl0_1635,
inference(avatar_split_clause,[],[f455,f15607]) ).
fof(f15607,plain,
( spl0_1635
<=> ! [X41,X3] :
( c_List_Oremdups(X41,X3) = X41
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f455,axiom,
! [X41,X3] :
( c_List_Oremdups(X41,X3) = X41
| c_Nat_Osize(X41,tc_List_Olist(X3)) != c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f15605,plain,
spl0_1634,
inference(avatar_split_clause,[],[f396,f15603]) ).
fof(f15603,plain,
( spl0_1634
<=> ! [X3,X43,X30] :
( c_List_Olist_ONil = X30
| c_List_Olist_ONil != c_List_Oconcat(X43,X3)
| ~ c_in(X30,c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f396,axiom,
! [X3,X30,X43] :
( c_List_Olist_ONil = X30
| c_List_Olist_ONil != c_List_Oconcat(X43,X3)
| ~ c_in(X30,c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).
fof(f15601,plain,
spl0_1633,
inference(avatar_split_clause,[],[f395,f15599]) ).
fof(f15599,plain,
( spl0_1633
<=> ! [X41,X3,X42] : c_List_Oconcat(c_append(X41,X42,tc_List_Olist(X3)),X3) = c_append(c_List_Oconcat(X41,X3),c_List_Oconcat(X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f395,axiom,
! [X41,X3,X42] : c_List_Oconcat(c_append(X41,X42,tc_List_Olist(X3)),X3) = c_append(c_List_Oconcat(X41,X3),c_List_Oconcat(X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f15597,plain,
spl0_1632,
inference(avatar_split_clause,[],[f388,f15595]) ).
fof(f15595,plain,
( spl0_1632
<=> ! [X13,X41,X11] :
( c_List_Olist_ONil = X41
| c_List_Obutlast(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Olist_OCons(X11,c_List_Obutlast(X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f388,axiom,
! [X41,X11,X13] :
( c_List_Olist_ONil = X41
| c_List_Obutlast(c_List_Olist_OCons(X11,X41,X13),X13) = c_List_Olist_OCons(X11,c_List_Obutlast(X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f15593,plain,
spl0_1631,
inference(avatar_split_clause,[],[f369,f15591]) ).
fof(f15591,plain,
( spl0_1631
<=> ! [X8,X3] :
( c_List_Olist_ONil = X8
| c_append(c_List_Obutlast(X8,X3),c_List_Olist_OCons(c_List_Olast(X8,X3),c_List_Olist_ONil,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f369,axiom,
! [X3,X8] :
( c_List_Olist_ONil = X8
| c_append(c_List_Obutlast(X8,X3),c_List_Olist_OCons(c_List_Olast(X8,X3),c_List_Olist_ONil,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f15575,plain,
spl0_1630,
inference(avatar_split_clause,[],[f365,f15573]) ).
fof(f15573,plain,
( spl0_1630
<=> ! [X20,X3,X42] : ~ c_in(c_Pair(c_List_Olist_ONil,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f365,axiom,
! [X3,X42,X20] : ~ c_in(c_Pair(c_List_Olist_ONil,X42,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f15571,plain,
spl0_1629,
inference(avatar_split_clause,[],[f356,f15569]) ).
fof(f15569,plain,
( spl0_1629
<=> ! [X41,X20,X3] : ~ c_in(c_Pair(X41,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f356,axiom,
! [X41,X3,X20] : ~ c_in(c_Pair(X41,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X20,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f15567,plain,
spl0_1628,
inference(avatar_split_clause,[],[f161,f15565]) ).
fof(f15565,plain,
( spl0_1628
<=> ! [X3,X10] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f161,axiom,
! [X3,X10] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f15563,plain,
spl0_1627,
inference(avatar_split_clause,[],[f153,f15561]) ).
fof(f15561,plain,
( spl0_1627
<=> ! [X25,X10] : c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,c_plus(X10,X25,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f153,axiom,
! [X10,X25] : c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,c_plus(X10,X25,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f15559,plain,
spl0_1626,
inference(avatar_split_clause,[],[f152,f15557]) ).
fof(f15557,plain,
( spl0_1626
<=> ! [X25,X10] : c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,c_plus(X25,X10,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f152,axiom,
! [X10,X25] : c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,c_plus(X25,X10,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f15555,plain,
spl0_1625,
inference(avatar_split_clause,[],[f151,f15553]) ).
fof(f15553,plain,
( spl0_1625
<=> ! [X25,X10] : c_GCD_Ogcd(c_Pair(c_plus(X25,X10,tc_nat),X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f151,axiom,
! [X10,X25] : c_GCD_Ogcd(c_Pair(c_plus(X25,X10,tc_nat),X10,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f15551,plain,
spl0_1624,
inference(avatar_split_clause,[],[f122,f15549]) ).
fof(f15549,plain,
( spl0_1624
<=> ! [X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Finite__Set_OMin(X27,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f122,axiom,
! [X3,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Finite__Set_OMin(X27,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f15547,plain,
spl0_1623,
inference(avatar_split_clause,[],[f107,f15545]) ).
fof(f15545,plain,
( spl0_1623
<=> ! [X27,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Finite__Set_OMax(X27,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f107,axiom,
! [X3,X27] :
( ~ class_Orderings_Olinorder(X3)
| c_emptyset = X27
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Finite__Set_OMax(X27,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f15543,plain,
spl0_1622,
inference(avatar_split_clause,[],[f3,f15541]) ).
fof(f15541,plain,
( spl0_1622
<=> ! [X5,X6,X4,X7,X0,X3,X2,X1] :
( X2 = X7
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X2 = X7
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_2) ).
fof(f15539,plain,
spl0_1621,
inference(avatar_split_clause,[],[f2,f15537]) ).
fof(f15537,plain,
( spl0_1621
<=> ! [X5,X3,X4,X2,X7,X0,X6,X1] :
( X1 = X6
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X1 = X6
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_1) ).
fof(f15535,plain,
( spl0_1620
| ~ spl0_789
| ~ spl0_1591 ),
inference(avatar_split_clause,[],[f15227,f14371,f7229,f15533]) ).
fof(f15227,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_789
| ~ spl0_1591 ),
inference(forward_demodulation,[],[f15212,f7230]) ).
fof(f15212,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_789
| ~ spl0_1591 ),
inference(superposition,[],[f14372,f7230]) ).
fof(f15531,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1,f15529]) ).
fof(f15529,plain,
( spl0_1619
<=> ! [X2,X6,X4,X1,X0,X5,X3,X7] :
( X0 = X5
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X0 = X5
| c_Tarski_Opotype_Opotype__ext(X0,X1,X2,X3,X4) != c_Tarski_Opotype_Opotype__ext(X5,X6,X7,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_0) ).
fof(f15185,plain,
( spl0_1618
| ~ spl0_720
| ~ spl0_1583 ),
inference(avatar_split_clause,[],[f15126,f14338,f6938,f15183]) ).
fof(f15183,plain,
( spl0_1618
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f14338,plain,
( spl0_1583
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X8,X11,X3)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X11,X3),c_SetInterval_OgreaterThan(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f15126,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_720
| ~ spl0_1583 ),
inference(resolution,[],[f14339,f6939]) ).
fof(f14339,plain,
( ! [X3,X11,X8] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X11,X3),c_SetInterval_OgreaterThan(X8,X3),tc_set(X3))
| c_lessequals(X8,X11,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_1583 ),
inference(avatar_component_clause,[],[f14338]) ).
fof(f14911,plain,
( spl0_1617
| ~ spl0_735
| ~ spl0_1556 ),
inference(avatar_split_clause,[],[f14873,f14227,f7011,f14909]) ).
fof(f14909,plain,
( spl0_1617
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f14873,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_735
| ~ spl0_1556 ),
inference(trivial_inequality_removal,[],[f14863]) ).
fof(f14863,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_735
| ~ spl0_1556 ),
inference(superposition,[],[f14228,f7012]) ).
fof(f14528,plain,
spl0_1616,
inference(avatar_split_clause,[],[f3157,f14526]) ).
fof(f14526,plain,
( spl0_1616
<=> ! [X11,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f3157,plain,
! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f3156,f965]) ).
fof(f965,axiom,
! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3156,plain,
! [X3,X11] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f2953,f2748]) ).
fof(f2748,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f976,f979]) ).
fof(f976,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f2953,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f167,f979]) ).
fof(f167,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f14524,plain,
spl0_1615,
inference(avatar_split_clause,[],[f3150,f14522]) ).
fof(f14522,plain,
( spl0_1615
<=> ! [X8,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f3150,plain,
! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f3149,f965]) ).
fof(f3149,plain,
! [X3,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2947,f2748]) ).
fof(f2947,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f171,f979]) ).
fof(f171,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f14520,plain,
( ~ spl0_40
| ~ spl0_1614
| ~ spl0_1268
| spl0_1445 ),
inference(avatar_split_clause,[],[f13684,f11733,f10126,f14517,f3356]) ).
fof(f14517,plain,
( spl0_1614
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f11733,plain,
( spl0_1445
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f13684,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1268
| spl0_1445 ),
inference(resolution,[],[f11735,f10127]) ).
fof(f11735,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1445 ),
inference(avatar_component_clause,[],[f11733]) ).
fof(f14515,plain,
spl0_1613,
inference(avatar_split_clause,[],[f3147,f14513]) ).
fof(f14513,plain,
( spl0_1613
<=> ! [X11,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f3147,plain,
! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f3146,f965]) ).
fof(f3146,plain,
! [X3,X11] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3) ),
inference(forward_demodulation,[],[f2945,f2748]) ).
fof(f2945,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f166,f979]) ).
fof(f166,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_Numeral_Onumber__of(X11,X3),c_0,X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f14511,plain,
spl0_1612,
inference(avatar_split_clause,[],[f3140,f14509]) ).
fof(f14509,plain,
( spl0_1612
<=> ! [X8,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f3140,plain,
! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f3139,f965]) ).
fof(f3139,plain,
! [X3,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3) ),
inference(forward_demodulation,[],[f2939,f2748]) ).
fof(f2939,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f170,f979]) ).
fof(f170,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X3),X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f14507,plain,
spl0_1611,
inference(avatar_split_clause,[],[f3121,f14505]) ).
fof(f14505,plain,
( spl0_1611
<=> ! [X25,X10] :
( c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_1,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f3121,plain,
! [X10,X25] :
( c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_1,X25,tc_nat) ),
inference(forward_demodulation,[],[f2925,f2749]) ).
fof(f2925,plain,
! [X10,X25] :
( ~ c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_1,X25,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X25,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f947,f1394]) ).
fof(f947,axiom,
! [X10,X25] :
( ~ c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_1,X25,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f14503,plain,
spl0_1610,
inference(avatar_split_clause,[],[f3037,f14501]) ).
fof(f14501,plain,
( spl0_1610
<=> ! [X36,X3] :
( c_plus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f3037,plain,
! [X3,X36] :
( c_plus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f180,f1006]) ).
fof(f180,axiom,
! [X3,X36] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_Numeral_Onumber__of(X36,X3),c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X36,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f14499,plain,
spl0_1609,
inference(avatar_split_clause,[],[f3036,f14497]) ).
fof(f14497,plain,
( spl0_1609
<=> ! [X3,X35] :
( c_plus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X35),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f3036,plain,
! [X3,X35] :
( c_plus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X35),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f179,f1006]) ).
fof(f179,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_1,c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X35),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f14495,plain,
spl0_1608,
inference(avatar_split_clause,[],[f3009,f14493]) ).
fof(f14493,plain,
( spl0_1608
<=> ! [X20,X3] : c_List_Olistset(c_List_Olist_ONil,X3) = c_Relation_OImage(c_List_Olistrel(X20,X3),c_List_Olistset(c_List_Olist_ONil,X3),tc_List_Olist(X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f3009,plain,
! [X3,X20] : c_List_Olistset(c_List_Olist_ONil,X3) = c_Relation_OImage(c_List_Olistrel(X20,X3),c_List_Olistset(c_List_Olist_ONil,X3),tc_List_Olist(X3),tc_List_Olist(X3)),
inference(forward_demodulation,[],[f486,f489]) ).
fof(f489,axiom,
! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f486,axiom,
! [X3,X20] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X3)) = c_Relation_OImage(c_List_Olistrel(X20,X3),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X3)),tc_List_Olist(X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f14491,plain,
spl0_1607,
inference(avatar_split_clause,[],[f3006,f14489]) ).
fof(f3006,plain,
! [X3,X57,X15] : c_Nat_Osize(c_List_Olist_OCons(X15,X57,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X57,tc_List_Olist(X3)),c_1,tc_nat),
inference(forward_demodulation,[],[f2830,f2749]) ).
fof(f2830,plain,
! [X3,X57,X15] : c_Nat_Osize(c_List_Olist_OCons(X15,X57,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X57,tc_List_Olist(X3)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f477,f1394]) ).
fof(f477,axiom,
! [X3,X57,X15] : c_Nat_Osize(c_List_Olist_OCons(X15,X57,X3),tc_List_Olist(X3)) = c_plus(c_Nat_Osize(X57,tc_List_Olist(X3)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f14487,plain,
spl0_1606,
inference(avatar_split_clause,[],[f3002,f14485]) ).
fof(f14485,plain,
( spl0_1606
<=> ! [X31,X3,X80,X15] : c_union(c_insert(X15,X31,X3),X80,X3) = c_union(X31,c_insert(X15,X80,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f3002,plain,
! [X31,X3,X80,X15] : c_union(c_insert(X15,X31,X3),X80,X3) = c_union(X31,c_insert(X15,X80,X3),X3),
inference(forward_demodulation,[],[f1493,f1494]) ).
fof(f1494,axiom,
! [X31,X3,X27,X15] : c_union(X27,c_insert(X15,X31,X3),X3) = c_insert(X15,c_union(X27,X31,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f1493,axiom,
! [X31,X3,X80,X15] : c_union(c_insert(X15,X31,X3),X80,X3) = c_insert(X15,c_union(X31,X80,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f14483,plain,
spl0_1605,
inference(avatar_split_clause,[],[f2907,f14481]) ).
fof(f14481,plain,
( spl0_1605
<=> ! [X8,X3,X10] :
( c_List_Osublist(X8,c_SetInterval_OlessThan(X10,tc_nat),X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f2907,plain,
! [X3,X10,X8] :
( c_List_Osublist(X8,c_SetInterval_OlessThan(X10,tc_nat),X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),X10,tc_nat) ),
inference(definition_unfolding,[],[f620,f616]) ).
fof(f620,axiom,
! [X3,X10,X8] :
( c_List_Otake(X10,X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f14463,plain,
( spl0_1604
| ~ spl0_866
| ~ spl0_1319 ),
inference(avatar_split_clause,[],[f13005,f10330,f7545,f14460]) ).
fof(f14460,plain,
( spl0_1604
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f10330,plain,
( spl0_1319
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f13005,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_866
| ~ spl0_1319 ),
inference(superposition,[],[f10332,f7546]) ).
fof(f10332,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1319 ),
inference(avatar_component_clause,[],[f10330]) ).
fof(f14458,plain,
( spl0_1603
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1602 ),
inference(avatar_split_clause,[],[f14454,f14451,f10415,f10092,f6703,f3695,f14456]) ).
fof(f14456,plain,
( spl0_1603
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_plus(c_1,X38,tc_nat),X74,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f14451,plain,
( spl0_1602
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X38,tc_nat),tc_nat),X74,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f14454,plain,
( ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_plus(c_1,X38,tc_nat),X74,tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1602 ),
inference(forward_demodulation,[],[f14452,f11235]) ).
fof(f14452,plain,
( ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X38,tc_nat),tc_nat),X74,tc_nat)
| ~ spl0_1602 ),
inference(avatar_component_clause,[],[f14451]) ).
fof(f14453,plain,
spl0_1602,
inference(avatar_split_clause,[],[f2801,f14451]) ).
fof(f14435,plain,
( spl0_1601
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f14431,f14428,f10415,f10092,f6703,f3695,f14433]) ).
fof(f14428,plain,
( spl0_1600
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X74,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f14431,plain,
( ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_plus(c_1,X74,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1600 ),
inference(forward_demodulation,[],[f14429,f11235]) ).
fof(f14429,plain,
( ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X74,tc_nat),tc_nat),tc_nat)
| ~ spl0_1600 ),
inference(avatar_component_clause,[],[f14428]) ).
fof(f14430,plain,
spl0_1600,
inference(avatar_split_clause,[],[f2800,f14428]) ).
fof(f14406,plain,
( spl0_1599
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1598 ),
inference(avatar_split_clause,[],[f14402,f14399,f10415,f10092,f6703,f3695,f14404]) ).
fof(f14404,plain,
( spl0_1599
<=> ! [X41,X3,X10] : c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3) = c_List_Orotate(c_plus(c_1,X10,tc_nat),X41,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f14399,plain,
( spl0_1598
<=> ! [X41,X3,X10] : c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X41,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f14402,plain,
( ! [X41,X10,X3] : c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3) = c_List_Orotate(c_plus(c_1,X10,tc_nat),X41,X3)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1598 ),
inference(forward_demodulation,[],[f14400,f11235]) ).
fof(f14400,plain,
( ! [X41,X10,X3] : c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X41,X3)
| ~ spl0_1598 ),
inference(avatar_component_clause,[],[f14399]) ).
fof(f14401,plain,
spl0_1598,
inference(avatar_split_clause,[],[f2799,f14399]) ).
fof(f2799,plain,
! [X41,X10,X3] : c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X41,X3),
inference(definition_unfolding,[],[f588,f1394]) ).
fof(f588,axiom,
! [X41,X10,X3] : c_List_Orotate(c_Suc(X10),X41,X3) = c_List_Orotate1(c_List_Orotate(X10,X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f14397,plain,
spl0_1597,
inference(avatar_split_clause,[],[f1704,f14395]) ).
fof(f14395,plain,
( spl0_1597
<=> ! [X17,X88,X3,X89] :
( ~ c_Wellfounded__Recursion_Owf(X88,X17)
| ~ c_Wellfounded__Recursion_Owf(X89,X3)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X89,X88,X3,X17),tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f1704,axiom,
! [X3,X88,X89,X17] :
( ~ c_Wellfounded__Recursion_Owf(X88,X17)
| ~ c_Wellfounded__Recursion_Owf(X89,X3)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X89,X88,X3,X17),tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f14393,plain,
spl0_1596,
inference(avatar_split_clause,[],[f1702,f14391]) ).
fof(f14391,plain,
( spl0_1596
<=> ! [X17,X3,X87,X86] :
( ~ c_Relation_Otrans(X86,X17)
| ~ c_Relation_Otrans(X87,X3)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X87,X86,X3,X17),tc_prod(X3,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f1702,axiom,
! [X3,X86,X87,X17] :
( ~ c_Relation_Otrans(X86,X17)
| ~ c_Relation_Otrans(X87,X3)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X87,X86,X3,X17),tc_prod(X3,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f14389,plain,
spl0_1595,
inference(avatar_split_clause,[],[f1657,f14387]) ).
fof(f14387,plain,
( spl0_1595
<=> ! [X27,X3,X26] :
( c_in(c_Main_OdiagE__1(X27,X26,X3),X27,X3)
| ~ c_in(X26,c_Relation_Odiag(X27,X3),tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f1657,axiom,
! [X3,X26,X27] :
( c_in(c_Main_OdiagE__1(X27,X26,X3),X27,X3)
| ~ c_in(X26,c_Relation_Odiag(X27,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f14385,plain,
spl0_1594,
inference(avatar_split_clause,[],[f1572,f14383]) ).
fof(f14383,plain,
( spl0_1594
<=> ! [X20,X11,X8,X3] :
( c_Wellfounded__Recursion_Owf(X20,X3)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f1572,axiom,
! [X3,X11,X8,X20] :
( c_Wellfounded__Recursion_Owf(X20,X3)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f14381,plain,
spl0_1593,
inference(avatar_split_clause,[],[f1569,f14379]) ).
fof(f14379,plain,
( spl0_1593
<=> ! [X20,X11,X8,X3] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f1569,axiom,
! [X3,X11,X8,X20] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X11,X3,X3),X20,tc_prod(X3,X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f14377,plain,
spl0_1592,
inference(avatar_split_clause,[],[f1507,f14375]) ).
fof(f14375,plain,
( spl0_1592
<=> ! [X30,X80,X27,X3] :
( ~ c_in(X27,X30,X3)
| ~ c_in(X30,X80,tc_set(X3))
| c_in(X27,c_Union(X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f1507,axiom,
! [X3,X80,X27,X30] :
( ~ c_in(X27,X30,X3)
| ~ c_in(X30,X80,tc_set(X3))
| c_in(X27,c_Union(X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f14373,plain,
spl0_1591,
inference(avatar_split_clause,[],[f1494,f14371]) ).
fof(f14369,plain,
spl0_1590,
inference(avatar_split_clause,[],[f1490,f14367]) ).
fof(f14367,plain,
( spl0_1590
<=> ! [X31,X27,X3,X26] :
( c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| ~ c_in(X26,c_union(X27,X31,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f1490,axiom,
! [X31,X3,X26,X27] :
( c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| ~ c_in(X26,c_union(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f14365,plain,
spl0_1589,
inference(avatar_split_clause,[],[f1470,f14363]) ).
fof(f14363,plain,
( spl0_1589
<=> ! [X30,X80,X27,X3] :
( c_in(X27,X30,X3)
| ~ c_in(X30,X80,tc_set(X3))
| ~ c_in(X27,c_Inter(X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f1470,axiom,
! [X3,X80,X27,X30] :
( c_in(X27,X30,X3)
| ~ c_in(X30,X80,tc_set(X3))
| ~ c_in(X27,c_Inter(X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f14361,plain,
spl0_1588,
inference(avatar_split_clause,[],[f1443,f14359]) ).
fof(f14359,plain,
( spl0_1588
<=> ! [X27,X3,X31] : c_minus(X27,X31,tc_set(X3)) = c_minus(c_minus(X27,X31,tc_set(X3)),X31,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f1443,axiom,
! [X31,X3,X27] : c_minus(X27,X31,tc_set(X3)) = c_minus(c_minus(X27,X31,tc_set(X3)),X31,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f14357,plain,
spl0_1587,
inference(avatar_split_clause,[],[f1422,f14355]) ).
fof(f14355,plain,
( spl0_1587
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X11,X8,X3)
| c_lessequals(c_SetInterval_OlessThan(X11,X3),c_SetInterval_OlessThan(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f1422,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X11,X8,X3)
| c_lessequals(c_SetInterval_OlessThan(X11,X3),c_SetInterval_OlessThan(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f14353,plain,
spl0_1586,
inference(avatar_split_clause,[],[f1421,f14351]) ).
fof(f14351,plain,
( spl0_1586
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X11,X8,X3)
| ~ c_lessequals(c_SetInterval_OlessThan(X11,X3),c_SetInterval_OlessThan(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f1421,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X11,X8,X3)
| ~ c_lessequals(c_SetInterval_OlessThan(X11,X3),c_SetInterval_OlessThan(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f14349,plain,
( ~ spl0_1585
| spl0_95
| ~ spl0_801
| ~ spl0_1089
| ~ spl0_1236 ),
inference(avatar_split_clause,[],[f12613,f9978,f8834,f7281,f3631,f14346]) ).
fof(f14346,plain,
( spl0_1585
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f7281,plain,
( spl0_801
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f8834,plain,
( spl0_1089
<=> ! [X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f12613,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_801
| ~ spl0_1089
| ~ spl0_1236 ),
inference(forward_demodulation,[],[f12605,f7283]) ).
fof(f7283,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7281]) ).
fof(f12605,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_1089
| ~ spl0_1236 ),
inference(superposition,[],[f8835,f9980]) ).
fof(f8835,plain,
( ! [X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) )
| ~ spl0_1089 ),
inference(avatar_component_clause,[],[f8834]) ).
fof(f14344,plain,
spl0_1584,
inference(avatar_split_clause,[],[f1411,f14342]) ).
fof(f14342,plain,
( spl0_1584
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X11,X3)
| c_lessequals(c_SetInterval_OgreaterThan(X11,X3),c_SetInterval_OgreaterThan(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f1411,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X11,X3)
| c_lessequals(c_SetInterval_OgreaterThan(X11,X3),c_SetInterval_OgreaterThan(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f14340,plain,
spl0_1583,
inference(avatar_split_clause,[],[f1410,f14338]) ).
fof(f1410,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X8,X11,X3)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X11,X3),c_SetInterval_OgreaterThan(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f14336,plain,
spl0_1582,
inference(avatar_split_clause,[],[f1398,f14334]) ).
fof(f14334,plain,
( spl0_1582
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,c_plus(X74,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f1398,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,c_plus(X74,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f14332,plain,
spl0_1581,
inference(avatar_split_clause,[],[f1391,f14330]) ).
fof(f14330,plain,
( spl0_1581
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X38,X74,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f1391,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X38,X74,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f14328,plain,
spl0_1580,
inference(avatar_split_clause,[],[f1389,f14326]) ).
fof(f14326,plain,
( spl0_1580
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X11,X8,X3)
| c_lessequals(c_SetInterval_OatMost(X11,X3),c_SetInterval_OatMost(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f1389,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X11,X8,X3)
| c_lessequals(c_SetInterval_OatMost(X11,X3),c_SetInterval_OatMost(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f14324,plain,
spl0_1579,
inference(avatar_split_clause,[],[f1388,f14322]) ).
fof(f14322,plain,
( spl0_1579
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X8,X3)
| ~ c_lessequals(c_SetInterval_OatMost(X11,X3),c_SetInterval_OatMost(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f1388,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X8,X3)
| ~ c_lessequals(c_SetInterval_OatMost(X11,X3),c_SetInterval_OatMost(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f14320,plain,
spl0_1578,
inference(avatar_split_clause,[],[f1383,f14318]) ).
fof(f14318,plain,
( spl0_1578
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X8,X11,X3)
| c_lessequals(c_SetInterval_OatLeast(X11,X3),c_SetInterval_OatLeast(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f1383,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X8,X11,X3)
| c_lessequals(c_SetInterval_OatLeast(X11,X3),c_SetInterval_OatLeast(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f14316,plain,
spl0_1577,
inference(avatar_split_clause,[],[f1382,f14314]) ).
fof(f14314,plain,
( spl0_1577
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X11,X3)
| ~ c_lessequals(c_SetInterval_OatLeast(X11,X3),c_SetInterval_OatLeast(X8,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f1382,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X11,X3)
| ~ c_lessequals(c_SetInterval_OatLeast(X11,X3),c_SetInterval_OatLeast(X8,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f14312,plain,
spl0_1576,
inference(avatar_split_clause,[],[f1340,f14310]) ).
fof(f1340,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_uminus(c_times(X15,X16,X3),X3) = c_times(X15,c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f14308,plain,
spl0_1575,
inference(avatar_split_clause,[],[f1339,f14306]) ).
fof(f1339,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_times(c_uminus(X15,X3),X16,X3) = c_uminus(c_times(X15,X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f14304,plain,
( spl0_1574
| ~ spl0_976
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f12317,f9691,f8179,f14302]) ).
fof(f14302,plain,
( spl0_1574
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f9691,plain,
( spl0_1216
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f12317,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_976
| ~ spl0_1216 ),
inference(superposition,[],[f8180,f9692]) ).
fof(f9692,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9691]) ).
fof(f14300,plain,
spl0_1573,
inference(avatar_split_clause,[],[f1317,f14298]) ).
fof(f14298,plain,
( spl0_1573
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_times(X15,X16,X3) = c_times(c_uminus(X15,X3),c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f1317,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oring(X3)
| c_times(X15,X16,X3) = c_times(c_uminus(X15,X3),c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f14296,plain,
spl0_1572,
inference(avatar_split_clause,[],[f1162,f14294]) ).
fof(f14294,plain,
( spl0_1572
<=> ! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f1162,axiom,
! [X3,X35] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Numeral_Onumber__of(X35,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X35,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f14292,plain,
spl0_1571,
inference(avatar_split_clause,[],[f1156,f14290]) ).
fof(f14290,plain,
( spl0_1571
<=> ! [X11,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f1156,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Power_Orecpower(X3)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f14288,plain,
spl0_1570,
inference(avatar_split_clause,[],[f1154,f14286]) ).
fof(f14286,plain,
( spl0_1570
<=> ! [X11,X3] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X3),X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f1154,axiom,
! [X3,X11] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X3),X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f14284,plain,
spl0_1569,
inference(avatar_split_clause,[],[f1059,f14282]) ).
fof(f14282,plain,
( spl0_1569
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_plus(X15,X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f1059,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_plus(X15,X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f14280,plain,
spl0_1568,
inference(avatar_split_clause,[],[f1058,f14278]) ).
fof(f14278,plain,
( spl0_1568
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_Orderings_Olinorder(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_plus(X15,X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f1058,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_Orderings_Olinorder(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_plus(X15,X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f14276,plain,
spl0_1567,
inference(avatar_split_clause,[],[f930,f14274]) ).
fof(f14274,plain,
( spl0_1567
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f930,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f14272,plain,
spl0_1566,
inference(avatar_split_clause,[],[f910,f14270]) ).
fof(f14270,plain,
( spl0_1566
<=> ! [X25,X9,X10] :
( X10 = X25
| c_0 = X9
| c_times(X10,X9,tc_nat) != c_times(X25,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f910,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_0 = X9
| c_times(X10,X9,tc_nat) != c_times(X25,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f14268,plain,
spl0_1565,
inference(avatar_split_clause,[],[f908,f14266]) ).
fof(f14266,plain,
( spl0_1565
<=> ! [X25,X9,X10] :
( X10 = X25
| c_0 = X9
| c_times(X9,X10,tc_nat) != c_times(X9,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f908,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_0 = X9
| c_times(X9,X10,tc_nat) != c_times(X9,X25,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f14264,plain,
spl0_1564,
inference(avatar_split_clause,[],[f887,f14262]) ).
fof(f14257,plain,
spl0_1563,
inference(avatar_split_clause,[],[f878,f14255]) ).
fof(f14255,plain,
( spl0_1563
<=> ! [X25,X10] :
( c_less(c_0,X25,tc_nat)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f878,axiom,
! [X10,X25] :
( c_less(c_0,X25,tc_nat)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f14253,plain,
spl0_1562,
inference(avatar_split_clause,[],[f713,f14251]) ).
fof(f14251,plain,
( spl0_1562
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f713,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f14249,plain,
spl0_1561,
inference(avatar_split_clause,[],[f710,f14247]) ).
fof(f14247,plain,
( spl0_1561
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f710,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f14245,plain,
spl0_1560,
inference(avatar_split_clause,[],[f697,f14243]) ).
fof(f14243,plain,
( spl0_1560
<=> ! [X36] :
( c_0 != c_Numeral_Onumber__of(X36,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f697,axiom,
! [X36] :
( c_0 != c_Numeral_Onumber__of(X36,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f14241,plain,
spl0_1559,
inference(avatar_split_clause,[],[f677,f14239]) ).
fof(f14239,plain,
( spl0_1559
<=> ! [X77,X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f677,axiom,
! [X36,X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X36,tc_nat),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f14237,plain,
spl0_1558,
inference(avatar_split_clause,[],[f651,f14235]) ).
fof(f14235,plain,
( spl0_1558
<=> ! [X25,X10] :
( ~ c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_minus(X25,X10,tc_nat),X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f651,axiom,
! [X10,X25] :
( ~ c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_minus(X25,X10,tc_nat),X25,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f14233,plain,
spl0_1557,
inference(avatar_split_clause,[],[f599,f14231]) ).
fof(f599,axiom,
! [X41,X3,X42] : c_List_Oset(c_append(X41,X42,X3),X3) = c_union(c_List_Oset(X41,X3),c_List_Oset(X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f14229,plain,
spl0_1556,
inference(avatar_split_clause,[],[f589,f14227]) ).
fof(f589,axiom,
! [X3,X10,X8] :
( c_List_Orotate(X10,X8,X3) = X8
| c_0 != c_Divides_Oop_Amod(X10,c_Nat_Osize(X8,tc_List_Olist(X3)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f14225,plain,
spl0_1555,
inference(avatar_split_clause,[],[f575,f14223]) ).
fof(f14223,plain,
( spl0_1555
<=> ! [X41,X3,X42] : c_List_Orev(c_append(X41,X42,X3),X3) = c_append(c_List_Orev(X42,X3),c_List_Orev(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f575,axiom,
! [X41,X3,X42] : c_List_Orev(c_append(X41,X42,X3),X3) = c_append(c_List_Orev(X42,X3),c_List_Orev(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f14221,plain,
spl0_1554,
inference(avatar_split_clause,[],[f558,f14219]) ).
fof(f558,axiom,
! [X41,X11,X42,X13] : c_append(c_List_Olist_OCons(X11,X41,X13),X42,X13) = c_List_Olist_OCons(X11,c_append(X41,X42,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f14202,plain,
spl0_1553,
inference(avatar_split_clause,[],[f546,f14200]) ).
fof(f14200,plain,
( spl0_1553
<=> ! [X41,X42,X3,X8] : c_List_Onth(c_append(X41,c_List_Olist_OCons(X8,X42,X3),X3),c_Nat_Osize(X41,tc_List_Olist(X3)),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f546,axiom,
! [X41,X3,X8,X42] : c_List_Onth(c_append(X41,c_List_Olist_OCons(X8,X42,X3),X3),c_Nat_Osize(X41,tc_List_Olist(X3)),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f14198,plain,
spl0_1552,
inference(avatar_split_clause,[],[f541,f14196]) ).
fof(f14196,plain,
( spl0_1552
<=> ! [X41,X51,X11,X3] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| ~ c_in(X11,c_List_Oset(c_List_Osublist(X41,X51,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f541,axiom,
! [X51,X41,X3,X11] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| ~ c_in(X11,c_List_Oset(c_List_Osublist(X41,X51,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f14194,plain,
spl0_1551,
inference(avatar_split_clause,[],[f540,f14192]) ).
fof(f14192,plain,
( spl0_1551
<=> ! [X41,X11,X3,X8] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| ~ c_in(X11,c_List_Oset(c_List_Oremove1(X8,X41,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f540,axiom,
! [X41,X3,X11,X8] :
( c_in(X11,c_List_Oset(X41,X3),X3)
| ~ c_in(X11,c_List_Oset(c_List_Oremove1(X8,X41,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f14190,plain,
spl0_1550,
inference(avatar_split_clause,[],[f451,f14188]) ).
fof(f14188,plain,
( spl0_1550
<=> ! [X41,X3,X10] : c_Nat_Osize(c_List_Odrop(X10,X41,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f451,axiom,
! [X41,X10,X3] : c_Nat_Osize(c_List_Odrop(X10,X41,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f14186,plain,
spl0_1549,
inference(avatar_split_clause,[],[f427,f14184]) ).
fof(f14184,plain,
( spl0_1549
<=> ! [X24,X11,X9,X3] : c_List_Odrop(X24,c_List_Oreplicate(X9,X11,X3),X3) = c_List_Oreplicate(c_minus(X9,X24,tc_nat),X11,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f427,axiom,
! [X3,X11,X9,X24] : c_List_Odrop(X24,c_List_Oreplicate(X9,X11,X3),X3) = c_List_Oreplicate(c_minus(X9,X24,tc_nat),X11,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f14182,plain,
spl0_1548,
inference(avatar_split_clause,[],[f424,f14180]) ).
fof(f14180,plain,
( spl0_1548
<=> ! [X41,X10,X3,X25] : c_List_Odrop(X10,c_List_Odrop(X25,X41,X3),X3) = c_List_Odrop(c_plus(X10,X25,tc_nat),X41,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f424,axiom,
! [X41,X10,X3,X25] : c_List_Odrop(X10,c_List_Odrop(X25,X41,X3),X3) = c_List_Odrop(c_plus(X10,X25,tc_nat),X41,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f14178,plain,
spl0_1547,
inference(avatar_split_clause,[],[f404,f14176]) ).
fof(f14176,plain,
( spl0_1547
<=> ! [X13,X41,X11] :
( ~ c_List_Odistinct(X41,X13)
| c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| c_in(X11,c_List_Oset(X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f404,axiom,
! [X41,X11,X13] :
( ~ c_List_Odistinct(X41,X13)
| c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| c_in(X11,c_List_Oset(X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f14174,plain,
spl0_1546,
inference(avatar_split_clause,[],[f397,f14172]) ).
fof(f14172,plain,
( spl0_1546
<=> ! [X43,X3] :
( c_List_Olist_ONil = c_List_Oconcat(X43,X3)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X43,X3),c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f397,axiom,
! [X3,X43] :
( c_List_Olist_ONil = c_List_Oconcat(X43,X3)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X43,X3),c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f14170,plain,
spl0_1545,
inference(avatar_split_clause,[],[f368,f14168]) ).
fof(f14168,plain,
( spl0_1545
<=> ! [X41,X42,X44,X3] : c_append(c_append(X41,X42,X3),X44,X3) = c_append(X41,c_append(X42,X44,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f368,axiom,
! [X41,X3,X44,X42] : c_append(c_append(X41,X42,X3),X44,X3) = c_append(X41,c_append(X42,X44,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f14166,plain,
spl0_1544,
inference(avatar_split_clause,[],[f358,f14164]) ).
fof(f14164,plain,
( spl0_1544
<=> ! [X43,X3] :
( c_List_Olist_ONil = c_List_Oconcat(X43,X3)
| c_in(c_Main_ONil__eq__concat__conv__1(X43,X3),c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f358,axiom,
! [X3,X43] :
( c_List_Olist_ONil = c_List_Oconcat(X43,X3)
| c_in(c_Main_ONil__eq__concat__conv__1(X43,X3),c_List_Oset(X43,tc_List_Olist(X3)),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f14161,plain,
spl0_1543,
inference(avatar_split_clause,[],[f345,f14159]) ).
fof(f14159,plain,
( spl0_1543
<=> ! [X16,X15] : c_Divides_Oop_Amod(c_uminus(X15,tc_IntDef_Oint),c_uminus(X16,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f345,axiom,
! [X16,X15] : c_Divides_Oop_Amod(c_uminus(X15,tc_IntDef_Oint),c_uminus(X16,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f14157,plain,
spl0_1542,
inference(avatar_split_clause,[],[f89,f14155]) ).
fof(f14155,plain,
( spl0_1542
<=> ! [X9,X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,c_times(X10,X9,tc_nat),tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f89,axiom,
! [X10,X9,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,c_times(X10,X9,tc_nat),tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f14153,plain,
spl0_1541,
inference(avatar_split_clause,[],[f87,f14151]) ).
fof(f14151,plain,
( spl0_1541
<=> ! [X9,X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,c_times(X9,X10,tc_nat),tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f87,axiom,
! [X10,X9,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,c_times(X9,X10,tc_nat),tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f14149,plain,
spl0_1540,
inference(avatar_split_clause,[],[f67,f14147]) ).
fof(f14147,plain,
( spl0_1540
<=> ! [X25,X10] :
( ~ c_less(c_1,X10,tc_nat)
| ~ c_less(c_0,X25,tc_nat)
| c_less(c_div(X25,X10,tc_nat),X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f67,axiom,
! [X10,X25] :
( ~ c_less(c_1,X10,tc_nat)
| ~ c_less(c_0,X25,tc_nat)
| c_less(c_div(X25,X10,tc_nat),X25,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f14077,plain,
( spl0_1539
| ~ spl0_697
| ~ spl0_698
| ~ spl0_700
| ~ spl0_775
| ~ spl0_1451 ),
inference(avatar_split_clause,[],[f12839,f11787,f7172,f6854,f6846,f6841,f14075]) ).
fof(f6854,plain,
( spl0_700
<=> ! [X35] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f11787,plain,
( spl0_1451
<=> ! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),X35) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35),X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f12839,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_697
| ~ spl0_698
| ~ spl0_700
| ~ spl0_775
| ~ spl0_1451 ),
inference(forward_demodulation,[],[f12838,f6847]) ).
fof(f12838,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_697
| ~ spl0_700
| ~ spl0_775
| ~ spl0_1451 ),
inference(forward_demodulation,[],[f12837,f7174]) ).
fof(f12837,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_697
| ~ spl0_700
| ~ spl0_1451 ),
inference(forward_demodulation,[],[f12826,f6855]) ).
fof(f6855,plain,
( ! [X35] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X35)
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f6854]) ).
fof(f12826,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_697
| ~ spl0_1451 ),
inference(superposition,[],[f11788,f6843]) ).
fof(f11788,plain,
( ! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),X35) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35),X35)
| ~ spl0_1451 ),
inference(avatar_component_clause,[],[f11787]) ).
fof(f13940,plain,
( spl0_1538
| ~ spl0_696
| ~ spl0_698
| ~ spl0_723
| ~ spl0_775
| ~ spl0_866
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f12821,f11783,f7545,f7172,f6950,f6846,f6836,f13937]) ).
fof(f12821,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_696
| ~ spl0_698
| ~ spl0_723
| ~ spl0_775
| ~ spl0_866
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12820,f6838]) ).
fof(f12820,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_698
| ~ spl0_723
| ~ spl0_775
| ~ spl0_866
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12819,f7174]) ).
fof(f12819,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_698
| ~ spl0_723
| ~ spl0_866
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12818,f6847]) ).
fof(f12818,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_723
| ~ spl0_866
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f12812,f7546]) ).
fof(f12812,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_723
| ~ spl0_1450 ),
inference(superposition,[],[f11784,f6952]) ).
fof(f13807,plain,
( spl0_1537
| ~ spl0_757
| ~ spl0_1367 ),
inference(avatar_split_clause,[],[f11936,f11381,f7100,f13805]) ).
fof(f13805,plain,
( spl0_1537
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f11936,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_757
| ~ spl0_1367 ),
inference(superposition,[],[f7101,f11382]) ).
fof(f13275,plain,
( ~ spl0_1535
| spl0_1536
| ~ spl0_122
| ~ spl0_1267 ),
inference(avatar_split_clause,[],[f10697,f10122,f3752,f13273,f13269]) ).
fof(f13269,plain,
( spl0_1535
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f13273,plain,
( spl0_1536
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f10122,plain,
( spl0_1267
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f10697,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_122
| ~ spl0_1267 ),
inference(resolution,[],[f10123,f3753]) ).
fof(f10123,plain,
( ! [X3,X15] :
( ~ c_lessequals(c_0,c_uminus(X15,X3),X3)
| c_lessequals(X15,c_0,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) )
| ~ spl0_1267 ),
inference(avatar_component_clause,[],[f10122]) ).
fof(f13196,plain,
spl0_1534,
inference(avatar_split_clause,[],[f3113,f13194]) ).
fof(f13194,plain,
( spl0_1534
<=> ! [X8,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f3113,plain,
! [X3,X8] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X8,X3) ),
inference(forward_demodulation,[],[f2919,f964]) ).
fof(f2919,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X8,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f184,f979]) ).
fof(f184,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X8,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f13192,plain,
spl0_1533,
inference(avatar_split_clause,[],[f3108,f13190]) ).
fof(f13190,plain,
( spl0_1533
<=> ! [X8,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f3108,plain,
! [X3,X8] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X8,X3) ),
inference(forward_demodulation,[],[f2915,f964]) ).
fof(f2915,plain,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X8,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X3),X3) ),
inference(definition_unfolding,[],[f183,f979]) ).
fof(f183,axiom,
! [X3,X8] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X8,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f13183,plain,
spl0_1532,
inference(avatar_split_clause,[],[f3001,f13181]) ).
fof(f13181,plain,
( spl0_1532
<=> ! [X77] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f3001,plain,
! [X77] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2823,f2749]) ).
fof(f2823,plain,
! [X77] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X77,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(X77,tc_nat),tc_nat),
inference(definition_unfolding,[],[f720,f1394]) ).
fof(f720,axiom,
! [X77] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f13179,plain,
spl0_1531,
inference(avatar_split_clause,[],[f2924,f13177]) ).
fof(f13177,plain,
( spl0_1531
<=> ! [X41,X3,X10] :
( c_List_Olist_ONil = X41
| c_0 = X10
| c_List_Olist_ONil != c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f2924,plain,
! [X41,X10,X3] :
( c_List_Olist_ONil = X41
| c_0 = X10
| c_List_Olist_ONil != c_List_Osublist(X41,c_SetInterval_OlessThan(X10,tc_nat),X3) ),
inference(definition_unfolding,[],[f622,f616]) ).
fof(f622,axiom,
! [X41,X10,X3] :
( c_List_Olist_ONil = X41
| c_0 = X10
| c_List_Olist_ONil != c_List_Otake(X10,X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f13170,plain,
( spl0_1530
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1529 ),
inference(avatar_split_clause,[],[f13166,f13163,f10415,f10092,f6703,f3695,f13168]) ).
fof(f13168,plain,
( spl0_1530
<=> ! [X36] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f13163,plain,
( spl0_1529
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f13166,plain,
( ! [X36] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1529 ),
inference(forward_demodulation,[],[f13164,f11235]) ).
fof(f13164,plain,
( ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1529 ),
inference(avatar_component_clause,[],[f13163]) ).
fof(f13165,plain,
spl0_1529,
inference(avatar_split_clause,[],[f2890,f13163]) ).
fof(f2890,plain,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X36,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f672,f1394]) ).
fof(f672,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X36,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f13161,plain,
spl0_1528,
inference(avatar_split_clause,[],[f2888,f13159]) ).
fof(f13159,plain,
( spl0_1528
<=> ! [X3,X31,X27,X26] :
( c_in(X26,X31,X3)
| ~ c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f2888,plain,
! [X31,X3,X26,X27] :
( c_in(X26,X31,X3)
| ~ c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ),
inference(definition_unfolding,[],[f1457,f1223]) ).
fof(f1457,axiom,
! [X31,X3,X26,X27] :
( c_in(X26,X31,X3)
| ~ c_in(X26,c_inter(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f13157,plain,
spl0_1527,
inference(avatar_split_clause,[],[f2887,f13155]) ).
fof(f13155,plain,
( spl0_1527
<=> ! [X31,X27,X3,X26] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f2887,plain,
! [X31,X3,X26,X27] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),X3) ),
inference(definition_unfolding,[],[f1456,f1223]) ).
fof(f1456,axiom,
! [X31,X3,X26,X27] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_inter(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f13153,plain,
spl0_1526,
inference(avatar_split_clause,[],[f2857,f13151]) ).
fof(f2857,plain,
! [X10,X25] :
( X10 = X25
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f867,f1394,f1394]) ).
fof(f867,axiom,
! [X10,X25] :
( X10 = X25
| c_Suc(X10) != c_Suc(X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f13149,plain,
spl0_1525,
inference(avatar_split_clause,[],[f2805,f13147]) ).
fof(f2805,plain,
! [X3,X10,X8] : c_append(c_List_Osublist(X8,c_SetInterval_OlessThan(X10,tc_nat),X3),c_List_Odrop(X10,X8,X3),X3) = X8,
inference(definition_unfolding,[],[f385,f616]) ).
fof(f385,axiom,
! [X3,X10,X8] : c_append(c_List_Otake(X10,X8,X3),c_List_Odrop(X10,X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f13145,plain,
spl0_1524,
inference(avatar_split_clause,[],[f1676,f13143]) ).
fof(f13143,plain,
( spl0_1524
<=> ! [X80,X27,X3] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(c_Main_OUnionE__1(X27,X80,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f1676,axiom,
! [X3,X80,X27] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(c_Main_OUnionE__1(X27,X80,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f13137,plain,
spl0_1523,
inference(avatar_split_clause,[],[f1673,f13135]) ).
fof(f13135,plain,
( spl0_1523
<=> ! [X80,X27,X3] :
( c_in(X27,c_Inter(X80,X3),X3)
| c_in(c_Main_OInterI__1(X27,X80,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f1673,axiom,
! [X3,X80,X27] :
( c_in(X27,c_Inter(X80,X3),X3)
| c_in(c_Main_OInterI__1(X27,X80,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13133,plain,
spl0_1522,
inference(avatar_split_clause,[],[f1636,f13131]) ).
fof(f13131,plain,
( spl0_1522
<=> ! [X11,X27,X74,X3] :
( c_in(X11,X27,X3)
| ~ c_in(c_List_Olist_OCons(X11,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f1636,axiom,
! [X3,X11,X27,X74] :
( c_in(X11,X27,X3)
| ~ c_in(c_List_Olist_OCons(X11,X74,X3),c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13129,plain,
spl0_1521,
inference(avatar_split_clause,[],[f1625,f13127]) ).
fof(f1625,axiom,
! [X41,X3,X27] :
( ~ c_in(c_Main_Oin__listsI__1(X27,X41,X3),X27,X3)
| c_in(X41,c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13125,plain,
spl0_1520,
inference(avatar_split_clause,[],[f1620,f13123]) ).
fof(f1620,axiom,
! [X81,X25] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_IntDef_Oint)
| c_times(X81,c_Main_Ozmod__eq__0D__dest__1(X81,X25),tc_IntDef_Oint) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13121,plain,
spl0_1519,
inference(avatar_split_clause,[],[f1604,f13119]) ).
fof(f1604,axiom,
! [X81,X25] :
( c_0 != c_Divides_Oop_Amod(X25,X81,tc_nat)
| c_times(X81,c_Main_Omod__eq__0D__dest__1(X81,X25),tc_nat) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13117,plain,
spl0_1518,
inference(avatar_split_clause,[],[f1577,f13115]) ).
fof(f13115,plain,
( spl0_1518
<=> ! [X11,X8] :
( ~ c_less(X11,X8,tc_nat)
| c_in(c_Pair(X11,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f1577,axiom,
! [X11,X8] :
( ~ c_less(X11,X8,tc_nat)
| c_in(c_Pair(X11,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f13113,plain,
spl0_1517,
inference(avatar_split_clause,[],[f1576,f13111]) ).
fof(f13111,plain,
( spl0_1517
<=> ! [X11,X8] :
( c_less(X11,X8,tc_nat)
| ~ c_in(c_Pair(X11,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f1576,axiom,
! [X11,X8] :
( c_less(X11,X8,tc_nat)
| ~ c_in(c_Pair(X11,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f13109,plain,
spl0_1516,
inference(avatar_split_clause,[],[f1533,f13107]) ).
fof(f13107,plain,
( spl0_1516
<=> ! [X15,X16,X27,X3] :
( X15 = X16
| c_in(X15,X27,X3)
| ~ c_in(X15,c_insert(X16,X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f1533,axiom,
! [X3,X16,X27,X15] :
( X15 = X16
| c_in(X15,X27,X3)
| ~ c_in(X15,c_insert(X16,X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f13105,plain,
spl0_1515,
inference(avatar_split_clause,[],[f1508,f13103]) ).
fof(f13103,plain,
( spl0_1515
<=> ! [X15,X3,X31] : c_Union(c_insert(X15,X31,tc_set(X3)),X3) = c_union(X15,c_Union(X31,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f1508,axiom,
! [X31,X3,X15] : c_Union(c_insert(X15,X31,tc_set(X3)),X3) = c_union(X15,c_Union(X31,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f13101,plain,
spl0_1514,
inference(avatar_split_clause,[],[f1505,f13099]) ).
fof(f13099,plain,
( spl0_1514
<=> ! [X80,X27,X3] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(c_Main_OUnion__iff__1(X27,X80,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f1505,axiom,
! [X3,X80,X27] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(c_Main_OUnion__iff__1(X27,X80,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f13097,plain,
spl0_1513,
inference(avatar_split_clause,[],[f1471,f13095]) ).
fof(f13095,plain,
( spl0_1513
<=> ! [X80,X27,X3] :
( c_in(X27,c_Inter(X80,X3),X3)
| c_in(c_Main_OInter__iff__1(X27,X80,X3),X80,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f1471,axiom,
! [X3,X80,X27] :
( c_in(X27,c_Inter(X80,X3),X3)
| c_in(c_Main_OInter__iff__1(X27,X80,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f13093,plain,
spl0_1512,
inference(avatar_split_clause,[],[f1338,f13091]) ).
fof(f13091,plain,
( spl0_1512
<=> ! [X16,X3,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_0 = X15
| c_0 = X16
| c_0 != c_times(X15,X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f1338,axiom,
! [X3,X16,X15] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_0 = X15
| c_0 = X16
| c_0 != c_times(X15,X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f13089,plain,
spl0_1511,
inference(avatar_split_clause,[],[f1322,f13087]) ).
fof(f13087,plain,
( spl0_1511
<=> ! [X16,X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = X16
| c_0 = X26
| c_times(X16,X26,X3) != X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f1322,axiom,
! [X3,X26,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = X16
| c_0 = X26
| c_times(X16,X26,X3) != X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
fof(f13085,plain,
spl0_1510,
inference(avatar_split_clause,[],[f1321,f13083]) ).
fof(f13083,plain,
( spl0_1510
<=> ! [X26,X3,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = X15
| c_0 = X26
| c_times(X26,X15,X3) != X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f1321,axiom,
! [X3,X26,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = X15
| c_0 = X26
| c_times(X26,X15,X3) != X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f13081,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1213,f13079]) ).
fof(f13079,plain,
( spl0_1509
<=> ! [X15,X17,X14,X78,X3,X16] :
( X16 = X78
| c_Pair(X15,X16,X3,X17) != c_Pair(X14,X78,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f1213,axiom,
! [X3,X78,X16,X14,X17,X15] :
( X16 = X78
| c_Pair(X15,X16,X3,X17) != c_Pair(X14,X78,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f13077,plain,
spl0_1508,
inference(avatar_split_clause,[],[f1212,f13075]) ).
fof(f13075,plain,
( spl0_1508
<=> ! [X17,X16,X14,X78,X3,X15] :
( X14 = X15
| c_Pair(X15,X16,X3,X17) != c_Pair(X14,X78,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1212,axiom,
! [X3,X78,X16,X14,X17,X15] :
( X14 = X15
| c_Pair(X15,X16,X3,X17) != c_Pair(X14,X78,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f13073,plain,
spl0_1507,
inference(avatar_split_clause,[],[f1199,f13071]) ).
fof(f13071,plain,
( spl0_1507
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_0 = c_Nat_Opower(c_0,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1199,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_0 = c_Nat_Opower(c_0,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f13069,plain,
spl0_1506,
inference(avatar_split_clause,[],[f1198,f13067]) ).
fof(f13067,plain,
( spl0_1506
<=> ! [X15,X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X10,tc_nat)
| c_0 != c_Nat_Opower(X15,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f1198,axiom,
! [X3,X10,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X10,tc_nat)
| c_0 != c_Nat_Opower(X15,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f13065,plain,
spl0_1505,
inference(avatar_split_clause,[],[f1118,f13063]) ).
fof(f13063,plain,
( spl0_1505
<=> ! [X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X11,X8,X17) = c_Orderings_Omax(X11,c_Orderings_Omax(X11,X8,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f1118,axiom,
! [X11,X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X11,X8,X17) = c_Orderings_Omax(X11,c_Orderings_Omax(X11,X8,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f13061,plain,
spl0_1504,
inference(avatar_split_clause,[],[f1113,f13059]) ).
fof(f13059,plain,
( spl0_1504
<=> ! [X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X11,X8,X17) = c_Orderings_Omin(X11,c_Orderings_Omin(X11,X8,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f1113,axiom,
! [X11,X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X11,X8,X17) = c_Orderings_Omin(X11,c_Orderings_Omin(X11,X8,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f13057,plain,
( ~ spl0_1502
| spl0_1503
| ~ spl0_122
| ~ spl0_1231 ),
inference(avatar_split_clause,[],[f10489,f9958,f3752,f13055,f13051]) ).
fof(f13051,plain,
( spl0_1502
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f13055,plain,
( spl0_1503
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f9958,plain,
( spl0_1231
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f10489,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_122
| ~ spl0_1231 ),
inference(resolution,[],[f9959,f3753]) ).
fof(f9959,plain,
( ! [X3,X37] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3)
| c_lessequals(c_0,X37,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_1231 ),
inference(avatar_component_clause,[],[f9958]) ).
fof(f13049,plain,
spl0_1501,
inference(avatar_split_clause,[],[f1096,f13047]) ).
fof(f13047,plain,
( spl0_1501
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_OrderedGroup_Opprt(X15,X3),c_OrderedGroup_Opprt(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f1096,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_OrderedGroup_Opprt(X15,X3),c_OrderedGroup_Opprt(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f13045,plain,
spl0_1500,
inference(avatar_split_clause,[],[f1092,f13043]) ).
fof(f13043,plain,
( spl0_1500
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_OrderedGroup_Onprt(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f1092,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_OrderedGroup_Onprt(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f13041,plain,
spl0_1499,
inference(avatar_split_clause,[],[f1086,f13039]) ).
fof(f13039,plain,
( spl0_1499
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_uminus(X16,X3),c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f1086,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_uminus(X16,X3),c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f13037,plain,
spl0_1498,
inference(avatar_split_clause,[],[f1085,f13035]) ).
fof(f13035,plain,
( spl0_1498
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_uminus(X16,X3),c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f1085,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_uminus(X16,X3),c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f13033,plain,
spl0_1497,
inference(avatar_split_clause,[],[f1082,f13031]) ).
fof(f13031,plain,
( spl0_1497
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_uminus(X16,X3),c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f1082,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_uminus(X16,X3),c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f13029,plain,
spl0_1496,
inference(avatar_split_clause,[],[f1081,f13027]) ).
fof(f13027,plain,
( spl0_1496
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_uminus(X16,X3),c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f1081,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_uminus(X16,X3),c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f13025,plain,
spl0_1495,
inference(avatar_split_clause,[],[f1045,f13023]) ).
fof(f13023,plain,
( spl0_1495
<=> ! [X3,X16,X15,X26] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X16 = X26
| c_plus(X26,X15,X3) != c_plus(X16,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f1045,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X16 = X26
| c_plus(X26,X15,X3) != c_plus(X16,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f13021,plain,
spl0_1494,
inference(avatar_split_clause,[],[f1040,f13019]) ).
fof(f13019,plain,
( spl0_1494
<=> ! [X3,X16,X15,X26] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X16 = X26
| c_plus(X15,X16,X3) != c_plus(X15,X26,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f1040,axiom,
! [X3,X26,X16,X15] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X16 = X26
| c_plus(X15,X16,X3) != c_plus(X15,X26,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f13017,plain,
spl0_1493,
inference(avatar_split_clause,[],[f961,f13015]) ).
fof(f961,axiom,
! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,c_Numeral_Obin__succ(X35)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f13013,plain,
spl0_1492,
inference(avatar_split_clause,[],[f935,f13011]) ).
fof(f13011,plain,
( spl0_1492
<=> ! [X25,X9,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f935,axiom,
! [X10,X9,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f13004,plain,
spl0_1491,
inference(avatar_split_clause,[],[f934,f13002]) ).
fof(f13002,plain,
( spl0_1491
<=> ! [X25,X9,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f934,axiom,
! [X10,X9,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f13000,plain,
spl0_1490,
inference(avatar_split_clause,[],[f933,f12998]) ).
fof(f12998,plain,
( spl0_1490
<=> ! [X25,X9,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f933,axiom,
! [X10,X9,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f12996,plain,
spl0_1489,
inference(avatar_split_clause,[],[f932,f12994]) ).
fof(f12994,plain,
( spl0_1489
<=> ! [X25,X9,X10] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f932,axiom,
! [X10,X9,X25] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_plus(X9,X25,tc_nat),c_plus(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f12992,plain,
spl0_1488,
inference(avatar_split_clause,[],[f926,f12990]) ).
fof(f12990,plain,
( spl0_1488
<=> ! [X25,X9,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f926,axiom,
! [X10,X9,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f12988,plain,
spl0_1487,
inference(avatar_split_clause,[],[f925,f12986]) ).
fof(f12986,plain,
( spl0_1487
<=> ! [X9,X25,X10] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f925,axiom,
! [X10,X9,X25] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f12984,plain,
spl0_1486,
inference(avatar_split_clause,[],[f923,f12982]) ).
fof(f12982,plain,
( spl0_1486
<=> ! [X25,X9,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f923,axiom,
! [X10,X9,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f12980,plain,
spl0_1485,
inference(avatar_split_clause,[],[f922,f12978]) ).
fof(f12978,plain,
( spl0_1485
<=> ! [X9,X25,X10] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f922,axiom,
! [X10,X9,X25] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f12976,plain,
spl0_1484,
inference(avatar_split_clause,[],[f921,f12974]) ).
fof(f12974,plain,
( spl0_1484
<=> ! [X25,X9,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f921,axiom,
! [X10,X9,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f12972,plain,
spl0_1483,
inference(avatar_split_clause,[],[f920,f12970]) ).
fof(f12970,plain,
( spl0_1483
<=> ! [X9,X25,X10] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f920,axiom,
! [X10,X9,X25] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X25,X9,tc_nat),c_times(X10,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f12968,plain,
spl0_1482,
inference(avatar_split_clause,[],[f918,f12966]) ).
fof(f12966,plain,
( spl0_1482
<=> ! [X25,X9,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f918,axiom,
! [X10,X9,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f12958,plain,
spl0_1481,
inference(avatar_split_clause,[],[f917,f12956]) ).
fof(f12956,plain,
( spl0_1481
<=> ! [X9,X25,X10] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f917,axiom,
! [X10,X9,X25] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X25,tc_nat),c_times(X9,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f12954,plain,
spl0_1480,
inference(avatar_split_clause,[],[f777,f12952]) ).
fof(f12952,plain,
( spl0_1480
<=> ! [X16,X17] :
( ~ class_HOL_Oone(X17)
| ~ class_OrderedGroup_Oab__group__add(X17)
| c_1 != c_uminus(X16,X17)
| c_uminus(c_1,X17) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f777,axiom,
! [X16,X17] :
( ~ class_HOL_Oone(X17)
| ~ class_OrderedGroup_Oab__group__add(X17)
| c_1 != c_uminus(X16,X17)
| c_uminus(c_1,X17) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f12950,plain,
spl0_1479,
inference(avatar_split_clause,[],[f718,f12948]) ).
fof(f12948,plain,
( spl0_1479
<=> ! [X36,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X36,tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f718,axiom,
! [X3,X36] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X36,tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f12946,plain,
spl0_1478,
inference(avatar_split_clause,[],[f670,f12944]) ).
fof(f12944,plain,
( spl0_1478
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(X25,X10,tc_nat)
| c_less(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f670,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(X25,X10,tc_nat)
| c_less(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f12942,plain,
spl0_1477,
inference(avatar_split_clause,[],[f669,f12940]) ).
fof(f12940,plain,
( spl0_1477
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(X25,X10,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f669,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(X25,X10,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f12938,plain,
spl0_1476,
inference(avatar_split_clause,[],[f667,f12936]) ).
fof(f12936,plain,
( spl0_1476
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f667,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f12934,plain,
spl0_1475,
inference(avatar_split_clause,[],[f666,f12932]) ).
fof(f12932,plain,
( spl0_1475
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f666,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f12930,plain,
spl0_1474,
inference(avatar_split_clause,[],[f606,f12928]) ).
fof(f12928,plain,
( spl0_1474
<=> ! [X11,X3,X10] :
( c_0 = X10
| c_insert(X11,c_emptyset,X3) = c_List_Oset(c_List_Oreplicate(X10,X11,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f606,axiom,
! [X3,X10,X11] :
( c_0 = X10
| c_insert(X11,c_emptyset,X3) = c_List_Oset(c_List_Oreplicate(X10,X11,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f12926,plain,
spl0_1473,
inference(avatar_split_clause,[],[f583,f12924]) ).
fof(f12924,plain,
( spl0_1473
<=> ! [X41,X11,X3] :
( c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = X41
| c_List_Orev(X41,X3) != c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f583,axiom,
! [X3,X41,X11] :
( c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = X41
| c_List_Orev(X41,X3) != c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
fof(f12922,plain,
spl0_1472,
inference(avatar_split_clause,[],[f560,f12920]) ).
fof(f12920,plain,
( spl0_1472
<=> ! [X42,X11,X13,X8] :
( X8 = X11
| c_List_Oop_Amem(X11,X42,X13)
| ~ c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f560,axiom,
! [X11,X8,X42,X13] :
( X8 = X11
| c_List_Oop_Amem(X11,X42,X13)
| ~ c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f12918,plain,
spl0_1471,
inference(avatar_split_clause,[],[f490,f12916]) ).
fof(f12916,plain,
( spl0_1471
<=> ! [X13,X27,X59] : c_List_Olistset(c_List_Olist_OCons(X27,X59,tc_set(X13)),X13) = c_List_Oset__Cons(X27,c_List_Olistset(X59,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f490,axiom,
! [X59,X27,X13] : c_List_Olistset(c_List_Olist_OCons(X27,X59,tc_set(X13)),X13) = c_List_Oset__Cons(X27,c_List_Olistset(X59,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f12914,plain,
spl0_1470,
inference(avatar_split_clause,[],[f482,f12912]) ).
fof(f12912,plain,
( spl0_1470
<=> ! [X24,X11,X3,X8] :
( ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),X24,tc_nat)
| c_List_Olist__update(X8,X24,X11,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f482,axiom,
! [X3,X11,X8,X24] :
( ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),X24,tc_nat)
| c_List_Olist__update(X8,X24,X11,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f12910,plain,
spl0_1469,
inference(avatar_split_clause,[],[f462,f12908]) ).
fof(f12908,plain,
( spl0_1469
<=> ! [X41,X3] : c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f462,axiom,
! [X41,X3] : c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f12906,plain,
spl0_1468,
inference(avatar_split_clause,[],[f450,f12904]) ).
fof(f12904,plain,
( spl0_1468
<=> ! [X41,X3] : c_Nat_Osize(c_List_Obutlast(X41,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f450,axiom,
! [X41,X3] : c_Nat_Osize(c_List_Obutlast(X41,X3),tc_List_Olist(X3)) = c_minus(c_Nat_Osize(X41,tc_List_Olist(X3)),c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f12902,plain,
spl0_1467,
inference(avatar_split_clause,[],[f446,f12900]) ).
fof(f446,axiom,
! [X52,X24] :
( ~ c_less(X24,X52,tc_nat)
| c_List_Olast(c_List_Oupt(X24,X52),tc_nat) = c_minus(X52,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f12898,plain,
spl0_1466,
inference(avatar_split_clause,[],[f394,f12896]) ).
fof(f12896,plain,
( spl0_1466
<=> ! [X13,X41,X11] : c_List_Oconcat(c_List_Olist_OCons(X11,X41,tc_List_Olist(X13)),X13) = c_append(X11,c_List_Oconcat(X41,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f394,axiom,
! [X41,X11,X13] : c_List_Oconcat(c_List_Olist_OCons(X11,X41,tc_List_Olist(X13)),X13) = c_append(X11,c_List_Oconcat(X41,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f12894,plain,
spl0_1465,
inference(avatar_split_clause,[],[f306,f12892]) ).
fof(f12892,plain,
( spl0_1465
<=> ! [X20,X39] : c_IntDiv_OnegateSnd(c_Pair(X39,X20,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X39,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f12890,plain,
spl0_1464,
inference(avatar_split_clause,[],[f281,f12888]) ).
fof(f281,axiom,
! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f12886,plain,
spl0_1463,
inference(avatar_split_clause,[],[f265,f12884]) ).
fof(f265,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,X37,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f12882,plain,
spl0_1462,
inference(avatar_split_clause,[],[f264,f12880]) ).
fof(f12880,plain,
( spl0_1462
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f264,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f12878,plain,
spl0_1461,
inference(avatar_split_clause,[],[f261,f12876]) ).
fof(f12876,plain,
( spl0_1461
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f261,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f12874,plain,
spl0_1460,
inference(avatar_split_clause,[],[f260,f12872]) ).
fof(f260,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f12870,plain,
spl0_1459,
inference(avatar_split_clause,[],[f131,f12868]) ).
fof(f12868,plain,
( spl0_1459
<=> ! [X32,X3,X31] :
( ~ c_in(X31,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_minus(X31,X32,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f131,axiom,
! [X31,X3,X32] :
( ~ c_in(X31,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_minus(X31,X32,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f12866,plain,
spl0_1458,
inference(avatar_split_clause,[],[f48,f12864]) ).
fof(f12864,plain,
( spl0_1458
<=> ! [X17,X23,X18,X22,X3,X19] :
( X19 = X23
| c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OScons(X22,X23,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f48,axiom,
! [X3,X18,X19,X17,X22,X23] :
( X19 = X23
| c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OScons(X22,X23,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f12862,plain,
spl0_1457,
inference(avatar_split_clause,[],[f47,f12860]) ).
fof(f12860,plain,
( spl0_1457
<=> ! [X18,X23,X19,X17,X3,X22] :
( X18 = X22
| c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OScons(X22,X23,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f47,axiom,
! [X3,X18,X19,X17,X22,X23] :
( X18 = X22
| c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OScons(X22,X23,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f12811,plain,
( spl0_1456
| ~ spl0_124
| ~ spl0_1430 ),
inference(avatar_split_clause,[],[f12688,f11664,f3760,f12809]) ).
fof(f12688,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_124
| ~ spl0_1430 ),
inference(resolution,[],[f11665,f3761]) ).
fof(f12705,plain,
( spl0_1455
| ~ spl0_1108
| ~ spl0_1430 ),
inference(avatar_split_clause,[],[f12683,f11664,f8911,f12703]) ).
fof(f12703,plain,
( spl0_1455
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f8911,plain,
( spl0_1108
<=> ! [X11,X3] : c_in(c_Pair(X11,X11,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f12683,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1108
| ~ spl0_1430 ),
inference(resolution,[],[f11665,f8912]) ).
fof(f8912,plain,
( ! [X3,X11] : c_in(c_Pair(X11,X11,X3,X3),c_Relation_OId,tc_prod(X3,X3))
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f8911]) ).
fof(f11801,plain,
spl0_1454,
inference(avatar_split_clause,[],[f3067,f11799]) ).
fof(f11799,plain,
( spl0_1454
<=> ! [X77] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f3067,plain,
! [X77] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X77,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2891,f2749]) ).
fof(f2891,plain,
! [X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,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(X77,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f721,f1394,f1394]) ).
fof(f721,axiom,
! [X77] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X77,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X77,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f11797,plain,
spl0_1453,
inference(avatar_split_clause,[],[f3050,f11795]) ).
fof(f11795,plain,
( spl0_1453
<=> ! [X24,X10] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X24,X10,tc_nat),tc_nat),X10,tc_nat)
| ~ c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f3050,plain,
! [X10,X24] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X24,X10,tc_nat),tc_nat),X10,tc_nat)
| ~ c_less(c_0,X10,tc_nat) ),
inference(forward_demodulation,[],[f2868,f2800]) ).
fof(f2868,plain,
! [X10,X24] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_minus(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat),X10,tc_nat) ),
inference(definition_unfolding,[],[f886,f1394]) ).
fof(f886,axiom,
! [X10,X24] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_minus(X10,c_Suc(X24),tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f11793,plain,
spl0_1452,
inference(avatar_split_clause,[],[f3005,f11791]) ).
fof(f3005,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f3004,f1006]) ).
fof(f3004,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f3003,f1004]) ).
fof(f3003,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f733,f1006]) ).
fof(f733,axiom,
! [X8] : c_div(c_plus(X8,X8,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) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f11789,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2993,f11787]) ).
fof(f2993,plain,
! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),X35) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35),X35),
inference(forward_demodulation,[],[f978,f977]) ).
fof(f977,axiom,
! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35) = c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f978,axiom,
! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),X35) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0),X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f11785,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2990,f11783]) ).
fof(f2990,plain,
! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X35)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2791,f2764]) ).
fof(f2764,plain,
! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin),
inference(definition_unfolding,[],[f962,f963]) ).
fof(f963,axiom,
! [X35] : c_Numeral_Obin__pred(X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f962,axiom,
! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__pred(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2791,plain,
! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f974,f979,f963,f979]) ).
fof(f974,axiom,
! [X35] : c_Numeral_Obin__minus(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X35)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f11781,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2901,f11779]) ).
fof(f2901,plain,
! [X36] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X36),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f703,f979]) ).
fof(f703,axiom,
! [X36] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X36),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f11777,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2899,f11775]) ).
fof(f11775,plain,
( spl0_1448
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f2899,plain,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X36),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f704,f979]) ).
fof(f704,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X36),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X36,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f11745,plain,
( spl0_1447
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1446 ),
inference(avatar_split_clause,[],[f11741,f11738,f10415,f10092,f6703,f3695,f11743]) ).
fof(f11738,plain,
( spl0_1446
<=> ! [X52,X24] :
( c_lessequals(X24,X52,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f11741,plain,
( ! [X52,X24] :
( c_List_Olist_ONil = c_List_Oupt(X24,c_plus(c_1,X52,tc_nat))
| c_lessequals(X24,X52,tc_nat) )
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1446 ),
inference(forward_demodulation,[],[f11739,f11235]) ).
fof(f11739,plain,
( ! [X52,X24] :
( c_lessequals(X24,X52,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) )
| ~ spl0_1446 ),
inference(avatar_component_clause,[],[f11738]) ).
fof(f11740,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2883,f11738]) ).
fof(f2883,plain,
! [X52,X24] :
( c_lessequals(X24,X52,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X52,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f633,f1394]) ).
fof(f633,axiom,
! [X52,X24] :
( c_lessequals(X24,X52,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,c_Suc(X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f11736,plain,
( ~ spl0_1445
| ~ spl0_110
| ~ spl0_1128
| ~ spl0_1204 ),
inference(avatar_split_clause,[],[f9503,f9497,f9126,f3700,f11733]) ).
fof(f9503,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1128
| ~ spl0_1204 ),
inference(forward_demodulation,[],[f9502,f9127]) ).
fof(f9502,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1204 ),
inference(superposition,[],[f9498,f3702]) ).
fof(f11731,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2847,f11729]) ).
fof(f2847,plain,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X35),X3) ),
inference(definition_unfolding,[],[f967,f979]) ).
fof(f967,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(c_Numeral_Onumber__of(X35,X3),X3) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X35),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f11723,plain,
( spl0_1443
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1442 ),
inference(avatar_split_clause,[],[f11719,f11716,f10415,f10092,f6703,f3695,f11721]) ).
fof(f11716,plain,
( spl0_1442
<=> ! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f11719,plain,
( ! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_plus(c_1,X25,tc_nat),tc_nat)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1442 ),
inference(forward_demodulation,[],[f11717,f11235]) ).
fof(f11717,plain,
( ! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat)
| ~ spl0_1442 ),
inference(avatar_component_clause,[],[f11716]) ).
fof(f11718,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2792,f11716]) ).
fof(f2792,plain,
! [X25] : c_insert(X25,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1377,f1394]) ).
fof(f1377,axiom,
! [X25] : c_SetInterval_OatLeastLessThan(X25,c_Suc(X25),tc_nat) = c_insert(X25,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f11714,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2790,f11712]) ).
fof(f11712,plain,
( spl0_1441
<=> ! [X27,X3,X31] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_minus(X31,X27,tc_set(X3)),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f2790,plain,
! [X31,X3,X27] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_minus(X31,X27,tc_set(X3)),X3,X3),
inference(definition_unfolding,[],[f1439,f1223]) ).
fof(f1439,axiom,
! [X31,X3,X27] : c_emptyset = c_inter(X27,c_minus(X31,X27,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f11710,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2779,f11708]) ).
fof(f2779,plain,
! [X3,X79] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3),
inference(definition_unfolding,[],[f1556,f1566]) ).
fof(f1556,axiom,
! [X3,X79] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X79,X3),X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f11706,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2778,f11704]) ).
fof(f2778,plain,
! [X3,X79] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X79,c_Relation_OId,tc_prod(X3,X3)),X3),X3,X3),
inference(definition_unfolding,[],[f1557,f1566]) ).
fof(f1557,axiom,
! [X3,X79] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X79,X3),X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f11699,plain,
( spl0_1438
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1437 ),
inference(avatar_split_clause,[],[f11695,f11692,f10415,f10092,f6703,f3695,f11697]) ).
fof(f11697,plain,
( spl0_1438
<=> ! [X10] : c_plus(c_1,X10,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X10,tc_nat),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f11692,plain,
( spl0_1437
<=> ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f11695,plain,
( ! [X10] : c_plus(c_1,X10,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X10,tc_nat),X10)
| ~ spl0_109
| ~ spl0_667
| ~ spl0_1261
| ~ spl0_1340
| ~ spl0_1437 ),
inference(forward_demodulation,[],[f11693,f11235]) ).
fof(f11693,plain,
( ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X10)
| ~ spl0_1437 ),
inference(avatar_component_clause,[],[f11692]) ).
fof(f11694,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2774,f11692]) ).
fof(f2774,plain,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X10),
inference(definition_unfolding,[],[f13,f1394,f1394]) ).
fof(f13,axiom,
! [X10] : c_Suc(X10) = c_Binomial_Obinomial(c_Suc(X10),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f11690,plain,
spl0_1436,
inference(avatar_split_clause,[],[f1688,f11688]) ).
fof(f1688,axiom,
! [X31,X3,X27] :
( X27 = X31
| ~ c_lessequals(X27,X31,tc_set(X3))
| ~ c_lessequals(X31,X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11686,plain,
spl0_1435,
inference(avatar_split_clause,[],[f1685,f11684]) ).
fof(f11684,plain,
( spl0_1435
<=> ! [X31,X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| ~ c_lessequals(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f1685,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| c_in(X26,X31,X3)
| ~ c_lessequals(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11682,plain,
spl0_1434,
inference(avatar_split_clause,[],[f1681,f11680]) ).
fof(f1681,axiom,
! [X31,X3,X27] :
( X27 = X31
| ~ c_lessequals(X27,X31,tc_set(X3))
| c_less(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11678,plain,
spl0_1433,
inference(avatar_split_clause,[],[f1677,f11676]) ).
fof(f11676,plain,
( spl0_1433
<=> ! [X80,X27,X3] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(X27,c_Main_OUnionE__1(X27,X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f1677,axiom,
! [X3,X80,X27] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(X27,c_Main_OUnionE__1(X27,X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11674,plain,
spl0_1432,
inference(avatar_split_clause,[],[f1674,f11672]) ).
fof(f11672,plain,
( spl0_1432
<=> ! [X80,X27,X3] :
( c_in(X27,c_Inter(X80,X3),X3)
| ~ c_in(X27,c_Main_OInterI__1(X27,X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f1674,axiom,
! [X3,X80,X27] :
( c_in(X27,c_Inter(X80,X3),X3)
| ~ c_in(X27,c_Main_OInterI__1(X27,X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11670,plain,
spl0_1431,
inference(avatar_split_clause,[],[f1606,f11668]) ).
fof(f11668,plain,
( spl0_1431
<=> ! [X27,X3,X15] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_insert(X15,X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f1606,axiom,
! [X3,X27,X15] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_insert(X15,X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11666,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1575,f11664]) ).
fof(f1575,axiom,
! [X3,X15,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| ~ c_in(c_Pair(X15,X15,X3,X3),X20,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f11662,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1539,f11660]) ).
fof(f1539,axiom,
! [X31,X3,X11,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f11658,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1506,f11656]) ).
fof(f11656,plain,
( spl0_1428
<=> ! [X80,X27,X3] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(X27,c_Main_OUnion__iff__1(X27,X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1506,axiom,
! [X3,X80,X27] :
( ~ c_in(X27,c_Union(X80,X3),X3)
| c_in(X27,c_Main_OUnion__iff__1(X27,X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f11654,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1502,f11652]) ).
fof(f11652,plain,
( spl0_1427
<=> ! [X3,X27,X30] :
( c_emptyset = X30
| c_emptyset != c_Union(X27,X3)
| ~ c_in(X30,X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f1502,axiom,
! [X3,X27,X30] :
( c_emptyset = X30
| c_emptyset != c_Union(X27,X3)
| ~ c_in(X30,X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f11650,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1496,f11648]) ).
fof(f1496,axiom,
! [X31,X3,X80,X27] :
( c_lessequals(X31,X80,tc_set(X3))
| ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f11646,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1495,f11644]) ).
fof(f1495,axiom,
! [X31,X3,X80,X27] :
( c_lessequals(X27,X80,tc_set(X3))
| ~ c_lessequals(c_union(X27,X31,X3),X80,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f11642,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1481,f11640]) ).
fof(f11640,plain,
( spl0_1424
<=> ! [X27,X3,X31] : c_union(X27,X31,X3) = c_union(X27,c_minus(X31,X27,tc_set(X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f1481,axiom,
! [X31,X3,X27] : c_union(X27,X31,X3) = c_union(X27,c_minus(X31,X27,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f11638,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1480,f11636]) ).
fof(f1480,axiom,
! [X31,X3,X27] : c_union(c_minus(X31,X27,tc_set(X3)),X27,X3) = c_union(X31,X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f11634,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1472,f11632]) ).
fof(f11632,plain,
( spl0_1422
<=> ! [X80,X27,X3] :
( c_in(X27,c_Inter(X80,X3),X3)
| ~ c_in(X27,c_Main_OInter__iff__1(X27,X80,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1472,axiom,
! [X3,X80,X27] :
( c_in(X27,c_Inter(X80,X3),X3)
| ~ c_in(X27,c_Main_OInter__iff__1(X27,X80,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f11630,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1463,f11628]) ).
fof(f11628,plain,
( spl0_1421
<=> ! [X3,X27,X30] :
( c_UNIV = X30
| c_UNIV != c_Inter(X27,X3)
| ~ c_in(X30,X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1463,axiom,
! [X3,X27,X30] :
( c_UNIV = X30
| c_UNIV != c_Inter(X27,X3)
| ~ c_in(X30,X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
fof(f11626,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1405,f11624]) ).
fof(f11624,plain,
( spl0_1420
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f1405,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f11622,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1404,f11620]) ).
fof(f11620,plain,
( spl0_1419
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1404,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_less(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f11618,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1402,f11616]) ).
fof(f11616,plain,
( spl0_1418
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1402,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f11614,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1401,f11612]) ).
fof(f11612,plain,
( spl0_1417
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1401,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_less(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThanAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f11595,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1375,f11593]) ).
fof(f11593,plain,
( spl0_1416
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1375,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f11591,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1374,f11589]) ).
fof(f11589,plain,
( spl0_1415
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1374,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeastLessThan(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f11587,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1370,f11585]) ).
fof(f11585,plain,
( spl0_1414
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1370,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X38,X3)
| ~ c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f11583,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1369,f11581]) ).
fof(f11581,plain,
( spl0_1413
<=> ! [X38,X3,X74,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1369,axiom,
! [X38,X3,X24,X74] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X74,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeastAtMost(X74,X38,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f11579,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1237,f11577]) ).
fof(f11577,plain,
( spl0_1412
<=> ! [X16,X3,X15] :
( X15 = X16
| ~ c_in(c_Pair(X15,X16,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1237,axiom,
! [X3,X16,X15] :
( X15 = X16
| ~ c_in(c_Pair(X15,X16,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f11575,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1217,f11573]) ).
fof(f1217,axiom,
! [X3,X37,X17] : c_Pair(c_Main_Osurj__pair__1(X37,X3,X17),c_Main_Osurj__pair__2(X37,X3,X17),X3,X17) = X37,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f11571,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1215,f11569]) ).
fof(f1215,axiom,
! [X3,X8,X17] : c_Pair(c_fst(X8,X3,X17),c_snd(X8,X3,X17),X3,X17) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f11567,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1211,f11565]) ).
fof(f11565,plain,
( spl0_1409
<=> ! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1211,axiom,
! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f11563,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1208,f11561]) ).
fof(f11561,plain,
( spl0_1408
<=> ! [X15,X3,X10] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1208,axiom,
! [X3,X10,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X15,X3),X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f11559,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1197,f11557]) ).
fof(f11557,plain,
( spl0_1407
<=> ! [X10,X3,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X15
| c_0 != c_Nat_Opower(X15,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1197,axiom,
! [X3,X10,X15] :
( ~ class_Power_Orecpower(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X15
| c_0 != c_Nat_Opower(X15,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f11546,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1189,f11544]) ).
fof(f11544,plain,
( spl0_1406
<=> ! [X11,X35] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1189,axiom,
! [X11,X35] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X11,c_Numeral_Onumber__of(X35,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f11542,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1145,f11540]) ).
fof(f11540,plain,
( spl0_1405
<=> ! [X11,X10] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1145,axiom,
! [X10,X11] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f11538,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1132,f11536]) ).
fof(f11536,plain,
( spl0_1404
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_less(c_0,X8,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1132,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_less(c_0,X8,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f11534,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1115,f11532]) ).
fof(f11532,plain,
( spl0_1403
<=> ! [X11,X37,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X8,X37,X17)
| ~ c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1115,axiom,
! [X11,X8,X37,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X8,X37,X17)
| ~ c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f11530,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1114,f11528]) ).
fof(f11528,plain,
( spl0_1402
<=> ! [X37,X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X37,X17)
| ~ c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f1114,axiom,
! [X11,X37,X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X37,X17)
| ~ c_lessequals(c_Orderings_Omax(X11,X8,X17),X37,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f11526,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1110,f11524]) ).
fof(f11524,plain,
( spl0_1401
<=> ! [X37,X11,X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X37,X17)
| ~ c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1110,axiom,
! [X11,X37,X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X37,X17)
| ~ c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f11522,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1109,f11520]) ).
fof(f1109,axiom,
! [X11,X8,X37,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_lessequals(X11,X8,X17)
| ~ c_lessequals(X11,c_Orderings_Omin(X8,X37,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f11518,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1107,f11516]) ).
fof(f11516,plain,
( spl0_1399
<=> ! [X37,X11,X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X37,X8,X3)
| ~ c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f1107,axiom,
! [X3,X11,X37,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X37,X8,X3)
| ~ c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f11514,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1106,f11512]) ).
fof(f11512,plain,
( spl0_1398
<=> ! [X37,X11,X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X37,X11,X3)
| ~ c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f1106,axiom,
! [X3,X11,X37,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X37,X11,X3)
| ~ c_less(X37,c_Orderings_Omin(X11,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f11510,plain,
spl0_1397,
inference(avatar_split_clause,[],[f1104,f11508]) ).
fof(f11508,plain,
( spl0_1397
<=> ! [X37,X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X8,X37,X3)
| ~ c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f1104,axiom,
! [X3,X11,X8,X37] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X8,X37,X3)
| ~ c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f11499,plain,
spl0_1396,
inference(avatar_split_clause,[],[f1103,f11497]) ).
fof(f1103,axiom,
! [X3,X11,X37,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_less(X11,X37,X3)
| ~ c_less(c_Orderings_Omax(X11,X8,X3),X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f11495,plain,
spl0_1395,
inference(avatar_split_clause,[],[f1099,f11493]) ).
fof(f11493,plain,
( spl0_1395
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_0,c_plus(X15,X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f1099,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_0,c_plus(X15,X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f11491,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1098,f11489]) ).
fof(f11489,plain,
( spl0_1394
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_0,c_plus(X15,X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f1098,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_0,c_plus(X15,X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f11487,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1065,f11485]) ).
fof(f11485,plain,
( spl0_1393
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_minus(X15,X16,X3),X3) = c_minus(X16,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1065,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_minus(X15,X16,X3),X3) = c_minus(X16,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f11483,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1062,f11481]) ).
fof(f11481,plain,
( spl0_1392
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = X15
| c_0 != c_LOrder_Omeet(X15,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f1062,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = X15
| c_0 != c_LOrder_Omeet(X15,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11479,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1060,f11477]) ).
fof(f11477,plain,
( spl0_1391
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = X15
| c_0 != c_LOrder_Ojoin(X15,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f1060,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = X15
| c_0 != c_LOrder_Ojoin(X15,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11475,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1057,f11473]) ).
fof(f11473,plain,
( spl0_1390
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_plus(X15,X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1057,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_plus(X15,X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11471,plain,
spl0_1389,
inference(avatar_split_clause,[],[f1056,f11469]) ).
fof(f11469,plain,
( spl0_1389
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_plus(X15,X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f1056,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_plus(X15,X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11467,plain,
spl0_1388,
inference(avatar_split_clause,[],[f1054,f11465]) ).
fof(f11465,plain,
( spl0_1388
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_plus(X15,X16,X3) = c_minus(X15,c_uminus(X16,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f1054,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_plus(X15,X16,X3) = c_minus(X15,c_uminus(X16,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11463,plain,
spl0_1387,
inference(avatar_split_clause,[],[f1053,f11461]) ).
fof(f11461,plain,
( spl0_1387
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_minus(X15,X16,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f1053,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,X16,X3)
| c_less(c_minus(X15,X16,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11459,plain,
( spl0_1386
| ~ spl0_1043
| ~ spl0_1335 ),
inference(avatar_split_clause,[],[f11168,f10395,f8497,f11457]) ).
fof(f10395,plain,
( spl0_1335
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X27,X31,X3),X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f11168,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1043
| ~ spl0_1335 ),
inference(resolution,[],[f10396,f8498]) ).
fof(f10396,plain,
( ! [X31,X3,X27] :
( ~ c_in(c_Main_OsubsetI__1(X27,X31,X3),X31,X3)
| c_lessequals(X27,X31,tc_set(X3)) )
| ~ spl0_1335 ),
inference(avatar_component_clause,[],[f10395]) ).
fof(f11455,plain,
spl0_1385,
inference(avatar_split_clause,[],[f1052,f11453]) ).
fof(f11453,plain,
( spl0_1385
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_minus(X15,X16,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f1052,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,X16,X3)
| ~ c_less(c_minus(X15,X16,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11451,plain,
spl0_1384,
inference(avatar_split_clause,[],[f1051,f11449]) ).
fof(f11449,plain,
( spl0_1384
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_minus(X15,X16,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1051,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,X16,X3)
| c_lessequals(c_minus(X15,X16,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11447,plain,
spl0_1383,
inference(avatar_split_clause,[],[f1050,f11445]) ).
fof(f11445,plain,
( spl0_1383
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_minus(X15,X16,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f1050,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,X16,X3)
| ~ c_lessequals(c_minus(X15,X16,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11443,plain,
spl0_1382,
inference(avatar_split_clause,[],[f1034,f11441]) ).
fof(f1034,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_uminus(X15,X3) = c_HOL_Oabs(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11439,plain,
spl0_1381,
inference(avatar_split_clause,[],[f960,f11437]) ).
fof(f960,axiom,
! [X36,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB1),c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11435,plain,
spl0_1380,
inference(avatar_split_clause,[],[f959,f11433]) ).
fof(f959,axiom,
! [X36,X8,X35] : c_Numeral_Obin__add(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),c_Numeral_OBit(X35,X8)) = c_Numeral_OBit(c_Numeral_Obin__add(X36,X35),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11431,plain,
spl0_1379,
inference(avatar_split_clause,[],[f895,f11429]) ).
fof(f11429,plain,
( spl0_1379
<=> ! [X8,X10] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_plus(X10,c_minus(X8,X10,tc_nat),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f895,axiom,
! [X10,X8] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_plus(X10,c_minus(X8,X10,tc_nat),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11427,plain,
spl0_1378,
inference(avatar_split_clause,[],[f894,f11425]) ).
fof(f11425,plain,
( spl0_1378
<=> ! [X8,X10] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_plus(c_minus(X8,X10,tc_nat),X10,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f894,axiom,
! [X10,X8] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_plus(c_minus(X8,X10,tc_nat),X10,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11423,plain,
spl0_1377,
inference(avatar_split_clause,[],[f702,f11421]) ).
fof(f11421,plain,
( spl0_1377
<=> ! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f702,axiom,
! [X36] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X36,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11419,plain,
spl0_1376,
inference(avatar_split_clause,[],[f649,f11417]) ).
fof(f11417,plain,
( spl0_1376
<=> ! [X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_minus(X10,c_minus(X10,X8,tc_nat),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f649,axiom,
! [X10,X8] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_minus(X10,c_minus(X10,X8,tc_nat),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11415,plain,
spl0_1375,
inference(avatar_split_clause,[],[f615,f11413]) ).
fof(f11413,plain,
( spl0_1375
<=> ! [X11,X27,X3] :
( c_in(c_0,X27,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f615,axiom,
! [X3,X11,X27] :
( c_in(c_0,X27,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11411,plain,
spl0_1374,
inference(avatar_split_clause,[],[f598,f11409]) ).
fof(f598,axiom,
! [X41,X11,X13] : c_List_Oset(c_List_Olist_OCons(X11,X41,X13),X13) = c_insert(X11,c_List_Oset(X41,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11407,plain,
spl0_1373,
inference(avatar_split_clause,[],[f592,f11405]) ).
fof(f11405,plain,
( spl0_1373
<=> ! [X8,X3,X10] :
( c_List_Orotate(X10,X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f592,axiom,
! [X3,X10,X8] :
( c_List_Orotate(X10,X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11403,plain,
spl0_1372,
inference(avatar_split_clause,[],[f552,f11401]) ).
fof(f552,axiom,
! [X3,X10,X8,X24] :
( ~ c_less(X24,X10,tc_nat)
| c_List_Onth(c_List_Oreplicate(X10,X8,X3),X24,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11399,plain,
spl0_1371,
inference(avatar_split_clause,[],[f454,f11397]) ).
fof(f11397,plain,
( spl0_1371
<=> ! [X41,X11,X3,X24] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Olist__update(X41,X24,X11,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f454,axiom,
! [X41,X3,X11,X24] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Olist__update(X41,X24,X11,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11395,plain,
spl0_1370,
inference(avatar_split_clause,[],[f441,f11393]) ).
fof(f11393,plain,
( spl0_1370
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olast(c_append(X41,X42,X3),X3) = c_List_Olast(X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f441,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olast(c_append(X41,X42,X3),X3) = c_List_Olast(X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11391,plain,
spl0_1369,
inference(avatar_split_clause,[],[f439,f11389]) ).
fof(f11389,plain,
( spl0_1369
<=> ! [X41,X11,X3] :
( c_List_Olist_ONil = X41
| c_List_Olast(c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Olast(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f439,axiom,
! [X41,X3,X11] :
( c_List_Olist_ONil = X41
| c_List_Olast(c_List_Olist_OCons(X11,X41,X3),X3) = c_List_Olast(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11387,plain,
spl0_1368,
inference(avatar_split_clause,[],[f431,f11385]) ).
fof(f11385,plain,
( spl0_1368
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Ohd(c_append(X41,X42,X3),X3) = c_List_Ohd(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f431,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Ohd(c_append(X41,X42,X3),X3) = c_List_Ohd(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11383,plain,
spl0_1367,
inference(avatar_split_clause,[],[f430,f11381]) ).
fof(f430,axiom,
! [X3,X8] :
( c_List_Olist_ONil = X8
| c_List_Olist_OCons(c_List_Ohd(X8,X3),c_List_Otl(X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11379,plain,
spl0_1366,
inference(avatar_split_clause,[],[f428,f11377]) ).
fof(f11377,plain,
( spl0_1366
<=> ! [X52,X24,X25] : c_List_Odrop(X25,c_List_Oupt(X24,X52),tc_nat) = c_List_Oupt(c_plus(X24,X25,tc_nat),X52) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f428,axiom,
! [X52,X24,X25] : c_List_Odrop(X25,c_List_Oupt(X24,X52),tc_nat) = c_List_Oupt(c_plus(X24,X25,tc_nat),X52),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11375,plain,
spl0_1365,
inference(avatar_split_clause,[],[f426,f11373]) ).
fof(f11373,plain,
( spl0_1365
<=> ! [X41,X3,X10] :
( c_List_Olist_ONil = c_List_Odrop(X10,X41,X3)
| ~ c_lessequals(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f426,axiom,
! [X41,X10,X3] :
( c_List_Olist_ONil = c_List_Odrop(X10,X41,X3)
| ~ c_lessequals(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11371,plain,
spl0_1364,
inference(avatar_split_clause,[],[f425,f11369]) ).
fof(f425,axiom,
! [X41,X10,X3] :
( c_List_Olist_ONil != c_List_Odrop(X10,X41,X3)
| c_lessequals(c_Nat_Osize(X41,tc_List_Olist(X3)),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11367,plain,
spl0_1363,
inference(avatar_split_clause,[],[f325,f11365]) ).
fof(f11365,plain,
( spl0_1363
<=> ! [X16,X15] : c_div(c_uminus(X15,tc_IntDef_Oint),c_uminus(X16,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X15,X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f325,axiom,
! [X16,X15] : c_div(c_uminus(X15,tc_IntDef_Oint),c_uminus(X16,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X15,X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11363,plain,
spl0_1362,
inference(avatar_split_clause,[],[f266,f11361]) ).
fof(f11361,plain,
( spl0_1362
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_uminus(X37,tc_IntDef_Oint),X3) = c_uminus(c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f266,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_uminus(X37,tc_IntDef_Oint),X3) = c_uminus(c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11359,plain,
spl0_1361,
inference(avatar_split_clause,[],[f155,f11357]) ).
fof(f11357,plain,
( spl0_1361
<=> ! [X9,X25,X10] :
( c_Divides_Oop_Advd(X9,X10,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f155,axiom,
! [X10,X9,X25] :
( c_Divides_Oop_Advd(X9,X10,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11355,plain,
spl0_1360,
inference(avatar_split_clause,[],[f154,f11353]) ).
fof(f154,axiom,
! [X10,X9,X25] :
( c_Divides_Oop_Advd(X9,X25,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11351,plain,
spl0_1359,
inference(avatar_split_clause,[],[f141,f11349]) ).
fof(f11349,plain,
( spl0_1359
<=> ! [X27,X3,X15] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_insert(X15,X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f141,axiom,
! [X3,X27,X15] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_insert(X15,X27,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11347,plain,
spl0_1358,
inference(avatar_split_clause,[],[f137,f11345]) ).
fof(f11345,plain,
( spl0_1358
<=> ! [X34,X3,X33] :
( c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f137,axiom,
! [X3,X34,X33] :
( c_in(X34,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11343,plain,
spl0_1357,
inference(avatar_split_clause,[],[f136,f11341]) ).
fof(f136,axiom,
! [X3,X34,X33] :
( c_in(X33,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_union(X33,X34,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11339,plain,
spl0_1356,
inference(avatar_split_clause,[],[f135,f11337]) ).
fof(f11337,plain,
( spl0_1356
<=> ! [X27,X3] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Pow(X27,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f135,axiom,
! [X3,X27] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_in(c_Pow(X27,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11335,plain,
( spl0_1355
| ~ spl0_797
| ~ spl0_798
| ~ spl0_1337 ),
inference(avatar_split_clause,[],[f11181,f10403,f7267,f7262,f11332]) ).
fof(f11332,plain,
( spl0_1355
<=> c_Relation_Otrans(v_r,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f10403,plain,
( spl0_1337
<=> ! [X93,X3] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f11181,plain,
( c_Relation_Otrans(v_r,t_a)
| ~ spl0_797
| ~ spl0_798
| ~ spl0_1337 ),
inference(forward_demodulation,[],[f11180,f7269]) ).
fof(f11180,plain,
( c_Relation_Otrans(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ spl0_797
| ~ spl0_1337 ),
inference(resolution,[],[f10404,f7264]) ).
fof(f7264,plain,
( c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7262]) ).
fof(f10404,plain,
( ! [X3,X93] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) )
| ~ spl0_1337 ),
inference(avatar_component_clause,[],[f10403]) ).
fof(f11330,plain,
spl0_1354,
inference(avatar_split_clause,[],[f134,f11328]) ).
fof(f11328,plain,
( spl0_1354
<=> ! [X27,X3] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_Pow(X27,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f134,axiom,
! [X3,X27] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_Pow(X27,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11326,plain,
spl0_1353,
inference(avatar_split_clause,[],[f126,f11324]) ).
fof(f11324,plain,
( spl0_1353
<=> ! [X27,X3] :
( c_emptyset = X27
| c_0 != c_Finite__Set_Ocard(X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f126,axiom,
! [X3,X27] :
( c_emptyset = X27
| c_0 != c_Finite__Set_Ocard(X27,X3)
| ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11322,plain,
spl0_1352,
inference(avatar_split_clause,[],[f73,f11320]) ).
fof(f11320,plain,
( spl0_1352
<=> ! [X8,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_times(X8,X10,tc_nat),X10,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f73,axiom,
! [X10,X8] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_times(X8,X10,tc_nat),X10,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11318,plain,
spl0_1351,
inference(avatar_split_clause,[],[f71,f11316]) ).
fof(f11316,plain,
( spl0_1351
<=> ! [X8,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_times(X10,X8,tc_nat),X10,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f71,axiom,
! [X10,X8] :
( ~ c_less(c_0,X10,tc_nat)
| c_div(c_times(X10,X8,tc_nat),X10,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11288,plain,
( spl0_1350
| ~ spl0_797
| ~ spl0_798
| ~ spl0_1336 ),
inference(avatar_split_clause,[],[f11177,f10399,f7267,f7262,f11285]) ).
fof(f11285,plain,
( spl0_1350
<=> c_Relation_Oantisym(v_r,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f10399,plain,
( spl0_1336
<=> ! [X93,X3] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f11177,plain,
( c_Relation_Oantisym(v_r,t_a)
| ~ spl0_797
| ~ spl0_798
| ~ spl0_1336 ),
inference(forward_demodulation,[],[f11176,f7269]) ).
fof(f11176,plain,
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| ~ spl0_797
| ~ spl0_1336 ),
inference(resolution,[],[f10400,f7264]) ).
fof(f10400,plain,
( ! [X3,X93] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) )
| ~ spl0_1336 ),
inference(avatar_component_clause,[],[f10399]) ).
fof(f10826,plain,
( spl0_1349
| ~ spl0_706
| ~ spl0_1107 ),
inference(avatar_split_clause,[],[f9173,f8907,f6880,f10824]) ).
fof(f10824,plain,
( spl0_1349
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f8907,plain,
( spl0_1107
<=> ! [X27,X3] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f9173,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_706
| ~ spl0_1107 ),
inference(superposition,[],[f8908,f6881]) ).
fof(f8908,plain,
( ! [X3,X27] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3)
| ~ spl0_1107 ),
inference(avatar_component_clause,[],[f8907]) ).
fof(f10640,plain,
( spl0_1348
| ~ spl0_113
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f9090,f8786,f3714,f10638]) ).
fof(f10638,plain,
( spl0_1348
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f3714,plain,
( spl0_113
<=> ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f9090,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1077 ),
inference(resolution,[],[f8787,f3715]) ).
fof(f3715,plain,
( ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3714]) ).
fof(f10581,plain,
( spl0_1347
| ~ spl0_113
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9080,f8773,f3714,f10579]) ).
fof(f10579,plain,
( spl0_1347
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f8773,plain,
( spl0_1074
<=> ! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f9080,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1074 ),
inference(resolution,[],[f8774,f3715]) ).
fof(f8774,plain,
( ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint) )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f8773]) ).
fof(f10441,plain,
spl0_1346,
inference(avatar_split_clause,[],[f3112,f10439]) ).
fof(f10439,plain,
( spl0_1346
<=> ! [X11,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f3112,plain,
! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f3111,f965]) ).
fof(f3111,plain,
! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2918,f2748]) ).
fof(f2918,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f188,f979]) ).
fof(f188,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10437,plain,
spl0_1345,
inference(avatar_split_clause,[],[f3042,f10435]) ).
fof(f3042,plain,
! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f3041,f1006]) ).
fof(f3041,plain,
! [X3] :
( 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),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f3040,f1004]) ).
fof(f3040,plain,
! [X3] :
( 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),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f728,f1006]) ).
fof(f728,axiom,
! [X3] :
( ~ class_Power_Orecpower(X3)
| 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),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10433,plain,
spl0_1344,
inference(avatar_split_clause,[],[f3035,f10431]) ).
fof(f3035,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f3034,f1006]) ).
fof(f3034,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f3033,f1004]) ).
fof(f3033,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f178,f1006]) ).
fof(f178,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10429,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2859,f10427]) ).
fof(f2859,plain,
! [X31,X3,X27] :
( c_UNIV = X31
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1449,f1223]) ).
fof(f1449,axiom,
! [X31,X3,X27] :
( c_UNIV = X31
| c_UNIV != c_inter(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10425,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2858,f10423]) ).
fof(f2858,plain,
! [X31,X3,X27] :
( c_UNIV = X27
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1448,f1223]) ).
fof(f1448,axiom,
! [X31,X3,X27] :
( c_UNIV = X27
| c_UNIV != c_inter(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10421,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2853,f10419]) ).
fof(f2853,plain,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) ),
inference(definition_unfolding,[],[f1196,f1394]) ).
fof(f1196,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Suc(X10),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10417,plain,
spl0_1340,
inference(avatar_split_clause,[],[f2785,f10415]) ).
fof(f2785,plain,
! [X25] : c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f222,f1394]) ).
fof(f222,axiom,
! [X25] : c_IntDef_Oint(c_Suc(X25)) = c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10413,plain,
spl0_1339,
inference(avatar_split_clause,[],[f2782,f10411]) ).
fof(f10411,plain,
( spl0_1339
<=> ! [X27,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),X27,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f2782,plain,
! [X3,X27] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),X27,X3,X3),
inference(definition_unfolding,[],[f1428,f1223]) ).
fof(f1428,axiom,
! [X3,X27] : c_emptyset = c_inter(c_uminus(X27,tc_set(X3)),X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10409,plain,
spl0_1338,
inference(avatar_split_clause,[],[f2781,f10407]) ).
fof(f10407,plain,
( spl0_1338
<=> ! [X27,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_uminus(X27,tc_set(X3)),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f2781,plain,
! [X3,X27] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_uminus(X27,tc_set(X3)),X3,X3),
inference(definition_unfolding,[],[f1429,f1223]) ).
fof(f1429,axiom,
! [X3,X27] : c_emptyset = c_inter(X27,c_uminus(X27,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10405,plain,
spl0_1337,
inference(avatar_split_clause,[],[f2740,f10403]) ).
fof(f2740,axiom,
! [X3,X93] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
fof(f10401,plain,
spl0_1336,
inference(avatar_split_clause,[],[f2739,f10399]) ).
fof(f2739,axiom,
! [X3,X93] :
( ~ c_in(X93,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X93,X3,tc_Product__Type_Ounit),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
fof(f10397,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1687,f10395]) ).
fof(f1687,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X27,X31,X3),X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10393,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1686,f10391]) ).
fof(f10391,plain,
( spl0_1334
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X27,X31,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1686,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X27,X31,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10389,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1626,f10387]) ).
fof(f10387,plain,
( spl0_1333
<=> ! [X41,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1626,axiom,
! [X41,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10385,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1579,f10383]) ).
fof(f10383,plain,
( spl0_1332
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Datatype__Universe_ONumb(X11,X3,X17) != c_Datatype__Universe_ONumb(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f1579,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Datatype__Universe_ONumb(X11,X3,X17) != c_Datatype__Universe_ONumb(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10381,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1578,f10379]) ).
fof(f10379,plain,
( spl0_1331
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Datatype__Universe_OLeaf(X11,X3,X17) != c_Datatype__Universe_OLeaf(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f1578,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Datatype__Universe_OLeaf(X11,X3,X17) != c_Datatype__Universe_OLeaf(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10377,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1553,f10375]) ).
fof(f10375,plain,
( spl0_1330
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Sum__Type_OInr(X11,X17,X3) != c_Sum__Type_OInr(X8,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1553,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Sum__Type_OInr(X11,X17,X3) != c_Sum__Type_OInr(X8,X17,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10373,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1551,f10371]) ).
fof(f10371,plain,
( spl0_1329
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Sum__Type_OInl(X11,X3,X17) != c_Sum__Type_OInl(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f1551,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Sum__Type_OInl(X11,X3,X17) != c_Sum__Type_OInl(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10369,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1542,f10367]) ).
fof(f10367,plain,
( spl0_1328
<=> ! [X15,X16,X27,X3] :
( X15 = X16
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f1542,axiom,
! [X3,X16,X27,X15] :
( X15 = X16
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f10365,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1538,f10363]) ).
fof(f10363,plain,
( spl0_1327
<=> ! [X31,X11,X27,X3] :
( c_in(X11,X31,X3)
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f1538,axiom,
! [X31,X3,X11,X27] :
( c_in(X11,X31,X3)
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10361,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1526,f10359]) ).
fof(f1526,axiom,
! [X3,X11,X27] : c_insert(X11,X27,X3) = c_insert(X11,c_insert(X11,X27,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10357,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1520,f10355]) ).
fof(f10355,plain,
( spl0_1325
<=> ! [X27,X3] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_Oempty__Union__conv__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1520,axiom,
! [X3,X27] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_Oempty__Union__conv__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10353,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1503,f10351]) ).
fof(f10351,plain,
( spl0_1324
<=> ! [X27,X3] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_OUnion__empty__conv__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f1503,axiom,
! [X3,X27] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_OUnion__empty__conv__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10349,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1478,f10347]) ).
fof(f10347,plain,
( spl0_1323
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_in(X27,c_Pow(X31,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1478,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_in(X27,c_Pow(X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10345,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1477,f10343]) ).
fof(f10343,plain,
( spl0_1322
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(X27,c_Pow(X31,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f1477,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(X27,c_Pow(X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10341,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1467,f10339]) ).
fof(f10339,plain,
( spl0_1321
<=> ! [X27,X3] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__2__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1467,axiom,
! [X3,X27] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__2__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10337,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1464,f10335]) ).
fof(f10335,plain,
( spl0_1320
<=> ! [X27,X3] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__1__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1464,axiom,
! [X3,X27] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__1__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10333,plain,
( spl0_1319
| ~ spl0_697
| ~ spl0_775
| ~ spl0_1037 ),
inference(avatar_split_clause,[],[f8647,f8426,f7172,f6841,f10330]) ).
fof(f8647,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_697
| ~ spl0_775
| ~ spl0_1037 ),
inference(forward_demodulation,[],[f8644,f6843]) ).
fof(f8644,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_775
| ~ spl0_1037 ),
inference(superposition,[],[f8427,f7174]) ).
fof(f10328,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1445,f10326]) ).
fof(f10326,plain,
( spl0_1318
<=> ! [X3,X31,X27,X26] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1445,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10324,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1444,f10322]) ).
fof(f10322,plain,
( spl0_1317
<=> ! [X31,X27,X3,X26] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1444,axiom,
! [X31,X3,X26,X27] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10320,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1442,f10318]) ).
fof(f1442,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10316,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1441,f10314]) ).
fof(f1441,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| c_emptyset != c_minus(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10312,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1431,f10310]) ).
fof(f1431,axiom,
! [X31,X3,X27] :
( X27 = X31
| c_uminus(X27,tc_set(X3)) != c_uminus(X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10308,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1420,f10306]) ).
fof(f10306,plain,
( spl0_1313
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X24,X9,X3)
| c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1420,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X24,X9,X3)
| c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10304,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1419,f10302]) ).
fof(f10302,plain,
( spl0_1312
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1419,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10300,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1418,f10298]) ).
fof(f1418,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OlessThan(X11,X3) != c_SetInterval_OlessThan(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10296,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1409,f10294]) ).
fof(f10294,plain,
( spl0_1310
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X9,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1409,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X9,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10292,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1408,f10290]) ).
fof(f10290,plain,
( spl0_1309
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_less(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1408,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10288,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1407,f10286]) ).
fof(f10286,plain,
( spl0_1308
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OgreaterThan(X11,X3) != c_SetInterval_OgreaterThan(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1407,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OgreaterThan(X11,X3) != c_SetInterval_OgreaterThan(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10284,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1400,f10282]) ).
fof(f1400,axiom,
! [X3,X9,X74] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X74,X9,X3)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X74,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10280,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1396,f10278]) ).
fof(f10278,plain,
( spl0_1306
<=> ! [X38,X74] : c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1396,axiom,
! [X38,X74] : c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10276,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1393,f10274]) ).
fof(f10274,plain,
( spl0_1305
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1393,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10272,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1387,f10270]) ).
fof(f10270,plain,
( spl0_1304
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X9,X3)
| c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1387,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X9,X3)
| c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10268,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1386,f10266]) ).
fof(f10266,plain,
( spl0_1303
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1386,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10264,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1385,f10262]) ).
fof(f10262,plain,
( spl0_1302
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatMost(X11,X3) != c_SetInterval_OatMost(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1385,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatMost(X11,X3) != c_SetInterval_OatMost(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10260,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1381,f10258]) ).
fof(f10258,plain,
( spl0_1301
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X9,X24,X3)
| c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1381,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X9,X24,X3)
| c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10256,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1380,f10254]) ).
fof(f10254,plain,
( spl0_1300
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1380,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10252,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1379,f10250]) ).
fof(f1379,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatLeast(X11,X3) != c_SetInterval_OatLeast(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10248,plain,
( spl0_1297
| ~ spl0_1298
| ~ spl0_777
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f8596,f8317,f7181,f10245,f10242]) ).
fof(f10242,plain,
( spl0_1297
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f10245,plain,
( spl0_1298
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f7181,plain,
( spl0_777
<=> ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f8317,plain,
( spl0_1010
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f8596,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_777
| ~ spl0_1010 ),
inference(superposition,[],[f8318,f7182]) ).
fof(f7182,plain,
( ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat)
| ~ spl0_777 ),
inference(avatar_component_clause,[],[f7181]) ).
fof(f8318,plain,
( ! [X11,X8] :
( ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat)
| c_Parity_Oeven(X11,tc_nat) )
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f8317]) ).
fof(f10240,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1373,f10238]) ).
fof(f1373,axiom,
! [X3,X10,X25] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10236,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1368,f10234]) ).
fof(f1368,axiom,
! [X3,X10,X25] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastAtMost(X25,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10232,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1367,f10230]) ).
fof(f1367,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatLeast(X9,X3) = c_uminus(c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10228,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1366,f10226]) ).
fof(f1366,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatMost(X9,X3) = c_uminus(c_SetInterval_OgreaterThan(X9,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10224,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1365,f10222]) ).
fof(f1365,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatMost(X9,X3),tc_set(X3)) = c_SetInterval_OgreaterThan(X9,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10220,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1364,f10218]) ).
fof(f1364,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatLeast(X9,X3),tc_set(X3)) = c_SetInterval_OlessThan(X9,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10216,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1152,f10214]) ).
fof(f10214,plain,
( spl0_1290
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1152,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10212,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1151,f10210]) ).
fof(f10210,plain,
( spl0_1289
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1151,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10208,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1150,f10206]) ).
fof(f10206,plain,
( spl0_1288
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1150,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10204,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1149,f10202]) ).
fof(f10202,plain,
( spl0_1287
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1149,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10200,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1146,f10198]) ).
fof(f10198,plain,
( spl0_1286
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1146,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10196,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1139,f10194]) ).
fof(f10194,plain,
( spl0_1285
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1139,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10192,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1138,f10190]) ).
fof(f10190,plain,
( spl0_1284
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1138,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10188,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1137,f10186]) ).
fof(f10186,plain,
( spl0_1283
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1137,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10184,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1136,f10182]) ).
fof(f10182,plain,
( spl0_1282
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1136,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10180,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1133,f10178]) ).
fof(f10178,plain,
( spl0_1281
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1133,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10176,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1127,f10174]) ).
fof(f10174,plain,
( spl0_1280
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1127,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10172,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1126,f10170]) ).
fof(f10170,plain,
( spl0_1279
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1126,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10168,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1125,f10166]) ).
fof(f10166,plain,
( spl0_1278
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1125,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10164,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1124,f10162]) ).
fof(f10162,plain,
( spl0_1277
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1124,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10160,plain,
( spl0_1276
| ~ spl0_743
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f8507,f8171,f7044,f10158]) ).
fof(f10158,plain,
( spl0_1276
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f7044,plain,
( spl0_743
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f8507,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_743
| ~ spl0_974 ),
inference(superposition,[],[f8172,f7045]) ).
fof(f7045,plain,
( ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8
| ~ spl0_743 ),
inference(avatar_component_clause,[],[f7044]) ).
fof(f10156,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1084,f10154]) ).
fof(f10154,plain,
( spl0_1275
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(c_0,X15,X3)
| c_less(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1084,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(c_0,X15,X3)
| c_less(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10152,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1083,f10150]) ).
fof(f10150,plain,
( spl0_1274
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(c_0,X15,X3)
| ~ c_less(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1083,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(c_0,X15,X3)
| ~ c_less(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10148,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1080,f10146]) ).
fof(f10146,plain,
( spl0_1273
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1080,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10144,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1079,f10142]) ).
fof(f10142,plain,
( spl0_1272
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1079,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10140,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1077,f10138]) ).
fof(f10138,plain,
( spl0_1271
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_uminus(X15,X3) != c_uminus(X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1077,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_uminus(X15,X3) != c_uminus(X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10136,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1074,f10134]) ).
fof(f10134,plain,
( spl0_1270
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f1074,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10132,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1073,f10130]) ).
fof(f10130,plain,
( spl0_1269
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f1073,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10128,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1072,f10126]) ).
fof(f1072,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10124,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1071,f10122]) ).
fof(f1071,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10120,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1017,f10118]) ).
fof(f1017,axiom,
! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(X37,X3) = c_times(X37,c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10110,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1016,f10108]) ).
fof(f1016,axiom,
! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X37,X3) = c_uminus(X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10106,plain,
spl0_1264,
inference(avatar_split_clause,[],[f936,f10104]) ).
fof(f936,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_plus(X25,X9,tc_nat) != c_plus(X10,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10102,plain,
spl0_1263,
inference(avatar_split_clause,[],[f931,f10100]) ).
fof(f931,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_plus(X9,X25,tc_nat) != c_plus(X9,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10098,plain,
spl0_1262,
inference(avatar_split_clause,[],[f915,f10096]) ).
fof(f10096,plain,
( spl0_1262
<=> ! [X25,X10] :
( c_0 = X25
| c_0 = X10
| c_0 != c_times(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f915,axiom,
! [X10,X25] :
( c_0 = X25
| c_0 = X10
| c_0 != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10094,plain,
spl0_1261,
inference(avatar_split_clause,[],[f700,f10092]) ).
fof(f700,axiom,
! [X10,X25] : c_IntDef_Oint(c_plus(X25,X10,tc_nat)) = c_plus(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10090,plain,
spl0_1260,
inference(avatar_split_clause,[],[f663,f10088]) ).
fof(f10088,plain,
( spl0_1260
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| c_NatArith_Oof__nat(X10,X3) != c_NatArith_Oof__nat(X25,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f663,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| c_NatArith_Oof__nat(X10,X3) != c_NatArith_Oof__nat(X25,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10086,plain,
spl0_1259,
inference(avatar_split_clause,[],[f657,f10084]) ).
fof(f10084,plain,
( spl0_1259
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f657,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10082,plain,
spl0_1258,
inference(avatar_split_clause,[],[f656,f10080]) ).
fof(f10080,plain,
( spl0_1258
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f656,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10078,plain,
spl0_1257,
inference(avatar_split_clause,[],[f634,f10076]) ).
fof(f10076,plain,
( spl0_1257
<=> ! [X52,X24] :
( c_0 = X52
| c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X24,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f634,axiom,
! [X52,X24] :
( c_0 = X52
| c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X24,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10074,plain,
spl0_1256,
inference(avatar_split_clause,[],[f593,f10072]) ).
fof(f593,axiom,
! [X41,X3,X44,X42] :
( X42 = X44
| c_append(X41,X42,X3) != c_append(X41,X44,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10064,plain,
spl0_1255,
inference(avatar_split_clause,[],[f587,f10062]) ).
fof(f10062,plain,
( spl0_1255
<=> ! [X8,X3] :
( c_List_Orotate1(X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f587,axiom,
! [X3,X8] :
( c_List_Orotate1(X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10060,plain,
spl0_1254,
inference(avatar_split_clause,[],[f476,f10058]) ).
fof(f10058,plain,
( spl0_1254
<=> ! [X57,X14,X56,X3,X15] :
( X56 = X57
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f476,axiom,
! [X3,X56,X57,X14,X15] :
( X56 = X57
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10056,plain,
spl0_1253,
inference(avatar_split_clause,[],[f475,f10054]) ).
fof(f10054,plain,
( spl0_1253
<=> ! [X57,X14,X56,X3,X15] :
( X14 = X15
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f475,axiom,
! [X3,X56,X57,X14,X15] :
( X14 = X15
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10052,plain,
spl0_1252,
inference(avatar_split_clause,[],[f460,f10050]) ).
fof(f10050,plain,
( spl0_1252
<=> ! [X41,X3,X10] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate(X10,X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f460,axiom,
! [X41,X3,X10] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate(X10,X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10048,plain,
spl0_1251,
inference(avatar_split_clause,[],[f402,f10046]) ).
fof(f10046,plain,
( spl0_1251
<=> ! [X13,X41,X11] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| ~ c_in(X11,c_List_Oset(X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f402,axiom,
! [X41,X11,X13] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| ~ c_in(X11,c_List_Oset(X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10044,plain,
spl0_1250,
inference(avatar_split_clause,[],[f380,f10042]) ).
fof(f380,axiom,
! [X41,X3,X44,X42] :
( X42 = X44
| c_append(X42,X41,X3) != c_append(X44,X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10040,plain,
spl0_1249,
inference(avatar_split_clause,[],[f343,f10038]) ).
fof(f10038,plain,
( spl0_1249
<=> ! [X16,X15] : c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f343,axiom,
! [X16,X15] : c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10036,plain,
spl0_1248,
inference(avatar_split_clause,[],[f342,f10034]) ).
fof(f10034,plain,
( spl0_1248
<=> ! [X16,X15] : c_Divides_Oop_Amod(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f342,axiom,
! [X16,X15] : c_Divides_Oop_Amod(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10032,plain,
spl0_1247,
inference(avatar_split_clause,[],[f335,f10030]) ).
fof(f10030,plain,
( spl0_1247
<=> ! [X11,X10] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f335,axiom,
! [X10,X11] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10022,plain,
( spl0_1246
| ~ spl0_871
| ~ spl0_1245 ),
inference(avatar_split_clause,[],[f10018,f10015,f7612,f10020]) ).
fof(f10020,plain,
( spl0_1246
<=> ! [X10] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f10015,plain,
( spl0_1245
<=> ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f10018,plain,
( ! [X10] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X10 )
| ~ spl0_871
| ~ spl0_1245 ),
inference(forward_demodulation,[],[f10016,f7614]) ).
fof(f10016,plain,
( ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1245 ),
inference(avatar_component_clause,[],[f10015]) ).
fof(f10017,plain,
spl0_1245,
inference(avatar_split_clause,[],[f334,f10015]) ).
fof(f334,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10013,plain,
spl0_1244,
inference(avatar_split_clause,[],[f327,f10011]) ).
fof(f10011,plain,
( spl0_1244
<=> ! [X16,X8] :
( c_0 = X16
| c_div(c_times(X16,X8,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f327,axiom,
! [X8,X16] :
( c_0 = X16
| c_div(c_times(X16,X8,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10009,plain,
spl0_1243,
inference(avatar_split_clause,[],[f326,f10007]) ).
fof(f10007,plain,
( spl0_1243
<=> ! [X16,X8] :
( c_0 = X16
| c_div(c_times(X8,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f326,axiom,
! [X8,X16] :
( c_0 = X16
| c_div(c_times(X8,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10005,plain,
spl0_1242,
inference(avatar_split_clause,[],[f307,f10003]) ).
fof(f10003,plain,
( spl0_1242
<=> ! [X16] : c_IntDiv_OposDivAlg(c_Pair(c_0,X16,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_1242])]) ).
fof(f307,axiom,
! [X16] : c_IntDiv_OposDivAlg(c_Pair(c_0,X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10001,plain,
spl0_1241,
inference(avatar_split_clause,[],[f292,f9999]) ).
fof(f9999,plain,
( spl0_1241
<=> ! [X16,X15] : c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f292,axiom,
! [X16,X15] : c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f9997,plain,
spl0_1240,
inference(avatar_split_clause,[],[f263,f9995]) ).
fof(f9995,plain,
( spl0_1240
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f263,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f9993,plain,
spl0_1239,
inference(avatar_split_clause,[],[f262,f9991]) ).
fof(f9991,plain,
( spl0_1239
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f262,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f9989,plain,
spl0_1238,
inference(avatar_split_clause,[],[f259,f9987]) ).
fof(f9987,plain,
( spl0_1238
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f259,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f9985,plain,
spl0_1237,
inference(avatar_split_clause,[],[f258,f9983]) ).
fof(f9983,plain,
( spl0_1237
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f258,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f9981,plain,
( spl0_1236
| ~ spl0_53
| ~ spl0_959 ),
inference(avatar_split_clause,[],[f8116,f7994,f3421,f9978]) ).
fof(f7994,plain,
( spl0_959
<=> ! [X3] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f8116,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_959 ),
inference(resolution,[],[f7995,f3423]) ).
fof(f7995,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3) )
| ~ spl0_959 ),
inference(avatar_component_clause,[],[f7994]) ).
fof(f9976,plain,
spl0_1235,
inference(avatar_split_clause,[],[f256,f9974]) ).
fof(f9974,plain,
( spl0_1235
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X35 = X37
| c_IntDef_Oof__int(X37,X3) != c_IntDef_Oof__int(X35,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f256,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X35 = X37
| c_IntDef_Oof__int(X37,X3) != c_IntDef_Oof__int(X35,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f9972,plain,
spl0_1234,
inference(avatar_split_clause,[],[f250,f9970]) ).
fof(f9970,plain,
( spl0_1234
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f250,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f9968,plain,
spl0_1233,
inference(avatar_split_clause,[],[f249,f9966]) ).
fof(f9966,plain,
( spl0_1233
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f249,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f9964,plain,
spl0_1232,
inference(avatar_split_clause,[],[f248,f9962]) ).
fof(f9962,plain,
( spl0_1232
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f248,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f9960,plain,
spl0_1231,
inference(avatar_split_clause,[],[f247,f9958]) ).
fof(f247,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f9956,plain,
spl0_1230,
inference(avatar_split_clause,[],[f211,f9954]) ).
fof(f9954,plain,
( spl0_1230
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| c_in(c_uminus(X15,X3),c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f211,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| c_in(c_uminus(X15,X3),c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f9952,plain,
spl0_1229,
inference(avatar_split_clause,[],[f206,f9950]) ).
fof(f9950,plain,
( spl0_1229
<=> ! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f206,axiom,
! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f9948,plain,
spl0_1228,
inference(avatar_split_clause,[],[f192,f9946]) ).
fof(f9946,plain,
( spl0_1228
<=> ! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f192,axiom,
! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f9944,plain,
spl0_1227,
inference(avatar_split_clause,[],[f191,f9942]) ).
fof(f9942,plain,
( spl0_1227
<=> ! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X36,tc_IntDef_Oint)) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f191,axiom,
! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X36,tc_IntDef_Oint)) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f9940,plain,
spl0_1226,
inference(avatar_split_clause,[],[f93,f9938]) ).
fof(f9938,plain,
( spl0_1226
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f93,axiom,
! [X10,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f9936,plain,
( spl0_1225
| ~ spl0_853
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f8099,f7907,f7491,f9933]) ).
fof(f9933,plain,
( spl0_1225
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f8099,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_853
| ~ spl0_938 ),
inference(superposition,[],[f7492,f7909]) ).
fof(f9931,plain,
spl0_1224,
inference(avatar_split_clause,[],[f83,f9929]) ).
fof(f9929,plain,
( spl0_1224
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f83,axiom,
! [X10,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f9927,plain,
spl0_1223,
inference(avatar_split_clause,[],[f82,f9925]) ).
fof(f9925,plain,
( spl0_1223
<=> ! [X25,X10] : c_Divides_Oop_Amod(c_plus(X10,X25,tc_nat),X10,tc_nat) = c_Divides_Oop_Amod(X25,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f82,axiom,
! [X10,X25] : c_Divides_Oop_Amod(c_plus(X10,X25,tc_nat),X10,tc_nat) = c_Divides_Oop_Amod(X25,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f9923,plain,
spl0_1222,
inference(avatar_split_clause,[],[f41,f9921]) ).
fof(f9921,plain,
( spl0_1222
<=> ! [X18,X17,X3,X19] :
( X18 = X19
| c_Datatype__Universe_OIn1(X19,X3,X17) != c_Datatype__Universe_OIn1(X18,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f41,axiom,
! [X3,X18,X19,X17] :
( X18 = X19
| c_Datatype__Universe_OIn1(X19,X3,X17) != c_Datatype__Universe_OIn1(X18,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f9919,plain,
spl0_1221,
inference(avatar_split_clause,[],[f39,f9917]) ).
fof(f9917,plain,
( spl0_1221
<=> ! [X18,X17,X3,X19] :
( X18 = X19
| c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn0(X19,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f39,axiom,
! [X3,X18,X19,X17] :
( X18 = X19
| c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn0(X19,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f9915,plain,
spl0_1220,
inference(avatar_split_clause,[],[f35,f9913]) ).
fof(f9913,plain,
( spl0_1220
<=> ! [X15,X17,X16,X3] :
( X15 = X16
| c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OAtom(X16,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f35,axiom,
! [X3,X16,X17,X15] :
( X15 = X16
| c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OAtom(X16,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f9857,plain,
( ~ spl0_1218
| spl0_1219
| ~ spl0_765
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9759,f9412,f7132,f9855,f9851]) ).
fof(f9851,plain,
( spl0_1218
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f9855,plain,
( spl0_1219
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f9759,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_765
| ~ spl0_1183 ),
inference(trivial_inequality_removal,[],[f9752]) ).
fof(f9752,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_765
| ~ spl0_1183 ),
inference(superposition,[],[f9413,f7133]) ).
fof(f9751,plain,
( spl0_1217
| ~ spl0_88
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8079,f7859,f3596,f9749]) ).
fof(f9749,plain,
( spl0_1217
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f7859,plain,
( spl0_926
<=> ! [X8,X3] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f8079,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_88
| ~ spl0_926 ),
inference(resolution,[],[f7860,f3598]) ).
fof(f7860,plain,
( ! [X3,X8] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f7859]) ).
fof(f9693,plain,
( spl0_1216
| ~ spl0_54
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8078,f7859,f3426,f9691]) ).
fof(f8078,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_54
| ~ spl0_926 ),
inference(resolution,[],[f7860,f3428]) ).
fof(f9646,plain,
( spl0_1215
| ~ spl0_88
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8077,f7855,f3596,f9644]) ).
fof(f9644,plain,
( spl0_1215
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f7855,plain,
( spl0_925
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f8077,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_88
| ~ spl0_925 ),
inference(resolution,[],[f7856,f3598]) ).
fof(f7856,plain,
( ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) )
| ~ spl0_925 ),
inference(avatar_component_clause,[],[f7855]) ).
fof(f9589,plain,
( spl0_1214
| ~ spl0_54
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8076,f7855,f3426,f9587]) ).
fof(f9587,plain,
( spl0_1214
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f8076,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_925 ),
inference(resolution,[],[f7856,f3428]) ).
fof(f9569,plain,
( spl0_1213
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1141 ),
inference(avatar_split_clause,[],[f9246,f9243,f8297,f3421,f9567]) ).
fof(f9243,plain,
( spl0_1141
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f9246,plain,
( ! [X3] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1141 ),
inference(forward_demodulation,[],[f9244,f8587]) ).
fof(f9244,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) )
| ~ spl0_1141 ),
inference(avatar_component_clause,[],[f9243]) ).
fof(f9557,plain,
( spl0_1212
| ~ spl0_92
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8072,f7843,f3616,f9555]) ).
fof(f9555,plain,
( spl0_1212
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f7843,plain,
( spl0_922
<=> ! [X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f8072,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_92
| ~ spl0_922 ),
inference(resolution,[],[f7844,f3618]) ).
fof(f7844,plain,
( ! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 )
| ~ spl0_922 ),
inference(avatar_component_clause,[],[f7843]) ).
fof(f9531,plain,
spl0_1211,
inference(avatar_split_clause,[],[f3060,f9529]) ).
fof(f9529,plain,
( spl0_1211
<=> ! [X25,X10] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f3060,plain,
! [X10,X25] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X10,tc_nat) ),
inference(forward_demodulation,[],[f2885,f2749]) ).
fof(f2885,plain,
! [X10,X25] :
( c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X25,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f946,f1394]) ).
fof(f946,axiom,
! [X10,X25] :
( c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9527,plain,
spl0_1210,
inference(avatar_split_clause,[],[f3059,f9525]) ).
fof(f3059,plain,
! [X10,X25] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X25,tc_nat) ),
inference(forward_demodulation,[],[f2884,f2749]) ).
fof(f2884,plain,
! [X10,X25] :
( c_lessequals(c_1,X25,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X25,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f945,f1394]) ).
fof(f945,axiom,
! [X10,X25] :
( c_lessequals(c_1,X25,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9523,plain,
spl0_1209,
inference(avatar_split_clause,[],[f3055,f9521]) ).
fof(f9521,plain,
( spl0_1209
<=> ! [X24,X10] :
( c_lessequals(c_1,c_Nat_Opower(X24,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f3055,plain,
! [X10,X24] :
( c_lessequals(c_1,c_Nat_Opower(X24,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2873,f2749]) ).
fof(f2873,plain,
! [X10,X24] :
( ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X24,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1190,f1394]) ).
fof(f1190,axiom,
! [X10,X24] :
( ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X24,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9519,plain,
( spl0_1208
| ~ spl0_28
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8071,f7843,f3296,f9517]) ).
fof(f9517,plain,
( spl0_1208
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f8071,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_922 ),
inference(resolution,[],[f7844,f3298]) ).
fof(f9515,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2989,f9513]) ).
fof(f2989,plain,
! [X10,X25] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2789,f2785]) ).
fof(f2789,plain,
! [X10,X25] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1615,f1394]) ).
fof(f1615,axiom,
! [X10,X25] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9511,plain,
spl0_1206,
inference(avatar_split_clause,[],[f2985,f9509]) ).
fof(f9509,plain,
( spl0_1206
<=> ! [X35] : c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f2985,plain,
! [X35] : c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2787,f2764]) ).
fof(f2787,plain,
! [X35] : c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f981,f963,f963]) ).
fof(f981,axiom,
! [X35] : c_Numeral_Obin__pred(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X35),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9507,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2788,f9505]) ).
fof(f2788,plain,
! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f973,f979,f979]) ).
fof(f973,axiom,
! [X35] : c_Numeral_Obin__minus(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9499,plain,
( spl0_1204
| ~ spl0_1203 ),
inference(avatar_split_clause,[],[f9495,f9492,f9497]) ).
fof(f9492,plain,
( spl0_1203
<=> ! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f9495,plain,
( ! [X10] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1203 ),
inference(forward_demodulation,[],[f9493,f2785]) ).
fof(f9493,plain,
( ! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1203 ),
inference(avatar_component_clause,[],[f9492]) ).
fof(f9494,plain,
spl0_1203,
inference(avatar_split_clause,[],[f2777,f9492]) ).
fof(f2777,plain,
! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f244,f1394]) ).
fof(f244,axiom,
! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9490,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1565,f9488]) ).
fof(f9488,plain,
( spl0_1202
<=> ! [X20,X3] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ORange(X20,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1565,axiom,
! [X3,X20] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ORange(X20,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9486,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1563,f9484]) ).
fof(f9484,plain,
( spl0_1201
<=> ! [X20,X3] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ODomain(X20,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1563,axiom,
! [X3,X20] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ODomain(X20,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9482,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1535,f9480]) ).
fof(f9480,plain,
( spl0_1200
<=> ! [X15,X16,X27,X3] :
( ~ c_in(X15,X27,X3)
| c_in(X15,c_insert(X16,X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1535,axiom,
! [X3,X16,X27,X15] :
( ~ c_in(X15,X27,X3)
| c_in(X15,c_insert(X16,X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9478,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1492,f9476]) ).
fof(f9476,plain,
( spl0_1199
<=> ! [X3,X31,X27,X26] :
( ~ c_in(X26,X31,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1492,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9474,plain,
( spl0_1198
| ~ spl0_92
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8070,f7839,f3616,f9472]) ).
fof(f9472,plain,
( spl0_1198
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f7839,plain,
( spl0_921
<=> ! [X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f8070,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_92
| ~ spl0_921 ),
inference(resolution,[],[f7840,f3618]) ).
fof(f7840,plain,
( ! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 )
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f7839]) ).
fof(f9470,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1491,f9468]) ).
fof(f9468,plain,
( spl0_1197
<=> ! [X31,X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1491,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9466,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1433,f9464]) ).
fof(f9464,plain,
( spl0_1196
<=> ! [X27,X3,X26] :
( c_in(X26,X27,X3)
| c_in(X26,c_uminus(X27,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1433,axiom,
! [X3,X26,X27] :
( c_in(X26,X27,X3)
| c_in(X26,c_uminus(X27,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9462,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1432,f9460]) ).
fof(f9460,plain,
( spl0_1195
<=> ! [X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| ~ c_in(X26,c_uminus(X27,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1432,axiom,
! [X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| ~ c_in(X26,c_uminus(X27,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9458,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1395,f9456]) ).
fof(f9456,plain,
( spl0_1194
<=> ! [X38,X74] : c_minus(X38,X74,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1395,axiom,
! [X38,X74] : c_minus(X38,X74,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9454,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1392,f9452]) ).
fof(f9452,plain,
( spl0_1193
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,X74,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1392,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,X74,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9450,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1372,f9448]) ).
fof(f1372,axiom,
! [X3,X15] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_OatLeastAtMost(X15,X15,X3) = c_insert(X15,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9446,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1121,f9444]) ).
fof(f9444,plain,
( spl0_1191
<=> ! [X36] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1121,axiom,
! [X36] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/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(f9442,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1120,f9440]) ).
fof(f9440,plain,
( spl0_1190
<=> ! [X36] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1120,axiom,
! [X36] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/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(f9438,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1102,f9436]) ).
fof(f9436,plain,
( spl0_1189
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_less(c_0,c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f1102,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_less(c_0,c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9434,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1095,f9432]) ).
fof(f1095,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_OrderedGroup_Opprt(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9430,plain,
( spl0_1187
| ~ spl0_28
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8069,f7839,f3296,f9428]) ).
fof(f9428,plain,
( spl0_1187
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f8069,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_921 ),
inference(resolution,[],[f7840,f3298]) ).
fof(f9426,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1094,f9424]) ).
fof(f1094,axiom,
! [X3,X11] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_OrderedGroup_Opprt(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9422,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1090,f9420]) ).
fof(f1090,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X8,c_0,X3)
| c_OrderedGroup_Onprt(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9418,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1089,f9416]) ).
fof(f1089,axiom,
! [X3,X11] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_0 = c_OrderedGroup_Onprt(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9414,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1049,f9412]) ).
fof(f1049,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_0 != c_minus(X15,X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9410,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1033,f9408]) ).
fof(f1033,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_HOL_Oabs(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9406,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1031,f9404]) ).
fof(f1031,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9402,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1029,f9400]) ).
fof(f9400,plain,
( spl0_1180
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| ~ c_lessequals(c_HOL_Oabs(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1029,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| ~ c_lessequals(c_HOL_Oabs(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9398,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1028,f9396]) ).
fof(f1028,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9394,plain,
spl0_1178,
inference(avatar_split_clause,[],[f997,f9392]) ).
fof(f997,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9390,plain,
spl0_1177,
inference(avatar_split_clause,[],[f977,f9388]) ).
fof(f9386,plain,
( spl0_1176
| ~ spl0_65
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8064,f7823,f3481,f9384]) ).
fof(f9384,plain,
( spl0_1176
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f3481,plain,
( spl0_65
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f7823,plain,
( spl0_917
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8064,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_65
| ~ spl0_917 ),
inference(resolution,[],[f7824,f3483]) ).
fof(f3483,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f3481]) ).
fof(f7824,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7823]) ).
fof(f9382,plain,
spl0_1175,
inference(avatar_split_clause,[],[f954,f9380]) ).
fof(f9380,plain,
( spl0_1175
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f954,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9378,plain,
spl0_1174,
inference(avatar_split_clause,[],[f953,f9376]) ).
fof(f953,axiom,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9374,plain,
spl0_1173,
inference(avatar_split_clause,[],[f929,f9372]) ).
fof(f929,axiom,
! [X10,X25] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9370,plain,
spl0_1172,
inference(avatar_split_clause,[],[f928,f9368]) ).
fof(f928,axiom,
! [X10,X25] :
( c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9366,plain,
spl0_1171,
inference(avatar_split_clause,[],[f880,f9364]) ).
fof(f9364,plain,
( spl0_1171
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f880,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9362,plain,
spl0_1170,
inference(avatar_split_clause,[],[f879,f9360]) ).
fof(f9360,plain,
( spl0_1170
<=> ! [X25,X10] :
( ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f879,axiom,
! [X10,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9358,plain,
spl0_1169,
inference(avatar_split_clause,[],[f701,f9356]) ).
fof(f9356,plain,
( spl0_1169
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f701,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9354,plain,
spl0_1168,
inference(avatar_split_clause,[],[f664,f9352]) ).
fof(f9352,plain,
( spl0_1168
<=> ! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f664,axiom,
! [X3,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9350,plain,
spl0_1167,
inference(avatar_split_clause,[],[f584,f9348]) ).
fof(f9348,plain,
( spl0_1167
<=> ! [X11,X3] : c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Orev(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f584,axiom,
! [X3,X11] : c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Orev(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9346,plain,
spl0_1166,
inference(avatar_split_clause,[],[f581,f9344]) ).
fof(f9344,plain,
( spl0_1166
<=> ! [X11,X3,X10] : c_List_Oreplicate(X10,X11,X3) = c_List_Orev(c_List_Oreplicate(X10,X11,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f581,axiom,
! [X3,X10,X11] : c_List_Oreplicate(X10,X11,X3) = c_List_Orev(c_List_Oreplicate(X10,X11,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9342,plain,
( spl0_1165
| ~ spl0_16
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8063,f7823,f3236,f9340]) ).
fof(f9340,plain,
( spl0_1165
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f3236,plain,
( spl0_16
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f8063,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_917 ),
inference(resolution,[],[f7824,f3238]) ).
fof(f3238,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f3236]) ).
fof(f9338,plain,
spl0_1164,
inference(avatar_split_clause,[],[f562,f9336]) ).
fof(f9336,plain,
( spl0_1164
<=> ! [X42,X11,X13,X8] :
( ~ c_List_Oop_Amem(X11,X42,X13)
| c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f562,axiom,
! [X11,X8,X42,X13] :
( ~ c_List_Oop_Amem(X11,X42,X13)
| c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9334,plain,
spl0_1163,
inference(avatar_split_clause,[],[f463,f9332]) ).
fof(f9332,plain,
( spl0_1163
<=> ! [X52,X24] : c_Nat_Osize(c_List_Oupt(X24,X52),tc_List_Olist(tc_nat)) = c_minus(X52,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f463,axiom,
! [X52,X24] : c_Nat_Osize(c_List_Oupt(X24,X52),tc_List_Olist(tc_nat)) = c_minus(X52,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9330,plain,
spl0_1162,
inference(avatar_split_clause,[],[f459,f9328]) ).
fof(f9328,plain,
( spl0_1162
<=> ! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate1(X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f459,axiom,
! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate1(X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9326,plain,
spl0_1161,
inference(avatar_split_clause,[],[f458,f9324]) ).
fof(f9324,plain,
( spl0_1161
<=> ! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orev(X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f458,axiom,
! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orev(X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9322,plain,
spl0_1160,
inference(avatar_split_clause,[],[f445,f9320]) ).
fof(f445,axiom,
! [X41,X3,X8] : c_List_Olast(c_append(X41,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9318,plain,
spl0_1159,
inference(avatar_split_clause,[],[f444,f9316]) ).
fof(f9316,plain,
( spl0_1159
<=> ! [X8,X3,X10] :
( c_0 = X10
| c_List_Olast(c_List_Oreplicate(X10,X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f444,axiom,
! [X3,X10,X8] :
( c_0 = X10
| c_List_Olast(c_List_Oreplicate(X10,X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9314,plain,
spl0_1158,
inference(avatar_split_clause,[],[f443,f9312]) ).
fof(f9312,plain,
( spl0_1158
<=> ! [X53,X3] :
( c_List_Olist_ONil = X53
| c_in(c_List_Olast(X53,X3),c_List_Oset(X53,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f443,axiom,
! [X3,X53] :
( c_List_Olist_ONil = X53
| c_in(c_List_Olast(X53,X3),c_List_Oset(X53,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9310,plain,
spl0_1157,
inference(avatar_split_clause,[],[f434,f9308]) ).
fof(f434,axiom,
! [X8,X52] :
( ~ c_less(X8,X52,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X52),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9306,plain,
spl0_1156,
inference(avatar_split_clause,[],[f433,f9304]) ).
fof(f9304,plain,
( spl0_1156
<=> ! [X8,X3,X10] :
( c_0 = X10
| c_List_Ohd(c_List_Oreplicate(X10,X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f433,axiom,
! [X3,X10,X8] :
( c_0 = X10
| c_List_Ohd(c_List_Oreplicate(X10,X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9302,plain,
spl0_1155,
inference(avatar_split_clause,[],[f432,f9300]) ).
fof(f9300,plain,
( spl0_1155
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_in(c_List_Ohd(X41,X3),c_List_Oset(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f432,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_in(c_List_Ohd(X41,X3),c_List_Oset(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9298,plain,
( spl0_1154
| ~ spl0_65
| ~ spl0_916 ),
inference(avatar_split_clause,[],[f8062,f7819,f3481,f9296]) ).
fof(f7819,plain,
( spl0_916
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f8062,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_65
| ~ spl0_916 ),
inference(resolution,[],[f7820,f3483]) ).
fof(f7820,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 )
| ~ spl0_916 ),
inference(avatar_component_clause,[],[f7819]) ).
fof(f9294,plain,
spl0_1153,
inference(avatar_split_clause,[],[f389,f9292]) ).
fof(f9292,plain,
( spl0_1153
<=> ! [X11,X8,X3] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f389,axiom,
! [X3,X11,X8] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9290,plain,
spl0_1152,
inference(avatar_split_clause,[],[f313,f9288]) ).
fof(f9288,plain,
( spl0_1152
<=> ! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f313,axiom,
! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9286,plain,
spl0_1151,
inference(avatar_split_clause,[],[f312,f9284]) ).
fof(f9284,plain,
( spl0_1151
<=> ! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f312,axiom,
! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9282,plain,
spl0_1150,
inference(avatar_split_clause,[],[f305,f9280]) ).
fof(f9280,plain,
( spl0_1150
<=> ! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f305,axiom,
! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9278,plain,
spl0_1149,
inference(avatar_split_clause,[],[f304,f9276]) ).
fof(f9276,plain,
( spl0_1149
<=> ! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_less(X16,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f304,axiom,
! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_less(X16,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9274,plain,
spl0_1148,
inference(avatar_split_clause,[],[f268,f9272]) ).
fof(f268,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_NatArith_Oof__nat(X10,X3) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X10,tc_IntDef_Oint),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9270,plain,
spl0_1147,
inference(avatar_split_clause,[],[f204,f9268]) ).
fof(f9268,plain,
( spl0_1147
<=> ! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f204,axiom,
! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9266,plain,
spl0_1146,
inference(avatar_split_clause,[],[f203,f9264]) ).
fof(f203,axiom,
! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9262,plain,
spl0_1145,
inference(avatar_split_clause,[],[f202,f9260]) ).
fof(f202,axiom,
! [X37,X35] :
( ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9258,plain,
spl0_1144,
inference(avatar_split_clause,[],[f201,f9256]) ).
fof(f9256,plain,
( spl0_1144
<=> ! [X37,X35] :
( c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f201,axiom,
! [X37,X35] :
( c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9254,plain,
( spl0_1143
| ~ spl0_16
| ~ spl0_916 ),
inference(avatar_split_clause,[],[f8061,f7819,f3236,f9252]) ).
fof(f8061,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_916 ),
inference(resolution,[],[f7820,f3238]) ).
fof(f9250,plain,
spl0_1142,
inference(avatar_split_clause,[],[f198,f9248]) ).
fof(f198,axiom,
! [X37,X35] : c_plus(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X37,X35,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9245,plain,
spl0_1141,
inference(avatar_split_clause,[],[f195,f9243]) ).
fof(f195,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9241,plain,
spl0_1140,
inference(avatar_split_clause,[],[f160,f9239]) ).
fof(f160,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9237,plain,
spl0_1139,
inference(avatar_split_clause,[],[f157,f9235]) ).
fof(f9235,plain,
( spl0_1139
<=> ! [X8,X10] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X10,tc_nat),tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f157,axiom,
! [X10,X8] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X10,tc_nat),tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9233,plain,
spl0_1138,
inference(avatar_split_clause,[],[f86,f9231]) ).
fof(f9231,plain,
( spl0_1138
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f86,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9229,plain,
spl0_1137,
inference(avatar_split_clause,[],[f84,f9227]) ).
fof(f9227,plain,
( spl0_1137
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f84,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9225,plain,
spl0_1136,
inference(avatar_split_clause,[],[f28,f9223]) ).
fof(f28,axiom,
! [X3,X16,X17,X15] : c_0 = c_Nat_Osize(c_Pair(X15,X16,X3,X17),tc_prod(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9221,plain,
spl0_1135,
inference(avatar_split_clause,[],[f16,f9219]) ).
fof(f9219,plain,
( spl0_1135
<=> ! [X11,X12,X3] :
( c_Datatype_Ooption_OSome(X11,X3) = X12
| ~ c_in(X11,c_Datatype_Oo2s(X12,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f16,axiom,
! [X3,X11,X12] :
( c_Datatype_Ooption_OSome(X11,X3) = X12
| ~ c_in(X11,c_Datatype_Oo2s(X12,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9217,plain,
spl0_1134,
inference(avatar_split_clause,[],[f6,f9215]) ).
fof(f9215,plain,
( spl0_1134
<=> ! [X0,X1,X8,X3] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X0,X1,X8,X3,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f6,axiom,
! [X3,X0,X1,X8] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X0,X1,X8,X3,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__3_0) ).
fof(f9213,plain,
spl0_1133,
inference(avatar_split_clause,[],[f5,f9211]) ).
fof(f9211,plain,
( spl0_1133
<=> ! [X4,X0,X8,X3,X2] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X0,X8,X2,X3,X4),X3,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f5,axiom,
! [X2,X3,X0,X8,X4] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X0,X8,X2,X3,X4),X3,X4) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).
fof(f9209,plain,
( spl0_1132
| ~ spl0_10
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f8060,f7815,f3206,f9207]) ).
fof(f9207,plain,
( spl0_1132
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f7815,plain,
( spl0_915
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8060,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_915 ),
inference(resolution,[],[f7816,f3208]) ).
fof(f7816,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) )
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f7815]) ).
fof(f9205,plain,
spl0_1131,
inference(avatar_split_clause,[],[f4,f9203]) ).
fof(f9203,plain,
( spl0_1131
<=> ! [X4,X8,X3,X2,X1] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X1,X2,X3,X4),X3,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f4,axiom,
! [X2,X3,X1,X8,X4] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X1,X2,X3,X4),X3,X4) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).
fof(f9180,plain,
( spl0_1130
| ~ spl0_10
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8059,f7811,f3206,f9178]) ).
fof(f9178,plain,
( spl0_1130
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f7811,plain,
( spl0_914
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f8059,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_914 ),
inference(resolution,[],[f7812,f3208]) ).
fof(f7812,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 )
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f7811]) ).
fof(f9165,plain,
( spl0_1129
| ~ spl0_5
| ~ spl0_913 ),
inference(avatar_split_clause,[],[f8057,f7807,f3181,f9163]) ).
fof(f9163,plain,
( spl0_1129
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3181,plain,
( spl0_5
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f7807,plain,
( spl0_913
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f8057,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_5
| ~ spl0_913 ),
inference(resolution,[],[f7808,f3183]) ).
fof(f3183,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f3181]) ).
fof(f7808,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 )
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f7807]) ).
fof(f9128,plain,
( spl0_1128
| ~ spl0_5
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f8055,f7803,f3181,f9126]) ).
fof(f7803,plain,
( spl0_912
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f8055,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_5
| ~ spl0_912 ),
inference(resolution,[],[f7804,f3183]) ).
fof(f7804,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 )
| ~ spl0_912 ),
inference(avatar_component_clause,[],[f7803]) ).
fof(f9089,plain,
( spl0_1127
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f8784,f8781,f8297,f3421,f9087]) ).
fof(f8781,plain,
( spl0_1076
<=> ! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f8784,plain,
( ! [X15] : c_uminus(X15,tc_IntDef_Oint) = c_div(X15,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1005
| ~ spl0_1076 ),
inference(forward_demodulation,[],[f8782,f8587]) ).
fof(f8782,plain,
( ! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint)
| ~ spl0_1076 ),
inference(avatar_component_clause,[],[f8781]) ).
fof(f9049,plain,
( spl0_1126
| spl0_665
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9026,f8724,f6694,f9046]) ).
fof(f8724,plain,
( spl0_1062
<=> ! [X27,X3] :
( c_0 = c_Finite__Set_Ocard(X27,X3)
| c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f9026,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_665
| ~ spl0_1062 ),
inference(resolution,[],[f8725,f6696]) ).
fof(f8725,plain,
( ! [X3,X27] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_0 = c_Finite__Set_Ocard(X27,X3) )
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f8724]) ).
fof(f8990,plain,
( spl0_1125
| ~ spl0_5
| ~ spl0_110
| ~ spl0_912
| ~ spl0_1119 ),
inference(avatar_split_clause,[],[f8962,f8957,f7803,f3700,f3181,f8987]) ).
fof(f8987,plain,
( spl0_1125
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f8962,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_5
| ~ spl0_110
| ~ spl0_912
| ~ spl0_1119 ),
inference(forward_demodulation,[],[f8961,f8055]) ).
fof(f8961,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_1119 ),
inference(superposition,[],[f8958,f3702]) ).
fof(f8982,plain,
spl0_1124,
inference(avatar_split_clause,[],[f3107,f8980]) ).
fof(f8980,plain,
( spl0_1124
<=> ! [X11,X3] :
( c_IntDef_Oiszero(c_0,X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f3107,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_0,X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(inner_rewriting,[],[f3106]) ).
fof(f3106,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f3105,f965]) ).
fof(f3105,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2914,f2748]) ).
fof(f2914,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f187,f979]) ).
fof(f187,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f8978,plain,
spl0_1123,
inference(avatar_split_clause,[],[f2992,f8976]) ).
fof(f8976,plain,
( spl0_1123
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f2992,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2794,f2749]) ).
fof(f2794,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f60,f1394]) ).
fof(f60,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f8974,plain,
spl0_1122,
inference(avatar_split_clause,[],[f2991,f8972]) ).
fof(f8972,plain,
( spl0_1122
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f2991,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2793,f2749]) ).
fof(f2793,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f59,f1394]) ).
fof(f59,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f8970,plain,
spl0_1121,
inference(avatar_split_clause,[],[f2865,f8968]) ).
fof(f8968,plain,
( spl0_1121
<=> ! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f2865,plain,
! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1129,f1394]) ).
fof(f1129,axiom,
! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f8966,plain,
spl0_1120,
inference(avatar_split_clause,[],[f2855,f8964]) ).
fof(f8964,plain,
( spl0_1120
<=> ! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f2855,plain,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1128,f1394]) ).
fof(f1128,axiom,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f8959,plain,
( spl0_1119
| ~ spl0_1118 ),
inference(avatar_split_clause,[],[f8955,f8952,f8957]) ).
fof(f8952,plain,
( spl0_1118
<=> ! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f8955,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1118 ),
inference(forward_demodulation,[],[f8953,f2785]) ).
fof(f8953,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1118 ),
inference(avatar_component_clause,[],[f8952]) ).
fof(f8954,plain,
spl0_1118,
inference(avatar_split_clause,[],[f2776,f8952]) ).
fof(f2776,plain,
! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f238,f1394]) ).
fof(f238,axiom,
! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f8950,plain,
( spl0_1117
| ~ spl0_792
| ~ spl0_1116 ),
inference(avatar_split_clause,[],[f8946,f8943,f7241,f8948]) ).
fof(f8948,plain,
( spl0_1117
<=> ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f8943,plain,
( spl0_1116
<=> ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f8946,plain,
( ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3)
| ~ spl0_792
| ~ spl0_1116 ),
inference(forward_demodulation,[],[f8944,f7242]) ).
fof(f8944,plain,
( ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3)
| ~ spl0_1116 ),
inference(avatar_component_clause,[],[f8943]) ).
fof(f8945,plain,
spl0_1116,
inference(avatar_split_clause,[],[f2750,f8943]) ).
fof(f2750,plain,
! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3),
inference(definition_unfolding,[],[f1559,f1566]) ).
fof(f1559,axiom,
! [X3] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f8941,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1682,f8939]) ).
fof(f1682,axiom,
! [X3,X16,X15] :
( X15 = X16
| ~ c_in(X16,c_insert(X15,c_emptyset,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8937,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1680,f8935]) ).
fof(f8935,plain,
( spl0_1114
<=> ! [X27,X3,X31] :
( ~ c_less(X27,X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1680,axiom,
! [X31,X3,X27] :
( ~ c_less(X27,X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8933,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1679,f8931]) ).
fof(f8931,plain,
( spl0_1113
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| ~ c_less(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1679,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| ~ c_less(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8929,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1521,f8927]) ).
fof(f8927,plain,
( spl0_1112
<=> ! [X27,X3] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1521,axiom,
! [X3,X27] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f8925,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1504,f8923]) ).
fof(f8923,plain,
( spl0_1111
<=> ! [X27,X3] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1504,axiom,
! [X3,X27] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f8921,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1468,f8919]) ).
fof(f8919,plain,
( spl0_1110
<=> ! [X27,X3] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1468,axiom,
! [X3,X27] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f8917,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1465,f8915]) ).
fof(f8915,plain,
( spl0_1109
<=> ! [X27,X3] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1465,axiom,
! [X3,X27] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f8913,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1238,f8911]) ).
fof(f1238,axiom,
! [X3,X11] : c_in(c_Pair(X11,X11,X3,X3),c_Relation_OId,tc_prod(X3,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f8909,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1233,f8907]) ).
fof(f1233,axiom,
! [X3,X27] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f8905,plain,
( spl0_1106
| ~ spl0_696
| ~ spl0_865
| ~ spl0_908 ),
inference(avatar_split_clause,[],[f8044,f7787,f7540,f6836,f8902]) ).
fof(f8902,plain,
( spl0_1106
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f8044,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_696
| ~ spl0_865
| ~ spl0_908 ),
inference(forward_demodulation,[],[f8042,f6838]) ).
fof(f8042,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_865
| ~ spl0_908 ),
inference(superposition,[],[f7788,f7542]) ).
fof(f8900,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1216,f8898]) ).
fof(f1216,axiom,
! [X3,X8,X17,X15] : c_snd(c_Pair(X15,X8,X17,X3),X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f8896,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1214,f8894]) ).
fof(f1214,axiom,
! [X3,X8,X16,X17] : c_fst(c_Pair(X8,X16,X3,X17),X3,X17) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f8892,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1192,f8890]) ).
fof(f8890,plain,
( spl0_1103
<=> ! [X11,X10] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(X11,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1192,axiom,
! [X10,X11] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(X11,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f8888,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1191,f8886]) ).
fof(f1191,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f8884,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1144,f8882]) ).
fof(f8882,plain,
( spl0_1101
<=> ! [X11,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1144,axiom,
! [X10,X11] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f8880,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1131,f8878]) ).
fof(f8878,plain,
( spl0_1100
<=> ! [X11,X8] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1131,axiom,
! [X11,X8] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f8876,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1097,f8874]) ).
fof(f1097,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(X15,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f8872,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1075,f8870]) ).
fof(f8870,plain,
( spl0_1098
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = X15
| c_0 != c_uminus(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1075,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = X15
| c_0 != c_uminus(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f8868,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1063,f8866]) ).
fof(f8866,plain,
( spl0_1097
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1063,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f8864,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1061,f8862]) ).
fof(f8862,plain,
( spl0_1096
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1061,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f8860,plain,
( spl0_1095
| ~ spl0_83
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f8021,f7705,f3571,f8858]) ).
fof(f8858,plain,
( spl0_1095
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f3571,plain,
( spl0_83
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f7705,plain,
( spl0_888
<=> ! [X8,X3] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f8021,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_83
| ~ spl0_888 ),
inference(resolution,[],[f7706,f3573]) ).
fof(f3573,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f3571]) ).
fof(f7706,plain,
( ! [X3,X8] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 )
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f7705]) ).
fof(f8856,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1047,f8854]) ).
fof(f1047,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(X15,X3) = c_minus(c_0,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f8852,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1022,f8850]) ).
fof(f8850,plain,
( spl0_1093
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_0 != c_HOL_Oabs(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1022,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_0 != c_HOL_Oabs(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f8848,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1021,f8846]) ).
fof(f1021,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(c_uminus(X15,X3),X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f8844,plain,
spl0_1091,
inference(avatar_split_clause,[],[f889,f8842]) ).
fof(f889,axiom,
! [X10,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_0 = c_minus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f8840,plain,
spl0_1090,
inference(avatar_split_clause,[],[f888,f8838]) ).
fof(f888,axiom,
! [X10,X25] :
( c_lessequals(X25,X10,tc_nat)
| c_0 != c_minus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f8836,plain,
spl0_1089,
inference(avatar_split_clause,[],[f699,f8834]) ).
fof(f699,axiom,
! [X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f8832,plain,
spl0_1088,
inference(avatar_split_clause,[],[f682,f8830]) ).
fof(f8830,plain,
( spl0_1088
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f682,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f8828,plain,
spl0_1087,
inference(avatar_split_clause,[],[f653,f8826]) ).
fof(f8826,plain,
( spl0_1087
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X10
| c_0 != c_NatArith_Oof__nat(X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f653,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X10
| c_0 != c_NatArith_Oof__nat(X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f8824,plain,
spl0_1086,
inference(avatar_split_clause,[],[f609,f8822]) ).
fof(f8822,plain,
( spl0_1086
<=> ! [X41,X3,X10] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate(X10,X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f609,axiom,
! [X41,X3,X10] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate(X10,X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f8820,plain,
spl0_1085,
inference(avatar_split_clause,[],[f580,f8818]) ).
fof(f580,axiom,
! [X41,X3,X42] :
( X41 = X42
| c_List_Orev(X41,X3) != c_List_Orev(X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f8816,plain,
( spl0_1084
| ~ spl0_25
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f8020,f7705,f3281,f8814]) ).
fof(f8814,plain,
( spl0_1084
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f3281,plain,
( spl0_25
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f8020,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_25
| ~ spl0_888 ),
inference(resolution,[],[f7706,f3283]) ).
fof(f3283,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f3281]) ).
fof(f8812,plain,
spl0_1083,
inference(avatar_split_clause,[],[f453,f8810]) ).
fof(f453,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_less(c_0,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f8808,plain,
spl0_1082,
inference(avatar_split_clause,[],[f398,f8806]) ).
fof(f8806,plain,
( spl0_1082
<=> ! [X43,X3] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f398,axiom,
! [X3,X43] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f8804,plain,
spl0_1081,
inference(avatar_split_clause,[],[f391,f8802]) ).
fof(f8802,plain,
( spl0_1081
<=> ! [X50,X48,X47,X49] :
( X48 = X50
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f391,axiom,
! [X50,X48,X49,X47] :
( X48 = X50
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f8800,plain,
spl0_1080,
inference(avatar_split_clause,[],[f390,f8798]) ).
fof(f8798,plain,
( spl0_1080
<=> ! [X48,X47,X50,X49] :
( X47 = X49
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f390,axiom,
! [X50,X48,X49,X47] :
( X47 = X49
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f8796,plain,
spl0_1079,
inference(avatar_split_clause,[],[f359,f8794]) ).
fof(f8794,plain,
( spl0_1079
<=> ! [X43,X3] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f359,axiom,
! [X3,X43] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f8792,plain,
spl0_1078,
inference(avatar_split_clause,[],[f338,f8790]) ).
fof(f8790,plain,
( spl0_1078
<=> ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f338,axiom,
! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f8788,plain,
spl0_1077,
inference(avatar_split_clause,[],[f337,f8786]) ).
fof(f337,axiom,
! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f8783,plain,
spl0_1076,
inference(avatar_split_clause,[],[f317,f8781]) ).
fof(f317,axiom,
! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f8779,plain,
spl0_1075,
inference(avatar_split_clause,[],[f290,f8777]) ).
fof(f290,axiom,
! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f8775,plain,
spl0_1074,
inference(avatar_split_clause,[],[f289,f8773]) ).
fof(f289,axiom,
! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f8771,plain,
( spl0_1073
| ~ spl0_90
| ~ spl0_887 ),
inference(avatar_split_clause,[],[f8019,f7701,f3606,f8769]) ).
fof(f8769,plain,
( spl0_1073
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f3606,plain,
( spl0_90
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f7701,plain,
( spl0_887
<=> ! [X8,X3] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f8019,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_90
| ~ spl0_887 ),
inference(resolution,[],[f7702,f3608]) ).
fof(f3608,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f3606]) ).
fof(f7702,plain,
( ! [X3,X8] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 )
| ~ spl0_887 ),
inference(avatar_component_clause,[],[f7701]) ).
fof(f8767,plain,
spl0_1072,
inference(avatar_split_clause,[],[f280,f8765]) ).
fof(f280,axiom,
! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f8763,plain,
spl0_1071,
inference(avatar_split_clause,[],[f279,f8761]) ).
fof(f279,axiom,
! [X37,X35] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f8759,plain,
spl0_1070,
inference(avatar_split_clause,[],[f278,f8757]) ).
fof(f278,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f8755,plain,
spl0_1069,
inference(avatar_split_clause,[],[f277,f8753]) ).
fof(f277,axiom,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f8751,plain,
spl0_1068,
inference(avatar_split_clause,[],[f276,f8749]) ).
fof(f276,axiom,
! [X10,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f8747,plain,
spl0_1067,
inference(avatar_split_clause,[],[f275,f8745]) ).
fof(f275,axiom,
! [X10,X25] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f8743,plain,
spl0_1066,
inference(avatar_split_clause,[],[f257,f8741]) ).
fof(f257,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_IntDef_Oint(X10),X3) = c_NatArith_Oof__nat(X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f8739,plain,
spl0_1065,
inference(avatar_split_clause,[],[f245,f8737]) ).
fof(f8737,plain,
( spl0_1065
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X37
| c_0 != c_IntDef_Oof__int(X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f245,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X37
| c_0 != c_IntDef_Oof__int(X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f8735,plain,
spl0_1064,
inference(avatar_split_clause,[],[f240,f8733]) ).
fof(f8733,plain,
( spl0_1064
<=> ! [X25,X10] :
( c_0 = X25
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f240,axiom,
! [X10,X25] :
( c_0 = X25
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f8731,plain,
spl0_1063,
inference(avatar_split_clause,[],[f239,f8729]) ).
fof(f239,axiom,
! [X10,X25] :
( c_0 = X10
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8726,plain,
spl0_1062,
inference(avatar_split_clause,[],[f129,f8724]) ).
fof(f129,axiom,
! [X3,X27] :
( c_0 = c_Finite__Set_Ocard(X27,X3)
| c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8722,plain,
spl0_1061,
inference(avatar_split_clause,[],[f125,f8720]) ).
fof(f125,axiom,
! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8718,plain,
spl0_1060,
inference(avatar_split_clause,[],[f115,f8716]) ).
fof(f115,axiom,
! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8714,plain,
spl0_1059,
inference(avatar_split_clause,[],[f85,f8712]) ).
fof(f85,axiom,
! [X10,X8] :
( ~ c_less(X8,X10,tc_nat)
| c_Divides_Oop_Amod(X8,X10,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8710,plain,
spl0_1058,
inference(avatar_split_clause,[],[f74,f8708]) ).
fof(f74,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_1 = c_div(X10,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8706,plain,
spl0_1057,
inference(avatar_split_clause,[],[f66,f8704]) ).
fof(f66,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_0 = c_div(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8702,plain,
spl0_1056,
inference(avatar_split_clause,[],[f46,f8700]) ).
fof(f8700,plain,
( spl0_1056
<=> ! [X17,X19,X18,X9,X3] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f46,axiom,
! [X3,X18,X19,X9,X17] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f8698,plain,
spl0_1055,
inference(avatar_split_clause,[],[f44,f8696]) ).
fof(f8696,plain,
( spl0_1055
<=> ! [X15,X17,X18,X3,X19] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OLeaf(X15,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f44,axiom,
! [X3,X18,X19,X17,X15] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OLeaf(X15,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
fof(f8694,plain,
spl0_1054,
inference(avatar_split_clause,[],[f36,f8692]) ).
fof(f8692,plain,
( spl0_1054
<=> ! [X15,X18,X17,X3,X19] : c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OScons(X18,X19,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f36,axiom,
! [X3,X18,X19,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OScons(X18,X19,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f8690,plain,
spl0_1053,
inference(avatar_split_clause,[],[f30,f8688]) ).
fof(f8688,plain,
( spl0_1053
<=> ! [X16,X17,X3] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X16,X17,X3),tc_sum(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f30,axiom,
! [X3,X16,X17] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X16,X17,X3),tc_sum(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8686,plain,
( spl0_1052
| ~ spl0_869
| ~ spl0_1002 ),
inference(avatar_split_clause,[],[f8566,f8285,f7570,f8684]) ).
fof(f8684,plain,
( spl0_1052
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f7570,plain,
( spl0_869
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f8566,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_869
| ~ spl0_1002 ),
inference(resolution,[],[f8286,f7571]) ).
fof(f7571,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f7570]) ).
fof(f8682,plain,
spl0_1051,
inference(avatar_split_clause,[],[f29,f8680]) ).
fof(f8680,plain,
( spl0_1051
<=> ! [X17,X3,X15] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X15,X3,X17),tc_sum(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f29,axiom,
! [X3,X17,X15] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X15,X3,X17),tc_sum(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8678,plain,
spl0_1050,
inference(avatar_split_clause,[],[f25,f8676]) ).
fof(f8676,plain,
( spl0_1050
<=> ! [X3,X14,X15] :
( X14 = X15
| c_Datatype_Ooption_OSome(X14,X3) != c_Datatype_Ooption_OSome(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f25,axiom,
! [X3,X14,X15] :
( X14 = X15
| c_Datatype_Ooption_OSome(X14,X3) != c_Datatype_Ooption_OSome(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8674,plain,
spl0_1049,
inference(avatar_split_clause,[],[f20,f8672]) ).
fof(f8672,plain,
( spl0_1049
<=> ! [X13,X11] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X13),X13) = c_insert(X11,c_emptyset,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f20,axiom,
! [X11,X13] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X13),X13) = c_insert(X11,c_emptyset,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8670,plain,
spl0_1048,
inference(avatar_split_clause,[],[f19,f8668]) ).
fof(f19,axiom,
! [X3,X11] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X11,X3),X3) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8666,plain,
spl0_1047,
inference(avatar_split_clause,[],[f18,f8664]) ).
fof(f18,axiom,
! [X3,X11] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X11,X3),X3) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8622,plain,
( spl0_1046
| ~ spl0_794
| ~ spl0_1019 ),
inference(avatar_split_clause,[],[f8605,f8353,f7249,f8620]) ).
fof(f8620,plain,
( spl0_1046
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f8605,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_794
| ~ spl0_1019 ),
inference(superposition,[],[f7250,f8354]) ).
fof(f8586,plain,
( spl0_1045
| ~ spl0_794
| ~ spl0_994 ),
inference(avatar_split_clause,[],[f8556,f8252,f7249,f8584]) ).
fof(f8584,plain,
( spl0_1045
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f8556,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_794
| ~ spl0_994 ),
inference(superposition,[],[f7250,f8253]) ).
fof(f8553,plain,
( spl0_1044
| ~ spl0_26
| ~ spl0_887 ),
inference(avatar_split_clause,[],[f8018,f7701,f3286,f8551]) ).
fof(f8551,plain,
( spl0_1044
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3286,plain,
( spl0_26
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f8018,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_26
| ~ spl0_887 ),
inference(resolution,[],[f7702,f3288]) ).
fof(f3288,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3286]) ).
fof(f8499,plain,
( ~ spl0_75
| spl0_1043
| ~ spl0_663
| ~ spl0_885 ),
inference(avatar_split_clause,[],[f8017,f7693,f6686,f8497,f3531]) ).
fof(f3531,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f6686,plain,
( spl0_663
<=> ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f7693,plain,
( spl0_885
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f8017,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_663
| ~ spl0_885 ),
inference(superposition,[],[f7694,f6687]) ).
fof(f6687,plain,
( ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f6686]) ).
fof(f7694,plain,
( ! [X3,X10] :
( c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) )
| ~ spl0_885 ),
inference(avatar_component_clause,[],[f7693]) ).
fof(f8448,plain,
( spl0_1042
| ~ spl0_818
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f7632,f7511,f7351,f8446]) ).
fof(f8446,plain,
( spl0_1042
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f7632,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_818
| ~ spl0_858 ),
inference(resolution,[],[f7512,f7352]) ).
fof(f8444,plain,
spl0_1041,
inference(avatar_split_clause,[],[f3058,f8442]) ).
fof(f3058,plain,
! [X37] :
( ~ c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| c_less(c_1,X37,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2881,f2749]) ).
fof(f2881,plain,
! [X37] :
( c_less(c_1,X37,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X37),tc_nat) ),
inference(definition_unfolding,[],[f196,f1394]) ).
fof(f196,axiom,
! [X37] :
( c_less(c_1,X37,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8440,plain,
spl0_1040,
inference(avatar_split_clause,[],[f3048,f8438]) ).
fof(f3048,plain,
! [X37] :
( c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_1,X37,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2866,f2749]) ).
fof(f2866,plain,
! [X37] :
( ~ c_less(c_1,X37,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X37),tc_nat) ),
inference(definition_unfolding,[],[f197,f1394]) ).
fof(f197,axiom,
! [X37] :
( ~ c_less(c_1,X37,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8436,plain,
spl0_1039,
inference(avatar_split_clause,[],[f3044,f8434]) ).
fof(f8434,plain,
( spl0_1039
<=> ! [X25,X10] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f3044,plain,
! [X10,X25] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X25 ),
inference(forward_demodulation,[],[f2861,f2749]) ).
fof(f2861,plain,
! [X10,X25] :
( c_1 = X25
| c_times(X25,X10,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f912,f1394]) ).
fof(f912,axiom,
! [X10,X25] :
( c_1 = X25
| c_Suc(c_0) != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
fof(f8432,plain,
spl0_1038,
inference(avatar_split_clause,[],[f3043,f8430]) ).
fof(f8430,plain,
( spl0_1038
<=> ! [X25,X10] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f3043,plain,
! [X10,X25] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X10 ),
inference(forward_demodulation,[],[f2860,f2749]) ).
fof(f2860,plain,
! [X10,X25] :
( c_1 = X10
| c_times(X25,X10,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f943,f1394]) ).
fof(f943,axiom,
! [X10,X25] :
( c_1 = X10
| c_Suc(c_0) != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f8428,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2780,f8426]) ).
fof(f2780,plain,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f982,f963]) ).
fof(f982,axiom,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8424,plain,
spl0_1036,
inference(avatar_split_clause,[],[f2769,f8422]) ).
fof(f8422,plain,
( spl0_1036
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(X8,X3),X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2769,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X3),X8,X3,X3) = X8,
inference(definition_unfolding,[],[f1453,f1223]) ).
fof(f1453,axiom,
! [X3,X8] : c_inter(X8,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8420,plain,
spl0_1035,
inference(avatar_split_clause,[],[f2768,f8418]) ).
fof(f8418,plain,
( spl0_1035
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X3),X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f2768,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X3),X8,X3,X3) = X8,
inference(definition_unfolding,[],[f1451,f1223]) ).
fof(f1451,axiom,
! [X3,X8] : c_inter(c_UNIV,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8416,plain,
spl0_1034,
inference(avatar_split_clause,[],[f2767,f8414]) ).
fof(f2767,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X3),c_UNIV,X3,X3) = X8,
inference(definition_unfolding,[],[f1452,f1223]) ).
fof(f1452,axiom,
! [X3,X8] : c_inter(X8,c_UNIV,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8412,plain,
( spl0_1033
| ~ spl0_818
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f7631,f7507,f7351,f8410]) ).
fof(f8410,plain,
( spl0_1033
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f7631,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_818
| ~ spl0_857 ),
inference(resolution,[],[f7508,f7352]) ).
fof(f8408,plain,
spl0_1032,
inference(avatar_split_clause,[],[f2761,f8406]) ).
fof(f8406,plain,
( spl0_1032
<=> ! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f2761,plain,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f10,f1394]) ).
fof(f10,axiom,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8404,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1640,f8402]) ).
fof(f8402,plain,
( spl0_1031
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1640,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8400,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1639,f8398]) ).
fof(f8398,plain,
( spl0_1030
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1639,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8396,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1612,f8394]) ).
fof(f1612,axiom,
! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8392,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1611,f8390]) ).
fof(f1611,axiom,
! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8388,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1568,f8386]) ).
fof(f8386,plain,
( spl0_1027
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1568,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8384,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1567,f8382]) ).
fof(f8382,plain,
( spl0_1026
<=> ! [X20,X3] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1567,axiom,
! [X3,X20] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8380,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1554,f8378]) ).
fof(f8378,plain,
( spl0_1025
<=> ! [X16,X17,X3,X15] : c_Sum__Type_OInl(X15,X3,X17) != c_Sum__Type_OInr(X16,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1554,axiom,
! [X3,X16,X17,X15] : c_Sum__Type_OInl(X15,X3,X17) != c_Sum__Type_OInr(X16,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f8376,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1517,f8374]) ).
fof(f1517,axiom,
! [X3,X8] : c_uminus(c_uminus(X8,tc_set(X3)),tc_set(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8372,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1509,f8370]) ).
fof(f1509,axiom,
! [X3,X27] :
( c_emptyset = X27
| c_in(c_Main_Oall__not__in__conv__1(X27,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8368,plain,
( spl0_1022
| ~ spl0_109
| ~ spl0_815 ),
inference(avatar_split_clause,[],[f7565,f7339,f3695,f8365]) ).
fof(f7339,plain,
( spl0_815
<=> ! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f7565,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_109
| ~ spl0_815 ),
inference(superposition,[],[f7340,f3697]) ).
fof(f7340,plain,
( ! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint))
| ~ spl0_815 ),
inference(avatar_component_clause,[],[f7339]) ).
fof(f8363,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1486,f8361]) ).
fof(f8361,plain,
( spl0_1021
<=> ! [X27,X3,X31] :
( c_emptyset = X31
| c_emptyset != c_union(X27,X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1486,axiom,
! [X31,X3,X27] :
( c_emptyset = X31
| c_emptyset != c_union(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8359,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1485,f8357]) ).
fof(f8357,plain,
( spl0_1020
<=> ! [X27,X3,X31] :
( c_emptyset = X27
| c_emptyset != c_union(X27,X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1485,axiom,
! [X31,X3,X27] :
( c_emptyset = X27
| c_emptyset != c_union(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8355,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1476,f8353]) ).
fof(f1476,axiom,
! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8351,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1240,f8349]) ).
fof(f8349,plain,
( spl0_1018
<=> ! [X13,X79] : c_Relation_OId = c_Nat_Opower(X79,c_0,tc_set(tc_prod(X13,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1240,axiom,
! [X79,X13] : c_Relation_OId = c_Nat_Opower(X79,c_0,tc_set(tc_prod(X13,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8347,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1239,f8345]) ).
fof(f8345,plain,
( spl0_1017
<=> ! [X8,X3] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X3,X3))) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1239,axiom,
! [X3,X8] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X3,X3))) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8343,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1232,f8341]) ).
fof(f8341,plain,
( spl0_1016
<=> ! [X17,X8,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X3,X17),X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1232,axiom,
! [X3,X8,X17] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X3,X17),X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8339,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1148,f8337]) ).
fof(f8337,plain,
( spl0_1015
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1148,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8335,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1147,f8333]) ).
fof(f8333,plain,
( spl0_1014
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1147,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8331,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1143,f8329]) ).
fof(f8329,plain,
( spl0_1013
<=> ! [X11,X10] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1143,axiom,
! [X10,X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8327,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1135,f8325]) ).
fof(f8325,plain,
( spl0_1012
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1135,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8323,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1134,f8321]) ).
fof(f8321,plain,
( spl0_1011
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1134,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8319,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1130,f8317]) ).
fof(f1130,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8315,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1066,f8313]) ).
fof(f1066,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_uminus(X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8311,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1004,f8309]) ).
fof(f8307,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1000,f8305]) ).
fof(f8305,plain,
( spl0_1007
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1000,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8303,plain,
spl0_1006,
inference(avatar_split_clause,[],[f986,f8301]) ).
fof(f8301,plain,
( spl0_1006
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f986,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8299,plain,
spl0_1005,
inference(avatar_split_clause,[],[f968,f8297]) ).
fof(f968,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8295,plain,
spl0_1004,
inference(avatar_split_clause,[],[f882,f8293]) ).
fof(f8293,plain,
( spl0_1004
<=> ! [X25,X10] :
( c_0 = X10
| c_0 != c_plus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f882,axiom,
! [X10,X25] :
( c_0 = X10
| c_0 != c_plus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8291,plain,
spl0_1003,
inference(avatar_split_clause,[],[f881,f8289]) ).
fof(f8289,plain,
( spl0_1003
<=> ! [X25,X10] :
( c_0 = X25
| c_0 != c_plus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f881,axiom,
! [X10,X25] :
( c_0 = X25
| c_0 != c_plus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8287,plain,
spl0_1002,
inference(avatar_split_clause,[],[f636,f8285]) ).
fof(f636,axiom,
! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8283,plain,
( ~ spl0_53
| spl0_1001
| ~ spl0_833
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8111,f7940,f7411,f8280,f3421]) ).
fof(f8280,plain,
( spl0_1001
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f7411,plain,
( spl0_833
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f7940,plain,
( spl0_946
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f8111,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_833
| ~ spl0_946 ),
inference(superposition,[],[f7412,f7942]) ).
fof(f7942,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f7940]) ).
fof(f7412,plain,
( ! [X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f7411]) ).
fof(f8278,plain,
spl0_1000,
inference(avatar_split_clause,[],[f608,f8276]) ).
fof(f608,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate1(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8274,plain,
spl0_999,
inference(avatar_split_clause,[],[f607,f8272]) ).
fof(f607,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orev(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8270,plain,
spl0_998,
inference(avatar_split_clause,[],[f604,f8268]) ).
fof(f604,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Oremdups(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8266,plain,
spl0_997,
inference(avatar_split_clause,[],[f590,f8264]) ).
fof(f8264,plain,
( spl0_997
<=> ! [X41,X3,X10] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate(X10,X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f590,axiom,
! [X41,X10,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate(X10,X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8262,plain,
spl0_996,
inference(avatar_split_clause,[],[f570,f8260]) ).
fof(f8260,plain,
( spl0_996
<=> ! [X41,X11,X3] : c_List_Oremove1(X11,c_List_Olist_OCons(X11,X41,X3),X3) = X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f570,axiom,
! [X41,X3,X11] : c_List_Oremove1(X11,c_List_Olist_OCons(X11,X41,X3),X3) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8258,plain,
spl0_995,
inference(avatar_split_clause,[],[f542,f8256]) ).
fof(f8256,plain,
( spl0_995
<=> ! [X41,X8,X3] : c_List_Onth(c_List_Olist_OCons(X8,X41,X3),c_0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f542,axiom,
! [X41,X3,X8] : c_List_Onth(c_List_Olist_OCons(X8,X41,X3),c_0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8254,plain,
spl0_994,
inference(avatar_split_clause,[],[f489,f8252]) ).
fof(f8250,plain,
spl0_993,
inference(avatar_split_clause,[],[f457,f8248]) ).
fof(f457,axiom,
! [X3,X11,X8] : c_Nat_Osize(c_List_Oreplicate(X8,X11,X3),tc_List_Olist(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8246,plain,
spl0_992,
inference(avatar_split_clause,[],[f447,f8244]) ).
fof(f447,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_0 != c_Nat_Osize(X41,tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8242,plain,
spl0_991,
inference(avatar_split_clause,[],[f415,f8240]) ).
fof(f8240,plain,
( spl0_991
<=> ! [X51,X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Osublist(X41,X51,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f415,axiom,
! [X51,X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Osublist(X41,X51,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8238,plain,
spl0_990,
inference(avatar_split_clause,[],[f414,f8236]) ).
fof(f8236,plain,
( spl0_990
<=> ! [X41,X3,X10] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f414,axiom,
! [X41,X3,X10] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8234,plain,
spl0_989,
inference(avatar_split_clause,[],[f413,f8232]) ).
fof(f8232,plain,
( spl0_989
<=> ! [X41,X3,X10] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f413,axiom,
! [X41,X3,X10] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8230,plain,
spl0_988,
inference(avatar_split_clause,[],[f410,f8228]) ).
fof(f8228,plain,
( spl0_988
<=> ! [X41,X11,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Oremove1(X11,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f410,axiom,
! [X41,X3,X11] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Oremove1(X11,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8226,plain,
spl0_987,
inference(avatar_split_clause,[],[f409,f8224]) ).
fof(f8224,plain,
( spl0_987
<=> ! [X41,X24,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Odrop(X24,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f409,axiom,
! [X41,X3,X24] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Odrop(X24,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8222,plain,
spl0_986,
inference(avatar_split_clause,[],[f406,f8220]) ).
fof(f8220,plain,
( spl0_986
<=> ! [X41,X3,X42] :
( c_List_Odistinct(X42,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f406,axiom,
! [X3,X41,X42] :
( c_List_Odistinct(X42,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8218,plain,
spl0_985,
inference(avatar_split_clause,[],[f405,f8216]) ).
fof(f8216,plain,
( spl0_985
<=> ! [X41,X3,X42] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f405,axiom,
! [X41,X3,X42] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8214,plain,
spl0_984,
inference(avatar_split_clause,[],[f403,f8212]) ).
fof(f8212,plain,
( spl0_984
<=> ! [X13,X41,X11] :
( c_List_Odistinct(X41,X13)
| ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f403,axiom,
! [X41,X11,X13] :
( c_List_Odistinct(X41,X13)
| ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8210,plain,
spl0_983,
inference(avatar_split_clause,[],[f383,f8208]) ).
fof(f8208,plain,
( spl0_983
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_append(X41,X42,X3) != X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f383,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_append(X41,X42,X3) != X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8206,plain,
spl0_982,
inference(avatar_split_clause,[],[f381,f8204]) ).
fof(f8204,plain,
( spl0_982
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_append(X41,X42,X3) != X42 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f381,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_append(X41,X42,X3) != X42 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).
fof(f8202,plain,
spl0_981,
inference(avatar_split_clause,[],[f378,f8200]) ).
fof(f378,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olist_ONil != c_append(X41,X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f8198,plain,
( ~ spl0_980
| ~ spl0_794
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f8100,f7907,f7249,f8195]) ).
fof(f8195,plain,
( spl0_980
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f8100,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_794
| ~ spl0_938 ),
inference(superposition,[],[f7250,f7909]) ).
fof(f8193,plain,
spl0_979,
inference(avatar_split_clause,[],[f377,f8191]) ).
fof(f8191,plain,
( spl0_979
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_append(X41,X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f377,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_append(X41,X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8189,plain,
spl0_978,
inference(avatar_split_clause,[],[f347,f8187]) ).
fof(f8187,plain,
( spl0_978
<=> ! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X16,X15,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f347,axiom,
! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X16,X15,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8185,plain,
spl0_977,
inference(avatar_split_clause,[],[f346,f8183]) ).
fof(f8183,plain,
( spl0_977
<=> ! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f346,axiom,
! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8181,plain,
spl0_976,
inference(avatar_split_clause,[],[f333,f8179]) ).
fof(f333,axiom,
! [X10,X11] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8177,plain,
spl0_975,
inference(avatar_split_clause,[],[f321,f8175]) ).
fof(f8175,plain,
( spl0_975
<=> ! [X15] :
( c_0 = X15
| c_1 = c_div(X15,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f321,axiom,
! [X15] :
( c_0 = X15
| c_1 = c_div(X15,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8173,plain,
spl0_974,
inference(avatar_split_clause,[],[f291,f8171]) ).
fof(f291,axiom,
! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8169,plain,
spl0_973,
inference(avatar_split_clause,[],[f273,f8167]) ).
fof(f8167,plain,
( spl0_973
<=> ! [X37] :
( ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f273,axiom,
! [X37] :
( ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8165,plain,
spl0_972,
inference(avatar_split_clause,[],[f272,f8163]) ).
fof(f272,axiom,
! [X37] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8161,plain,
spl0_971,
inference(avatar_split_clause,[],[f271,f8159]) ).
fof(f8159,plain,
( spl0_971
<=> ! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f271,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8157,plain,
spl0_970,
inference(avatar_split_clause,[],[f270,f8155]) ).
fof(f8155,plain,
( spl0_970
<=> ! [X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f270,axiom,
! [X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8152,plain,
spl0_969,
inference(avatar_split_clause,[],[f230,f8150]) ).
fof(f230,axiom,
! [X37] :
( c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8148,plain,
spl0_968,
inference(avatar_split_clause,[],[f229,f8146]) ).
fof(f229,axiom,
! [X37] :
( ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X37)) = X37 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8144,plain,
spl0_967,
inference(avatar_split_clause,[],[f199,f8142]) ).
fof(f199,axiom,
! [X37] :
( c_0 = X37
| ~ c_less(c_HOL_Oabs(X37,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8140,plain,
spl0_966,
inference(avatar_split_clause,[],[f96,f8138]) ).
fof(f8138,plain,
( spl0_966
<=> ! [X20,X27,X3] :
( c_emptyset = X27
| c_emptyset != c_Equiv__Relations_Oquotient(X27,X20,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f96,axiom,
! [X3,X27,X20] :
( c_emptyset = X27
| c_emptyset != c_Equiv__Relations_Oquotient(X27,X20,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8136,plain,
spl0_965,
inference(avatar_split_clause,[],[f92,f8134]) ).
fof(f8134,plain,
( spl0_965
<=> ! [X25,X10] : c_0 = c_div(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f92,axiom,
! [X10,X25] : c_0 = c_div(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8132,plain,
spl0_964,
inference(avatar_split_clause,[],[f90,f8130]) ).
fof(f8130,plain,
( spl0_964
<=> ! [X25,X10] : c_0 = c_Divides_Oop_Amod(c_times(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f90,axiom,
! [X10,X25] : c_0 = c_Divides_Oop_Amod(c_times(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8128,plain,
spl0_963,
inference(avatar_split_clause,[],[f88,f8126]) ).
fof(f8126,plain,
( spl0_963
<=> ! [X25,X10] : c_0 = c_Divides_Oop_Amod(c_times(X10,X25,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f88,axiom,
! [X10,X25] : c_0 = c_Divides_Oop_Amod(c_times(X10,X25,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8124,plain,
spl0_962,
inference(avatar_split_clause,[],[f43,f8122]) ).
fof(f8122,plain,
( spl0_962
<=> ! [X9,X17,X3,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f43,axiom,
! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb_0) ).
fof(f8120,plain,
spl0_961,
inference(avatar_split_clause,[],[f40,f8118]) ).
fof(f8118,plain,
( spl0_961
<=> ! [X19,X18,X17,X3] : c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn1(X19,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f40,axiom,
! [X3,X18,X19,X17] : c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn1(X19,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8011,plain,
( spl0_960
| ~ spl0_41
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7609,f7451,f3361,f8008]) ).
fof(f8008,plain,
( spl0_960
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f7451,plain,
( spl0_843
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f7609,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_41
| ~ spl0_843 ),
inference(resolution,[],[f7452,f3363]) ).
fof(f3363,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f3361]) ).
fof(f7452,plain,
( ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) )
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7451]) ).
fof(f7996,plain,
spl0_959,
inference(avatar_split_clause,[],[f3032,f7994]) ).
fof(f3032,plain,
! [X3] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f1020,f1006]) ).
fof(f1020,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f7992,plain,
spl0_958,
inference(avatar_split_clause,[],[f2984,f7990]) ).
fof(f7990,plain,
( spl0_958
<=> ! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X25,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2984,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X25,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2784,f2749]) ).
fof(f2784,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X25,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f150,f1394]) ).
fof(f150,axiom,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X25,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f7988,plain,
( spl0_957
| ~ spl0_41
| ~ spl0_842 ),
inference(avatar_split_clause,[],[f7608,f7447,f3361,f7985]) ).
fof(f7985,plain,
( spl0_957
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f7447,plain,
( spl0_842
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f7608,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_41
| ~ spl0_842 ),
inference(resolution,[],[f7448,f3363]) ).
fof(f7448,plain,
( ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) )
| ~ spl0_842 ),
inference(avatar_component_clause,[],[f7447]) ).
fof(f7983,plain,
spl0_956,
inference(avatar_split_clause,[],[f2983,f7981]) ).
fof(f2983,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2783,f2749]) ).
fof(f2783,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f149,f1394]) ).
fof(f149,axiom,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f7979,plain,
spl0_955,
inference(avatar_split_clause,[],[f2755,f7977]) ).
fof(f2755,plain,
! [X10] : c_less(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1642,f1394]) ).
fof(f1642,axiom,
! [X10] : c_less(X10,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f7975,plain,
spl0_954,
inference(avatar_split_clause,[],[f2754,f7973]) ).
fof(f7973,plain,
( spl0_954
<=> ! [X10] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2754,plain,
! [X10] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1644,f1394]) ).
fof(f1644,axiom,
! [X10] : c_less(c_0,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f7971,plain,
spl0_953,
inference(avatar_split_clause,[],[f1829,f7969]) ).
fof(f7969,plain,
( spl0_953
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_sum(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1829,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_sum(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f7967,plain,
spl0_952,
inference(avatar_split_clause,[],[f1823,f7965]) ).
fof(f7965,plain,
( spl0_952
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_prod(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1823,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_prod(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7963,plain,
spl0_951,
inference(avatar_split_clause,[],[f1773,f7961]) ).
fof(f7961,plain,
( spl0_951
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_fun(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1773,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7959,plain,
spl0_950,
inference(avatar_split_clause,[],[f1671,f7957]) ).
fof(f7957,plain,
( spl0_950
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f1671,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f7955,plain,
spl0_949,
inference(avatar_split_clause,[],[f1670,f7953]) ).
fof(f7953,plain,
( spl0_949
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1670,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7951,plain,
spl0_948,
inference(avatar_split_clause,[],[f1669,f7949]) ).
fof(f7949,plain,
( spl0_948
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1669,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f7947,plain,
spl0_947,
inference(avatar_split_clause,[],[f1668,f7945]) ).
fof(f7945,plain,
( spl0_947
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1668,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7943,plain,
( spl0_946
| ~ spl0_53
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f7605,f7435,f3421,f7940]) ).
fof(f7435,plain,
( spl0_839
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f7605,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_839 ),
inference(resolution,[],[f7436,f3423]) ).
fof(f7436,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) )
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f7435]) ).
fof(f7938,plain,
spl0_945,
inference(avatar_split_clause,[],[f1666,f7936]) ).
fof(f7936,plain,
( spl0_945
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1666,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7934,plain,
spl0_944,
inference(avatar_split_clause,[],[f1665,f7932]) ).
fof(f1665,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7930,plain,
spl0_943,
inference(avatar_split_clause,[],[f1664,f7928]) ).
fof(f7928,plain,
( spl0_943
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1664,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7926,plain,
spl0_942,
inference(avatar_split_clause,[],[f1663,f7924]) ).
fof(f7924,plain,
( spl0_942
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1663,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7922,plain,
spl0_941,
inference(avatar_split_clause,[],[f1614,f7920]) ).
fof(f1614,axiom,
! [X10,X25] : c_lessequals(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7918,plain,
spl0_940,
inference(avatar_split_clause,[],[f1549,f7916]) ).
fof(f7916,plain,
( spl0_940
<=> ! [X27,X3] :
( c_emptyset = X27
| ~ c_lessequals(X27,c_emptyset,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1549,axiom,
! [X3,X27] :
( c_emptyset = X27
| ~ c_lessequals(X27,c_emptyset,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f7914,plain,
spl0_939,
inference(avatar_split_clause,[],[f1510,f7912]) ).
fof(f1510,axiom,
! [X3,X8] : c_Set_Ocontents(c_insert(X8,c_emptyset,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f7910,plain,
spl0_938,
inference(avatar_split_clause,[],[f1384,f7907]) ).
fof(f1384,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f7905,plain,
spl0_937,
inference(avatar_split_clause,[],[f1342,f7903]) ).
fof(f7903,plain,
( spl0_937
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(X15,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1342,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(X15,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f7901,plain,
spl0_936,
inference(avatar_split_clause,[],[f1341,f7899]) ).
fof(f7899,plain,
( spl0_936
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(c_0,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1341,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(c_0,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f7897,plain,
spl0_935,
inference(avatar_split_clause,[],[f1324,f7895]) ).
fof(f7895,plain,
( spl0_935
<=> ! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(c_1,X26,X3) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1324,axiom,
! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(c_1,X26,X3) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f7893,plain,
spl0_934,
inference(avatar_split_clause,[],[f1323,f7891]) ).
fof(f7891,plain,
( spl0_934
<=> ! [X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(X16,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1323,axiom,
! [X3,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(X16,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f7889,plain,
spl0_933,
inference(avatar_split_clause,[],[f1320,f7887]) ).
fof(f7887,plain,
( spl0_933
<=> ! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(X26,c_1,X3) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1320,axiom,
! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(X26,c_1,X3) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f7885,plain,
spl0_932,
inference(avatar_split_clause,[],[f1319,f7883]) ).
fof(f7883,plain,
( spl0_932
<=> ! [X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(c_0,X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1319,axiom,
! [X3,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(c_0,X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f7881,plain,
spl0_931,
inference(avatar_split_clause,[],[f1229,f7879]) ).
fof(f7879,plain,
( spl0_931
<=> ! [X8,X3] : c_Relation_ORange(c_Relation_Odiag(X8,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1229,axiom,
! [X3,X8] : c_Relation_ORange(c_Relation_Odiag(X8,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f7877,plain,
spl0_930,
inference(avatar_split_clause,[],[f1227,f7875]) ).
fof(f7875,plain,
( spl0_930
<=> ! [X17,X8,X3] : c_Relation_Orel__comp(X8,c_Relation_OId,X3,X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1227,axiom,
! [X3,X8,X17] : c_Relation_Orel__comp(X8,c_Relation_OId,X3,X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f7873,plain,
spl0_929,
inference(avatar_split_clause,[],[f1221,f7871]) ).
fof(f7871,plain,
( spl0_929
<=> ! [X17,X8,X3] : c_Relation_Orel__comp(c_Relation_OId,X8,X17,X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1221,axiom,
! [X3,X8,X17] : c_Relation_Orel__comp(c_Relation_OId,X8,X17,X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f7869,plain,
spl0_928,
inference(avatar_split_clause,[],[f1219,f7867]) ).
fof(f7867,plain,
( spl0_928
<=> ! [X8,X3] : c_Relation_ODomain(c_Relation_Odiag(X8,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1219,axiom,
! [X3,X8] : c_Relation_ODomain(c_Relation_Odiag(X8,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f7865,plain,
spl0_927,
inference(avatar_split_clause,[],[f1207,f7863]) ).
fof(f7863,plain,
( spl0_927
<=> ! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(X15,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1207,axiom,
! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(X15,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f7861,plain,
spl0_926,
inference(avatar_split_clause,[],[f1204,f7859]) ).
fof(f1204,axiom,
! [X3,X8] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f7857,plain,
spl0_925,
inference(avatar_split_clause,[],[f1203,f7855]) ).
fof(f1203,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f7853,plain,
spl0_924,
inference(avatar_split_clause,[],[f1142,f7851]) ).
fof(f7851,plain,
( spl0_924
<=> ! [X11] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1142,axiom,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f7849,plain,
spl0_923,
inference(avatar_split_clause,[],[f1141,f7847]) ).
fof(f7847,plain,
( spl0_923
<=> ! [X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1141,axiom,
! [X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f7845,plain,
spl0_922,
inference(avatar_split_clause,[],[f1117,f7843]) ).
fof(f1117,axiom,
! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f7841,plain,
spl0_921,
inference(avatar_split_clause,[],[f1112,f7839]) ).
fof(f1112,axiom,
! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f7837,plain,
spl0_920,
inference(avatar_split_clause,[],[f1101,f7835]) ).
fof(f7835,plain,
( spl0_920
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1101,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f7833,plain,
spl0_919,
inference(avatar_split_clause,[],[f1100,f7831]) ).
fof(f1100,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f7829,plain,
spl0_918,
inference(avatar_split_clause,[],[f1091,f7827]) ).
fof(f1091,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f7825,plain,
spl0_917,
inference(avatar_split_clause,[],[f1068,f7823]) ).
fof(f1068,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f7821,plain,
spl0_916,
inference(avatar_split_clause,[],[f1067,f7819]) ).
fof(f1067,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f7817,plain,
spl0_915,
inference(avatar_split_clause,[],[f1055,f7815]) ).
fof(f1055,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f7813,plain,
spl0_914,
inference(avatar_split_clause,[],[f1048,f7811]) ).
fof(f1048,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f7809,plain,
spl0_913,
inference(avatar_split_clause,[],[f1046,f7807]) ).
fof(f1046,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f7805,plain,
spl0_912,
inference(avatar_split_clause,[],[f1035,f7803]) ).
fof(f1035,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f7801,plain,
spl0_911,
inference(avatar_split_clause,[],[f1032,f7799]) ).
fof(f7799,plain,
( spl0_911
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_HOL_Oabs(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1032,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_HOL_Oabs(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f7797,plain,
spl0_910,
inference(avatar_split_clause,[],[f1030,f7795]) ).
fof(f7795,plain,
( spl0_910
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_HOL_Oabs(c_0,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1030,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_HOL_Oabs(c_0,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f7793,plain,
spl0_909,
inference(avatar_split_clause,[],[f1027,f7791]) ).
fof(f7791,plain,
( spl0_909
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_0,c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1027,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_0,c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7789,plain,
spl0_908,
inference(avatar_split_clause,[],[f1003,f7787]) ).
fof(f1003,axiom,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f7785,plain,
spl0_907,
inference(avatar_split_clause,[],[f715,f7783]) ).
fof(f715,axiom,
! [X35] : c_IntDef_Onat(c_Numeral_Onumber__of(X35,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X35,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f7781,plain,
spl0_906,
inference(avatar_split_clause,[],[f668,f7779]) ).
fof(f7779,plain,
( spl0_906
<=> ! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f668,axiom,
! [X3,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7777,plain,
( ~ spl0_904
| spl0_905
| ~ spl0_695
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f7599,f7411,f6831,f7774,f7770]) ).
fof(f7770,plain,
( spl0_904
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f7774,plain,
( spl0_905
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f7599,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_695
| ~ spl0_833 ),
inference(superposition,[],[f7412,f6833]) ).
fof(f7768,plain,
spl0_903,
inference(avatar_split_clause,[],[f665,f7766]) ).
fof(f7766,plain,
( spl0_903
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_NatArith_Oof__nat(c_0,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f665,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_NatArith_Oof__nat(c_0,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7764,plain,
spl0_902,
inference(avatar_split_clause,[],[f655,f7762]) ).
fof(f7762,plain,
( spl0_902
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f655,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7760,plain,
spl0_901,
inference(avatar_split_clause,[],[f629,f7758]) ).
fof(f7758,plain,
( spl0_901
<=> ! [X13,X11,X8] : c_List_Otl(c_List_Olist_OCons(X11,X8,X13),X13) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f629,axiom,
! [X11,X8,X13] : c_List_Otl(c_List_Olist_OCons(X11,X8,X13),X13) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7756,plain,
spl0_900,
inference(avatar_split_clause,[],[f600,f7754]) ).
fof(f600,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_emptyset != c_List_Oset(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7752,plain,
spl0_899,
inference(avatar_split_clause,[],[f585,f7750]) ).
fof(f7750,plain,
( spl0_899
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate1(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f585,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate1(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7748,plain,
spl0_898,
inference(avatar_split_clause,[],[f565,f7746]) ).
fof(f7746,plain,
( spl0_898
<=> ! [X11,X3] :
( c_List_Olist_ONil = X11
| c_List_Olist_ONil != c_List_Oremdups(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f565,axiom,
! [X3,X11] :
( c_List_Olist_ONil = X11
| c_List_Olist_ONil != c_List_Oremdups(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).
fof(f7744,plain,
spl0_897,
inference(avatar_split_clause,[],[f438,f7742]) ).
fof(f7742,plain,
( spl0_897
<=> ! [X11,X3] : c_List_Olast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f438,axiom,
! [X3,X11] : c_List_Olast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7740,plain,
spl0_896,
inference(avatar_split_clause,[],[f429,f7738]) ).
fof(f7738,plain,
( spl0_896
<=> ! [X41,X8,X3] : c_List_Ohd(c_List_Olist_OCons(X8,X41,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f429,axiom,
! [X41,X3,X8] : c_List_Ohd(c_List_Olist_OCons(X8,X41,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7736,plain,
spl0_895,
inference(avatar_split_clause,[],[f412,f7734]) ).
fof(f7734,plain,
( spl0_895
<=> ! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orev(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f412,axiom,
! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orev(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7732,plain,
spl0_894,
inference(avatar_split_clause,[],[f411,f7730]) ).
fof(f7730,plain,
( spl0_894
<=> ! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orev(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f411,axiom,
! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orev(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7728,plain,
( spl0_893
| ~ spl0_49
| ~ spl0_826 ),
inference(avatar_split_clause,[],[f7579,f7383,f3401,f7725]) ).
fof(f7725,plain,
( spl0_893
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f3401,plain,
( spl0_49
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f7383,plain,
( spl0_826
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f7579,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_49
| ~ spl0_826 ),
inference(resolution,[],[f7384,f3403]) ).
fof(f3403,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f3401]) ).
fof(f7384,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) )
| ~ spl0_826 ),
inference(avatar_component_clause,[],[f7383]) ).
fof(f7723,plain,
spl0_892,
inference(avatar_split_clause,[],[f400,f7721]) ).
fof(f7721,plain,
( spl0_892
<=> ! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f400,axiom,
! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7719,plain,
spl0_891,
inference(avatar_split_clause,[],[f399,f7717]) ).
fof(f7717,plain,
( spl0_891
<=> ! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f399,axiom,
! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7715,plain,
spl0_890,
inference(avatar_split_clause,[],[f387,f7713]) ).
fof(f7713,plain,
( spl0_890
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f387,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7711,plain,
spl0_889,
inference(avatar_split_clause,[],[f363,f7709]) ).
fof(f363,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orev(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7707,plain,
spl0_888,
inference(avatar_split_clause,[],[f349,f7705]) ).
fof(f349,axiom,
! [X3,X8] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7703,plain,
spl0_887,
inference(avatar_split_clause,[],[f348,f7701]) ).
fof(f348,axiom,
! [X3,X8] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7699,plain,
spl0_886,
inference(avatar_split_clause,[],[f340,f7697]) ).
fof(f340,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7695,plain,
spl0_885,
inference(avatar_split_clause,[],[f269,f7693]) ).
fof(f269,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7691,plain,
spl0_884,
inference(avatar_split_clause,[],[f242,f7689]) ).
fof(f242,axiom,
! [X10,X25] : ~ c_less(c_IntDef_Oint(X10),c_uminus(c_IntDef_Oint(X25),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7687,plain,
spl0_883,
inference(avatar_split_clause,[],[f235,f7685]) ).
fof(f235,axiom,
! [X37] :
( ~ c_lessequals(X37,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7683,plain,
( spl0_882
| ~ spl0_22
| ~ spl0_825 ),
inference(avatar_split_clause,[],[f7577,f7379,f3266,f7680]) ).
fof(f7680,plain,
( spl0_882
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f3266,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f7379,plain,
( spl0_825
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f7577,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_825 ),
inference(resolution,[],[f7380,f3268]) ).
fof(f3268,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f3266]) ).
fof(f7380,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) )
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f7379]) ).
fof(f7678,plain,
spl0_881,
inference(avatar_split_clause,[],[f226,f7676]) ).
fof(f7676,plain,
( spl0_881
<=> ! [X10] :
( c_0 = X10
| ~ c_lessequals(c_IntDef_Oint(X10),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f226,axiom,
! [X10] :
( c_0 = X10
| ~ c_lessequals(c_IntDef_Oint(X10),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7674,plain,
spl0_880,
inference(avatar_split_clause,[],[f225,f7672]) ).
fof(f225,axiom,
! [X10,X25] :
( X10 = X25
| c_IntDef_Oint(X25) != c_IntDef_Oint(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7670,plain,
spl0_879,
inference(avatar_split_clause,[],[f158,f7668]) ).
fof(f7668,plain,
( spl0_879
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f158,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7666,plain,
spl0_878,
inference(avatar_split_clause,[],[f148,f7664]) ).
fof(f7664,plain,
( spl0_878
<=> ! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f148,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7662,plain,
spl0_877,
inference(avatar_split_clause,[],[f147,f7660]) ).
fof(f7660,plain,
( spl0_877
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f147,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7658,plain,
spl0_876,
inference(avatar_split_clause,[],[f27,f7656]) ).
fof(f27,axiom,
! [X3,X15] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X15,X3),tc_Datatype_Ooption(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7654,plain,
spl0_875,
inference(avatar_split_clause,[],[f21,f7652]) ).
fof(f7652,plain,
( spl0_875
<=> ! [X12,X3] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Oo2s(X12,X3) != c_emptyset ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f21,axiom,
! [X3,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Oo2s(X12,X3) != c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7649,plain,
spl0_874,
inference(avatar_split_clause,[],[f17,f7647]) ).
fof(f7647,plain,
( spl0_874
<=> ! [X11,X3] : c_in(X11,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X3),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f17,axiom,
! [X3,X11] : c_in(X11,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X3),X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7643,plain,
( spl0_873
| ~ spl0_51
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f7573,f7347,f3411,f7640]) ).
fof(f7640,plain,
( spl0_873
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f7347,plain,
( spl0_817
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f7573,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_817 ),
inference(resolution,[],[f7348,f3413]) ).
fof(f7348,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) )
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7347]) ).
fof(f7630,plain,
( spl0_872
| ~ spl0_23
| ~ spl0_816 ),
inference(avatar_split_clause,[],[f7568,f7343,f3271,f7627]) ).
fof(f7627,plain,
( spl0_872
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f7343,plain,
( spl0_816
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f7568,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_816 ),
inference(resolution,[],[f7344,f3273]) ).
fof(f7344,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) )
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7343]) ).
fof(f7615,plain,
( spl0_871
| ~ spl0_110
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f7562,f7331,f3700,f7612]) ).
fof(f7562,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_813 ),
inference(superposition,[],[f7332,f3702]) ).
fof(f7604,plain,
( spl0_870
| ~ spl0_109
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f7561,f7331,f3695,f7601]) ).
fof(f7561,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_813 ),
inference(superposition,[],[f7332,f3697]) ).
fof(f7572,plain,
( spl0_869
| ~ spl0_804
| ~ spl0_807 ),
inference(avatar_split_clause,[],[f7557,f7307,f7295,f7570]) ).
fof(f7295,plain,
( spl0_804
<=> ! [X8] : c_div(X8,c_1,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f7557,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_804
| ~ spl0_807 ),
inference(superposition,[],[f7308,f7296]) ).
fof(f7296,plain,
( ! [X8] : c_div(X8,c_1,tc_nat) = X8
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f7295]) ).
fof(f7555,plain,
spl0_868,
inference(avatar_split_clause,[],[f3057,f7553]) ).
fof(f7553,plain,
( spl0_868
<=> ! [X25] :
( ~ c_Divides_Oop_Advd(X25,c_1,tc_nat)
| c_1 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f3057,plain,
! [X25] :
( ~ c_Divides_Oop_Advd(X25,c_1,tc_nat)
| c_1 = X25 ),
inference(forward_demodulation,[],[f3056,f2749]) ).
fof(f3056,plain,
! [X25] :
( c_1 = X25
| ~ c_Divides_Oop_Advd(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2880,f2749]) ).
fof(f2880,plain,
! [X25] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X25
| ~ c_Divides_Oop_Advd(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f77,f1394,f1394]) ).
fof(f77,axiom,
! [X25] :
( c_Suc(c_0) = X25
| ~ c_Divides_Oop_Advd(X25,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7551,plain,
spl0_867,
inference(avatar_split_clause,[],[f2971,f7549]) ).
fof(f2971,plain,
! [X31,X3] : c_emptyset = c_Relation_OImage(c_emptyset,X31,X3,X3),
inference(forward_demodulation,[],[f2760,f1236]) ).
fof(f1236,axiom,
! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2760,plain,
! [X31,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X3),X31,X3,X3),
inference(definition_unfolding,[],[f1454,f1223]) ).
fof(f1454,axiom,
! [X31,X3] : c_emptyset = c_inter(c_emptyset,X31,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7547,plain,
spl0_866,
inference(avatar_split_clause,[],[f2764,f7545]) ).
fof(f7543,plain,
spl0_865,
inference(avatar_split_clause,[],[f2762,f7540]) ).
fof(f2762,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f983,f963]) ).
fof(f983,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7538,plain,
spl0_864,
inference(avatar_split_clause,[],[f2749,f7535]) ).
fof(f7533,plain,
spl0_863,
inference(avatar_split_clause,[],[f2745,f7531]) ).
fof(f2745,plain,
! [X25] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),
inference(definition_unfolding,[],[f875,f1394]) ).
fof(f875,axiom,
! [X25] : c_0 != c_Suc(X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
fof(f7529,plain,
spl0_862,
inference(avatar_split_clause,[],[f1672,f7527]) ).
fof(f7527,plain,
( spl0_862
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1672,axiom,
! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7525,plain,
spl0_861,
inference(avatar_split_clause,[],[f1667,f7523]) ).
fof(f7523,plain,
( spl0_861
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1667,axiom,
! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7521,plain,
spl0_860,
inference(avatar_split_clause,[],[f1638,f7519]) ).
fof(f7519,plain,
( spl0_860
<=> ! [X27,X3] : c_in(c_List_Olist_ONil,c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1638,axiom,
! [X3,X27] : c_in(c_List_Olist_ONil,c_List_Olists(X27,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7517,plain,
spl0_859,
inference(avatar_split_clause,[],[f1622,f7515]) ).
fof(f7515,plain,
( spl0_859
<=> ! [X41,X3] : c_in(c_List_Oset(X41,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1622,axiom,
! [X41,X3] : c_in(c_List_Oset(X41,X3),c_Finite__Set_OFinites,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7513,plain,
spl0_858,
inference(avatar_split_clause,[],[f1619,f7511]) ).
fof(f1619,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7509,plain,
spl0_857,
inference(avatar_split_clause,[],[f1618,f7507]) ).
fof(f1618,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7505,plain,
spl0_856,
inference(avatar_split_clause,[],[f1603,f7503]) ).
fof(f1603,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7501,plain,
spl0_855,
inference(avatar_split_clause,[],[f1602,f7499]) ).
fof(f1602,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7497,plain,
spl0_854,
inference(avatar_split_clause,[],[f1555,f7495]) ).
fof(f1555,axiom,
! [X3,X17] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7493,plain,
spl0_853,
inference(avatar_split_clause,[],[f1534,f7491]) ).
fof(f1534,axiom,
! [X3,X11,X27] : c_in(X11,c_insert(X11,X27,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7489,plain,
spl0_852,
inference(avatar_split_clause,[],[f1518,f7487]) ).
fof(f7487,plain,
( spl0_852
<=> ! [X27,X3] : c_emptyset = c_minus(c_emptyset,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1518,axiom,
! [X3,X27] : c_emptyset = c_minus(c_emptyset,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7485,plain,
spl0_851,
inference(avatar_split_clause,[],[f1498,f7483]) ).
fof(f7483,plain,
( spl0_851
<=> ! [X8,X3] : c_Union(c_Pow(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1498,axiom,
! [X3,X8] : c_Union(c_Pow(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7481,plain,
spl0_850,
inference(avatar_split_clause,[],[f1440,f7479]) ).
fof(f1440,axiom,
! [X3,X8] : c_minus(X8,c_emptyset,tc_set(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7477,plain,
spl0_849,
inference(avatar_split_clause,[],[f1438,f7475]) ).
fof(f1438,axiom,
! [X3,X27] : c_emptyset = c_minus(X27,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7473,plain,
spl0_848,
inference(avatar_split_clause,[],[f1437,f7471]) ).
fof(f1437,axiom,
! [X3,X27] : c_emptyset = c_minus(X27,c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7469,plain,
spl0_847,
inference(avatar_split_clause,[],[f1399,f7467]) ).
fof(f7467,plain,
( spl0_847
<=> ! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1399,axiom,
! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7465,plain,
spl0_846,
inference(avatar_split_clause,[],[f1244,f7463]) ).
fof(f7463,plain,
( spl0_846
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1244,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7461,plain,
spl0_845,
inference(avatar_split_clause,[],[f1224,f7459]) ).
fof(f7459,plain,
( spl0_845
<=> ! [X17,X3,X79] : c_emptyset = c_Relation_OImage(X79,c_emptyset,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1224,axiom,
! [X3,X79,X17] : c_emptyset = c_Relation_OImage(X79,c_emptyset,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7457,plain,
spl0_844,
inference(avatar_split_clause,[],[f1222,f7455]) ).
fof(f7455,plain,
( spl0_844
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_OId,X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1222,axiom,
! [X3,X8] : c_Relation_OImage(c_Relation_OId,X8,X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7453,plain,
spl0_843,
inference(avatar_split_clause,[],[f1093,f7451]) ).
fof(f1093,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7449,plain,
spl0_842,
inference(avatar_split_clause,[],[f1088,f7447]) ).
fof(f1088,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7445,plain,
spl0_841,
inference(avatar_split_clause,[],[f1070,f7443]) ).
fof(f7443,plain,
( spl0_841
<=> ! [X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_uminus(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1070,axiom,
! [X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_uminus(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
fof(f7441,plain,
spl0_840,
inference(avatar_split_clause,[],[f1026,f7439]) ).
fof(f7439,plain,
( spl0_840
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = c_HOL_Oabs(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1026,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = c_HOL_Oabs(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7437,plain,
spl0_839,
inference(avatar_split_clause,[],[f1019,f7435]) ).
fof(f1019,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7433,plain,
spl0_838,
inference(avatar_split_clause,[],[f1012,f7431]) ).
fof(f7431,plain,
( spl0_838
<=> ! [X29,X8,X3] : c_Numeral_Obit_Obit__rec(X29,X8,c_Numeral_Obit_OB1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1012,axiom,
! [X3,X29,X8] : c_Numeral_Obit_Obit__rec(X29,X8,c_Numeral_Obit_OB1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7429,plain,
spl0_837,
inference(avatar_split_clause,[],[f1011,f7427]) ).
fof(f7427,plain,
( spl0_837
<=> ! [X28,X8,X3] : c_Numeral_Obit_Obit__rec(X8,X28,c_Numeral_Obit_OB0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1011,axiom,
! [X28,X3,X8] : c_Numeral_Obit_Obit__rec(X8,X28,c_Numeral_Obit_OB0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7425,plain,
spl0_836,
inference(avatar_split_clause,[],[f1008,f7423]) ).
fof(f7423,plain,
( spl0_836
<=> ! [X29,X8,X3] : c_Numeral_Obit_Obit__case(X29,X8,c_Numeral_Obit_OB1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f1008,axiom,
! [X3,X29,X8] : c_Numeral_Obit_Obit__case(X29,X8,c_Numeral_Obit_OB1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7421,plain,
spl0_835,
inference(avatar_split_clause,[],[f1007,f7419]) ).
fof(f7419,plain,
( spl0_835
<=> ! [X28,X8,X3] : c_Numeral_Obit_Obit__case(X8,X28,c_Numeral_Obit_OB0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f1007,axiom,
! [X28,X3,X8] : c_Numeral_Obit_Obit__case(X8,X28,c_Numeral_Obit_OB0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7417,plain,
spl0_834,
inference(avatar_split_clause,[],[f994,f7415]) ).
fof(f994,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7413,plain,
spl0_833,
inference(avatar_split_clause,[],[f993,f7411]) ).
fof(f993,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7409,plain,
spl0_832,
inference(avatar_split_clause,[],[f939,f7407]) ).
fof(f939,axiom,
! [X10] :
( c_0 = X10
| c_less(c_0,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7405,plain,
spl0_831,
inference(avatar_split_clause,[],[f938,f7403]) ).
fof(f938,axiom,
! [X52,X24] : ~ c_less(c_plus(X52,X24,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7401,plain,
spl0_830,
inference(avatar_split_clause,[],[f937,f7399]) ).
fof(f937,axiom,
! [X52,X24] : ~ c_less(c_plus(X24,X52,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7397,plain,
spl0_829,
inference(avatar_split_clause,[],[f898,f7395]) ).
fof(f7395,plain,
( spl0_829
<=> ! [X10] :
( c_0 = X10
| ~ c_less(X10,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f898,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(X10,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7393,plain,
spl0_828,
inference(avatar_split_clause,[],[f892,f7391]) ).
fof(f892,axiom,
! [X24] :
( c_0 = X24
| ~ c_lessequals(X24,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7389,plain,
spl0_827,
inference(avatar_split_clause,[],[f890,f7387]) ).
fof(f890,axiom,
! [X10,X25] : c_lessequals(c_minus(X25,X10,tc_nat),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7385,plain,
spl0_826,
inference(avatar_split_clause,[],[f662,f7383]) ).
fof(f662,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f7381,plain,
spl0_825,
inference(avatar_split_clause,[],[f658,f7379]) ).
fof(f658,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7377,plain,
spl0_824,
inference(avatar_split_clause,[],[f640,f7375]) ).
fof(f7375,plain,
( spl0_824
<=> ! [X17,X3,X42] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X42,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f640,axiom,
! [X3,X17,X42] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X42,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7373,plain,
spl0_823,
inference(avatar_split_clause,[],[f638,f7371]) ).
fof(f7371,plain,
( spl0_823
<=> ! [X13,X41,X76] : c_List_Olist_ONil = c_List_Ozip(X41,c_List_Olist_ONil,X13,X76) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f638,axiom,
! [X41,X76,X13] : c_List_Olist_ONil = c_List_Ozip(X41,c_List_Olist_ONil,X13,X76),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7369,plain,
spl0_822,
inference(avatar_split_clause,[],[f582,f7367]) ).
fof(f582,axiom,
! [X3,X8] : c_List_Orev(c_List_Orev(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7365,plain,
spl0_821,
inference(avatar_split_clause,[],[f561,f7363]) ).
fof(f561,axiom,
! [X3,X11,X42] : c_List_Oop_Amem(X11,c_List_Olist_OCons(X11,X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7361,plain,
spl0_820,
inference(avatar_split_clause,[],[f481,f7359]) ).
fof(f7359,plain,
( spl0_820
<=> ! [X13,X36,X24] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X24,X36,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f481,axiom,
! [X36,X24,X13] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X24,X36,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7357,plain,
spl0_819,
inference(avatar_split_clause,[],[f392,f7355]) ).
fof(f7355,plain,
( spl0_819
<=> ! [X48,X47] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X47,X48),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f392,axiom,
! [X48,X47] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X47,X48),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7353,plain,
spl0_818,
inference(avatar_split_clause,[],[f328,f7351]) ).
fof(f328,axiom,
! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7349,plain,
spl0_817,
inference(avatar_split_clause,[],[f255,f7347]) ).
fof(f255,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
fof(f7345,plain,
spl0_816,
inference(avatar_split_clause,[],[f251,f7343]) ).
fof(f251,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7341,plain,
spl0_815,
inference(avatar_split_clause,[],[f237,f7339]) ).
fof(f237,axiom,
! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7337,plain,
spl0_814,
inference(avatar_split_clause,[],[f223,f7335]) ).
fof(f7335,plain,
( spl0_814
<=> ! [X10] :
( c_0 = X10
| c_0 != c_IntDef_Oint(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f223,axiom,
! [X10] :
( c_0 = X10
| c_0 != c_IntDef_Oint(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7333,plain,
spl0_813,
inference(avatar_split_clause,[],[f217,f7331]) ).
fof(f217,axiom,
! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7329,plain,
spl0_812,
inference(avatar_split_clause,[],[f103,f7327]) ).
fof(f7327,plain,
( spl0_812
<=> ! [X29,X8,X3] : c_Extraction_Osumbool_Osumbool__rec(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f103,axiom,
! [X3,X29,X8] : c_Extraction_Osumbool_Osumbool__rec(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7325,plain,
spl0_811,
inference(avatar_split_clause,[],[f102,f7323]) ).
fof(f7323,plain,
( spl0_811
<=> ! [X28,X8,X3] : c_Extraction_Osumbool_Osumbool__rec(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f102,axiom,
! [X28,X3,X8] : c_Extraction_Osumbool_Osumbool__rec(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7321,plain,
spl0_810,
inference(avatar_split_clause,[],[f99,f7319]) ).
fof(f7319,plain,
( spl0_810
<=> ! [X29,X8,X3] : c_Extraction_Osumbool_Osumbool__case(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f99,axiom,
! [X3,X29,X8] : c_Extraction_Osumbool_Osumbool__case(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7317,plain,
spl0_809,
inference(avatar_split_clause,[],[f98,f7315]) ).
fof(f7315,plain,
( spl0_809
<=> ! [X28,X8,X3] : c_Extraction_Osumbool_Osumbool__case(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f98,axiom,
! [X28,X3,X8] : c_Extraction_Osumbool_Osumbool__case(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7313,plain,
spl0_808,
inference(avatar_split_clause,[],[f75,f7311]) ).
fof(f7311,plain,
( spl0_808
<=> ! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f75,axiom,
! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7309,plain,
spl0_807,
inference(avatar_split_clause,[],[f65,f7307]) ).
fof(f65,axiom,
! [X10,X25] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7305,plain,
spl0_806,
inference(avatar_split_clause,[],[f52,f7303]) ).
fof(f7303,plain,
( spl0_806
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X18,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f52,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X18,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7301,plain,
spl0_805,
inference(avatar_split_clause,[],[f31,f7299]) ).
fof(f31,axiom,
! [X3,X8] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7297,plain,
spl0_804,
inference(avatar_split_clause,[],[f2981,f7295]) ).
fof(f2981,plain,
! [X8] : c_div(X8,c_1,tc_nat) = X8,
inference(forward_demodulation,[],[f2775,f2749]) ).
fof(f2775,plain,
! [X8] : c_div(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X8,
inference(definition_unfolding,[],[f64,f1394]) ).
fof(f64,axiom,
! [X8] : c_div(X8,c_Suc(c_0),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7293,plain,
spl0_803,
inference(avatar_split_clause,[],[f2979,f7290]) ).
fof(f7290,plain,
( spl0_803
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2979,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2772,f2749]) ).
fof(f2772,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,[],[f944,f1394]) ).
fof(f944,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f7288,plain,
spl0_802,
inference(avatar_split_clause,[],[f2977,f7286]) ).
fof(f2977,plain,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_1,tc_nat),
inference(forward_demodulation,[],[f2771,f2749]) ).
fof(f2771,plain,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f81,f1394]) ).
fof(f81,axiom,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7284,plain,
spl0_801,
inference(avatar_split_clause,[],[f2976,f7281]) ).
fof(f2976,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f717,f1006]) ).
fof(f717,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7279,plain,
spl0_800,
inference(avatar_split_clause,[],[f2974,f7277]) ).
fof(f2974,plain,
! [X8,X13] : c_append(c_List_Olist_ONil,X8,X13) = X8,
inference(forward_demodulation,[],[f2766,f579]) ).
fof(f579,axiom,
! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2766,plain,
! [X8,X13] : c_append(c_List_Orev(c_List_Olist_ONil,X13),X8,X13) = X8,
inference(definition_unfolding,[],[f436,f435]) ).
fof(f436,axiom,
! [X8,X13] : c_List_Oitrev(c_List_Olist_ONil,X8,X13) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7275,plain,
spl0_799,
inference(avatar_split_clause,[],[f2972,f7272]) ).
fof(f2972,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2763,f1006]) ).
fof(f2763,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f975,f979]) ).
fof(f975,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7270,plain,
spl0_798,
inference(avatar_split_clause,[],[f2743,f7267]) ).
fof(f2743,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
fof(f7265,plain,
spl0_797,
inference(avatar_split_clause,[],[f2742,f7262]) ).
fof(f2742,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
fof(f7260,plain,
spl0_796,
inference(avatar_split_clause,[],[f2737,f7257]) ).
fof(f2737,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
fof(f7255,plain,
spl0_795,
inference(avatar_split_clause,[],[f1645,f7253]) ).
fof(f1645,axiom,
! [X3,X11] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7251,plain,
spl0_794,
inference(avatar_split_clause,[],[f1523,f7249]) ).
fof(f1523,axiom,
! [X3,X27,X15] : c_emptyset != c_insert(X15,X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f7247,plain,
spl0_793,
inference(avatar_split_clause,[],[f1489,f7245]) ).
fof(f7245,plain,
( spl0_793
<=> ! [X8,X3] : c_union(X8,c_emptyset,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1489,axiom,
! [X3,X8] : c_union(X8,c_emptyset,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7243,plain,
spl0_792,
inference(avatar_split_clause,[],[f1488,f7241]) ).
fof(f1488,axiom,
! [X3,X8] : c_union(c_emptyset,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7239,plain,
spl0_791,
inference(avatar_split_clause,[],[f1484,f7237]) ).
fof(f1484,axiom,
! [X3,X8] : c_union(X8,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7235,plain,
spl0_790,
inference(avatar_split_clause,[],[f1483,f7233]) ).
fof(f1483,axiom,
! [X3,X27] : c_UNIV = c_union(X27,c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7231,plain,
spl0_789,
inference(avatar_split_clause,[],[f1482,f7229]) ).
fof(f1482,axiom,
! [X31,X3] : c_UNIV = c_union(c_UNIV,X31,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7227,plain,
spl0_788,
inference(avatar_split_clause,[],[f1430,f7225]) ).
fof(f1430,axiom,
! [X3] : c_UNIV = c_uminus(c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7223,plain,
spl0_787,
inference(avatar_split_clause,[],[f1426,f7221]) ).
fof(f1426,axiom,
! [X3] : c_emptyset = c_uminus(c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7219,plain,
spl0_786,
inference(avatar_split_clause,[],[f1361,f7217]) ).
fof(f1361,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7215,plain,
spl0_785,
inference(avatar_split_clause,[],[f1349,f7213]) ).
fof(f1349,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7211,plain,
spl0_784,
inference(avatar_split_clause,[],[f1344,f7209]) ).
fof(f7209,plain,
( spl0_784
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1344,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7207,plain,
spl0_783,
inference(avatar_split_clause,[],[f1343,f7205]) ).
fof(f7205,plain,
( spl0_783
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_1,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1343,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_1,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7203,plain,
spl0_782,
inference(avatar_split_clause,[],[f1231,f7201]) ).
fof(f7201,plain,
( spl0_782
<=> ! [X3] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1231,axiom,
! [X3] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7199,plain,
spl0_781,
inference(avatar_split_clause,[],[f1230,f7197]) ).
fof(f7197,plain,
( spl0_781
<=> ! [X17,X3] : c_emptyset = c_Relation_ORange(c_emptyset,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1230,axiom,
! [X3,X17] : c_emptyset = c_Relation_ORange(c_emptyset,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7195,plain,
spl0_780,
inference(avatar_split_clause,[],[f1228,f7193]) ).
fof(f7193,plain,
( spl0_780
<=> ! [X3] : c_UNIV = c_Relation_ORange(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1228,axiom,
! [X3] : c_UNIV = c_Relation_ORange(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7191,plain,
spl0_779,
inference(avatar_split_clause,[],[f1220,f7189]) ).
fof(f7189,plain,
( spl0_779
<=> ! [X17,X3] : c_emptyset = c_Relation_ODomain(c_emptyset,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1220,axiom,
! [X3,X17] : c_emptyset = c_Relation_ODomain(c_emptyset,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7187,plain,
spl0_778,
inference(avatar_split_clause,[],[f1218,f7185]) ).
fof(f7185,plain,
( spl0_778
<=> ! [X3] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1218,axiom,
! [X3] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7183,plain,
spl0_777,
inference(avatar_split_clause,[],[f1194,f7181]) ).
fof(f1194,axiom,
! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7179,plain,
spl0_776,
inference(avatar_split_clause,[],[f1119,f7177]) ).
fof(f1119,axiom,
! [X3,X11] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X11,X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7175,plain,
spl0_775,
inference(avatar_split_clause,[],[f1006,f7172]) ).
fof(f7170,plain,
spl0_774,
inference(avatar_split_clause,[],[f952,f7168]) ).
fof(f952,axiom,
! [X8] : c_minus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7166,plain,
spl0_773,
inference(avatar_split_clause,[],[f950,f7164]) ).
fof(f950,axiom,
! [X8] : c_plus(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7162,plain,
spl0_772,
inference(avatar_split_clause,[],[f948,f7160]) ).
fof(f7160,plain,
( spl0_772
<=> ! [X10] : c_0 = c_times(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f948,axiom,
! [X10] : c_0 = c_times(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7158,plain,
spl0_771,
inference(avatar_split_clause,[],[f906,f7156]) ).
fof(f906,axiom,
! [X25] : c_0 = c_times(X25,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7154,plain,
spl0_770,
inference(avatar_split_clause,[],[f904,f7152]) ).
fof(f904,axiom,
! [X10] : c_0 = c_Orderings_Omin(X10,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7150,plain,
spl0_769,
inference(avatar_split_clause,[],[f903,f7148]) ).
fof(f903,axiom,
! [X10] : c_0 = c_Orderings_Omin(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7146,plain,
spl0_768,
inference(avatar_split_clause,[],[f901,f7144]) ).
fof(f7144,plain,
( spl0_768
<=> ! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f901,axiom,
! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7142,plain,
spl0_767,
inference(avatar_split_clause,[],[f900,f7140]) ).
fof(f900,axiom,
! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7138,plain,
spl0_766,
inference(avatar_split_clause,[],[f891,f7136]) ).
fof(f891,axiom,
! [X25] : c_0 = c_minus(X25,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7134,plain,
spl0_765,
inference(avatar_split_clause,[],[f884,f7132]) ).
fof(f884,axiom,
! [X10] : c_0 = c_minus(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7130,plain,
spl0_764,
inference(avatar_split_clause,[],[f876,f7128]) ).
fof(f876,axiom,
! [X8] : c_plus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7126,plain,
spl0_763,
inference(avatar_split_clause,[],[f613,f7124]) ).
fof(f7124,plain,
( spl0_763
<=> ! [X27,X3] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X27,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f613,axiom,
! [X3,X27] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7122,plain,
spl0_762,
inference(avatar_split_clause,[],[f612,f7120]) ).
fof(f7120,plain,
( spl0_762
<=> ! [X41,X3] : c_List_Olist_ONil = c_List_Osublist(X41,c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f612,axiom,
! [X41,X3] : c_List_Olist_ONil = c_List_Osublist(X41,c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7118,plain,
spl0_761,
inference(avatar_split_clause,[],[f597,f7116]) ).
fof(f597,axiom,
! [X41,X3] : c_append(X41,c_List_Olist_ONil,X3) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7114,plain,
spl0_760,
inference(avatar_split_clause,[],[f591,f7112]) ).
fof(f7112,plain,
( spl0_760
<=> ! [X3,X10] : c_List_Olist_ONil = c_List_Orotate(X10,c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f591,axiom,
! [X3,X10] : c_List_Olist_ONil = c_List_Orotate(X10,c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7110,plain,
spl0_759,
inference(avatar_split_clause,[],[f572,f7108]) ).
fof(f572,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X11,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7106,plain,
spl0_758,
inference(avatar_split_clause,[],[f569,f7104]) ).
fof(f7104,plain,
( spl0_758
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Oremove1(X11,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f569,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Oremove1(X11,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7102,plain,
spl0_757,
inference(avatar_split_clause,[],[f557,f7100]) ).
fof(f557,axiom,
! [X41,X11,X13] : ~ c_List_Onull(c_List_Olist_OCons(X11,X41,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7098,plain,
spl0_756,
inference(avatar_split_clause,[],[f539,f7096]) ).
fof(f539,axiom,
! [X41,X3,X11] : c_List_Olist_OCons(X11,X41,X3) != X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
fof(f7094,plain,
spl0_755,
inference(avatar_split_clause,[],[f478,f7092]) ).
fof(f7092,plain,
( spl0_755
<=> ! [X13,X58] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X58,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f478,axiom,
! [X58,X13] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X58,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7090,plain,
spl0_754,
inference(avatar_split_clause,[],[f474,f7088]) ).
fof(f474,axiom,
! [X3,X56,X14] : c_List_Olist_ONil != c_List_Olist_OCons(X14,X56,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7086,plain,
spl0_753,
inference(avatar_split_clause,[],[f465,f7084]) ).
fof(f7084,plain,
( spl0_753
<=> ! [X13,X20] : c_emptyset = c_List_Olexn(X20,c_0,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f465,axiom,
! [X13,X20] : c_emptyset = c_List_Olexn(X20,c_0,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7082,plain,
spl0_752,
inference(avatar_split_clause,[],[f448,f7080]) ).
fof(f448,axiom,
! [X3] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7078,plain,
spl0_751,
inference(avatar_split_clause,[],[f419,f7076]) ).
fof(f419,axiom,
! [X3,X8] : c_List_Odrop(c_0,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7074,plain,
spl0_750,
inference(avatar_split_clause,[],[f418,f7072]) ).
fof(f7072,plain,
( spl0_750
<=> ! [X13,X10] : c_List_Olist_ONil = c_List_Odrop(X10,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f418,axiom,
! [X10,X13] : c_List_Olist_ONil = c_List_Odrop(X10,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7070,plain,
spl0_749,
inference(avatar_split_clause,[],[f344,f7068]) ).
fof(f344,axiom,
! [X16] : c_0 = c_Divides_Oop_Amod(c_0,X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7066,plain,
spl0_748,
inference(avatar_split_clause,[],[f341,f7064]) ).
fof(f341,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7062,plain,
spl0_747,
inference(avatar_split_clause,[],[f339,f7060]) ).
fof(f339,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7058,plain,
spl0_746,
inference(avatar_split_clause,[],[f324,f7056]) ).
fof(f7056,plain,
( spl0_746
<=> ! [X16] : c_0 = c_div(c_0,X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f324,axiom,
! [X16] : c_0 = c_div(c_0,X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7054,plain,
spl0_745,
inference(avatar_split_clause,[],[f316,f7052]) ).
fof(f7052,plain,
( spl0_745
<=> ! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f316,axiom,
! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7050,plain,
spl0_744,
inference(avatar_split_clause,[],[f314,f7048]) ).
fof(f7048,plain,
( spl0_744
<=> ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f314,axiom,
! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7046,plain,
spl0_743,
inference(avatar_split_clause,[],[f282,f7044]) ).
fof(f282,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7042,plain,
spl0_742,
inference(avatar_split_clause,[],[f214,f7040]) ).
fof(f7040,plain,
( spl0_742
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_1,c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f214,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_1,c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7038,plain,
spl0_741,
inference(avatar_split_clause,[],[f213,f7036]) ).
fof(f7036,plain,
( spl0_741
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_0,c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f213,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_0,c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7034,plain,
spl0_740,
inference(avatar_split_clause,[],[f208,f7032]) ).
fof(f7032,plain,
( spl0_740
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_1,c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f208,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_1,c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7030,plain,
spl0_739,
inference(avatar_split_clause,[],[f207,f7028]) ).
fof(f7028,plain,
( spl0_739
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_0,c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f207,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_0,c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7026,plain,
spl0_738,
inference(avatar_split_clause,[],[f200,f7023]) ).
fof(f7023,plain,
( spl0_738
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f200,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7021,plain,
spl0_737,
inference(avatar_split_clause,[],[f97,f7019]) ).
fof(f7019,plain,
( spl0_737
<=> ! [X20,X3] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f97,axiom,
! [X3,X20] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
fof(f7017,plain,
spl0_736,
inference(avatar_split_clause,[],[f91,f7015]) ).
fof(f91,axiom,
! [X10] : c_0 = c_Divides_Oop_Amod(X10,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7013,plain,
spl0_735,
inference(avatar_split_clause,[],[f80,f7011]) ).
fof(f80,axiom,
! [X25] : c_0 = c_Divides_Oop_Amod(c_0,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7009,plain,
spl0_734,
inference(avatar_split_clause,[],[f63,f7007]) ).
fof(f7007,plain,
( spl0_734
<=> ! [X25] : c_0 = c_div(c_0,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f63,axiom,
! [X25] : c_0 = c_div(c_0,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7005,plain,
spl0_733,
inference(avatar_split_clause,[],[f62,f7003]) ).
fof(f7003,plain,
( spl0_733
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f62,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7001,plain,
spl0_732,
inference(avatar_split_clause,[],[f61,f6999]) ).
fof(f6999,plain,
( spl0_732
<=> ! [X15] : c_0 = c_div(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f61,axiom,
! [X15] : c_0 = c_div(X15,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f6997,plain,
spl0_731,
inference(avatar_split_clause,[],[f33,f6995]) ).
fof(f6995,plain,
( spl0_731
<=> ! [X8,X3] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f33,axiom,
! [X3,X8] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f6993,plain,
spl0_730,
inference(avatar_split_clause,[],[f32,f6991]) ).
fof(f6991,plain,
( spl0_730
<=> ! [X8,X3] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f32,axiom,
! [X3,X8] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f6989,plain,
spl0_729,
inference(avatar_split_clause,[],[f26,f6987]) ).
fof(f6987,plain,
( spl0_729
<=> ! [X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f26,axiom,
! [X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f6983,plain,
( spl0_728
| ~ spl0_109
| ~ spl0_668 ),
inference(avatar_split_clause,[],[f6967,f6707,f3695,f6980]) ).
fof(f6967,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_668 ),
inference(superposition,[],[f6708,f3697]) ).
fof(f6978,plain,
( ~ spl0_727
| ~ spl0_110
| ~ spl0_666 ),
inference(avatar_split_clause,[],[f6964,f6699,f3700,f6975]) ).
fof(f6975,plain,
( spl0_727
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f6699,plain,
( spl0_666
<=> ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f6964,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_666 ),
inference(superposition,[],[f6700,f3702]) ).
fof(f6700,plain,
( ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint)
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f6699]) ).
fof(f6973,plain,
( ~ spl0_726
| ~ spl0_109
| ~ spl0_666 ),
inference(avatar_split_clause,[],[f6963,f6699,f3695,f6970]) ).
fof(f6970,plain,
( spl0_726
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f6963,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_666 ),
inference(superposition,[],[f6700,f3697]) ).
fof(f6962,plain,
spl0_725,
inference(avatar_split_clause,[],[f2978,f6959]) ).
fof(f6959,plain,
( spl0_725
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2978,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f241,f224]) ).
fof(f224,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f241,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f6957,plain,
spl0_724,
inference(avatar_split_clause,[],[f2973,f6955]) ).
fof(f6955,plain,
( spl0_724
<=> ! [X8] : c_Binomial_Obinomial(X8,c_1) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2973,plain,
! [X8] : c_Binomial_Obinomial(X8,c_1) = X8,
inference(forward_demodulation,[],[f2765,f2749]) ).
fof(f2765,plain,
! [X8] : c_Binomial_Obinomial(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X8,
inference(definition_unfolding,[],[f11,f1394]) ).
fof(f11,axiom,
! [X8] : c_Binomial_Obinomial(X8,c_Suc(c_0)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f6953,plain,
spl0_723,
inference(avatar_split_clause,[],[f2748,f6950]) ).
fof(f6948,plain,
spl0_722,
inference(avatar_split_clause,[],[f1827,f6946]) ).
fof(f6946,plain,
( spl0_722
<=> ! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_set(X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1827,axiom,
! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_set(X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6944,plain,
spl0_721,
inference(avatar_split_clause,[],[f1705,f6942]) ).
fof(f6942,plain,
( spl0_721
<=> ! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1705,axiom,
! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6940,plain,
spl0_720,
inference(avatar_split_clause,[],[f1689,f6938]) ).
fof(f1689,axiom,
! [X3,X27] : c_lessequals(X27,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6936,plain,
spl0_719,
inference(avatar_split_clause,[],[f1678,f6934]) ).
fof(f1678,axiom,
! [X3,X27] : c_lessequals(c_emptyset,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6932,plain,
spl0_718,
inference(avatar_split_clause,[],[f1621,f6930]) ).
fof(f6930,plain,
( spl0_718
<=> ! [X41,X3] : c_List_Odistinct(c_List_Oremdups(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1621,axiom,
! [X41,X3] : c_List_Odistinct(c_List_Oremdups(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6928,plain,
spl0_717,
inference(avatar_split_clause,[],[f1605,f6926]) ).
fof(f6926,plain,
( spl0_717
<=> ! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1605,axiom,
! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6924,plain,
spl0_716,
inference(avatar_split_clause,[],[f1564,f6922]) ).
fof(f6922,plain,
( spl0_716
<=> ! [X3] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1564,axiom,
! [X3] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f6920,plain,
spl0_715,
inference(avatar_split_clause,[],[f1548,f6918]) ).
fof(f1548,axiom,
! [X3,X27] : c_lessequals(X27,c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f6916,plain,
spl0_714,
inference(avatar_split_clause,[],[f1541,f6914]) ).
fof(f6914,plain,
( spl0_714
<=> ! [X27,X3] : ~ c_less(X27,c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1541,axiom,
! [X3,X27] : ~ c_less(X27,c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f6912,plain,
spl0_713,
inference(avatar_split_clause,[],[f1501,f6910]) ).
fof(f6910,plain,
( spl0_713
<=> ! [X3] : c_emptyset = c_Union(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1501,axiom,
! [X3] : c_emptyset = c_Union(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f6908,plain,
spl0_712,
inference(avatar_split_clause,[],[f1499,f6906]) ).
fof(f1499,axiom,
! [X3] : c_UNIV = c_Union(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f6904,plain,
spl0_711,
inference(avatar_split_clause,[],[f1475,f6902]) ).
fof(f1475,axiom,
! [X3] : c_UNIV = c_Pow(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f6900,plain,
spl0_710,
inference(avatar_split_clause,[],[f1469,f6898]) ).
fof(f1469,axiom,
! [X3] : c_UNIV = c_Inter(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f6896,plain,
spl0_709,
inference(avatar_split_clause,[],[f1462,f6894]) ).
fof(f1462,axiom,
! [X3] : c_emptyset = c_Inter(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6892,plain,
spl0_708,
inference(avatar_split_clause,[],[f1417,f6889]) ).
fof(f1417,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f6887,plain,
spl0_707,
inference(avatar_split_clause,[],[f1378,f6884]) ).
fof(f1378,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f6882,plain,
spl0_706,
inference(avatar_split_clause,[],[f1236,f6880]) ).
fof(f6878,plain,
spl0_705,
inference(avatar_split_clause,[],[f1014,f6875]) ).
fof(f6875,plain,
( spl0_705
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1014,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f6873,plain,
spl0_704,
inference(avatar_split_clause,[],[f1013,f6870]) ).
fof(f6870,plain,
( spl0_704
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1013,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f6868,plain,
spl0_703,
inference(avatar_split_clause,[],[f1002,f6866]) ).
fof(f6866,plain,
( spl0_703
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1002,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f6864,plain,
spl0_702,
inference(avatar_split_clause,[],[f1001,f6862]) ).
fof(f6862,plain,
( spl0_702
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1001,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f6860,plain,
spl0_701,
inference(avatar_split_clause,[],[f985,f6858]) ).
fof(f6858,plain,
( spl0_701
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_IntDef_Oiszero(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f985,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_IntDef_Oiszero(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6856,plain,
spl0_700,
inference(avatar_split_clause,[],[f980,f6854]) ).
fof(f980,axiom,
! [X35] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6852,plain,
spl0_699,
inference(avatar_split_clause,[],[f965,f6850]) ).
fof(f6848,plain,
spl0_698,
inference(avatar_split_clause,[],[f964,f6846]) ).
fof(f6844,plain,
spl0_697,
inference(avatar_split_clause,[],[f956,f6841]) ).
fof(f956,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f6839,plain,
spl0_696,
inference(avatar_split_clause,[],[f955,f6836]) ).
fof(f955,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f6834,plain,
spl0_695,
inference(avatar_split_clause,[],[f716,f6831]) ).
fof(f716,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f6829,plain,
spl0_694,
inference(avatar_split_clause,[],[f635,f6827]) ).
fof(f6827,plain,
( spl0_694
<=> ! [X24] : c_List_Olist_ONil = c_List_Oupt(X24,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f635,axiom,
! [X24] : c_List_Olist_ONil = c_List_Oupt(X24,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6825,plain,
spl0_693,
inference(avatar_split_clause,[],[f628,f6823]) ).
fof(f6823,plain,
( spl0_693
<=> ! [X13] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f628,axiom,
! [X13] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6821,plain,
spl0_692,
inference(avatar_split_clause,[],[f603,f6819]) ).
fof(f6819,plain,
( spl0_692
<=> ! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f603,axiom,
! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f6817,plain,
spl0_691,
inference(avatar_split_clause,[],[f586,f6815]) ).
fof(f6815,plain,
( spl0_691
<=> ! [X3] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f586,axiom,
! [X3] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6813,plain,
spl0_690,
inference(avatar_split_clause,[],[f579,f6811]) ).
fof(f6811,plain,
( spl0_690
<=> ! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f6809,plain,
spl0_689,
inference(avatar_split_clause,[],[f566,f6807]) ).
fof(f6807,plain,
( spl0_689
<=> ! [X3] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f566,axiom,
! [X3] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f6805,plain,
spl0_688,
inference(avatar_split_clause,[],[f538,f6802]) ).
fof(f6802,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f538,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f6800,plain,
spl0_687,
inference(avatar_split_clause,[],[f537,f6797]) ).
fof(f6797,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f537,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f6795,plain,
spl0_686,
inference(avatar_split_clause,[],[f536,f6792]) ).
fof(f6792,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f536,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f6790,plain,
spl0_685,
inference(avatar_split_clause,[],[f535,f6787]) ).
fof(f6787,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f535,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f6785,plain,
spl0_684,
inference(avatar_split_clause,[],[f534,f6782]) ).
fof(f6782,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f534,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f6780,plain,
spl0_683,
inference(avatar_split_clause,[],[f533,f6777]) ).
fof(f6777,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f533,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f6775,plain,
spl0_682,
inference(avatar_split_clause,[],[f532,f6772]) ).
fof(f6772,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f532,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f6770,plain,
spl0_681,
inference(avatar_split_clause,[],[f531,f6767]) ).
fof(f6767,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f531,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f6765,plain,
spl0_680,
inference(avatar_split_clause,[],[f530,f6762]) ).
fof(f6762,plain,
( spl0_680
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f530,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f6760,plain,
spl0_679,
inference(avatar_split_clause,[],[f529,f6757]) ).
fof(f6757,plain,
( spl0_679
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f529,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f6755,plain,
spl0_678,
inference(avatar_split_clause,[],[f528,f6752]) ).
fof(f6752,plain,
( spl0_678
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f528,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f6750,plain,
spl0_677,
inference(avatar_split_clause,[],[f527,f6747]) ).
fof(f6747,plain,
( spl0_677
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f527,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f6745,plain,
spl0_676,
inference(avatar_split_clause,[],[f526,f6742]) ).
fof(f6742,plain,
( spl0_676
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f526,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f6740,plain,
spl0_675,
inference(avatar_split_clause,[],[f525,f6737]) ).
fof(f6737,plain,
( spl0_675
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f525,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f6735,plain,
spl0_674,
inference(avatar_split_clause,[],[f524,f6732]) ).
fof(f6732,plain,
( spl0_674
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f524,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f6730,plain,
spl0_673,
inference(avatar_split_clause,[],[f523,f6727]) ).
fof(f6727,plain,
( spl0_673
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f523,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f6725,plain,
spl0_672,
inference(avatar_split_clause,[],[f488,f6723]) ).
fof(f488,axiom,
! [X3] : c_UNIV = c_List_Olists(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6721,plain,
spl0_671,
inference(avatar_split_clause,[],[f417,f6719]) ).
fof(f6719,plain,
( spl0_671
<=> ! [X52,X24] : c_List_Odistinct(c_List_Oupt(X24,X52),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f417,axiom,
! [X52,X24] : c_List_Odistinct(c_List_Oupt(X24,X52),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6717,plain,
spl0_670,
inference(avatar_split_clause,[],[f393,f6715]) ).
fof(f6715,plain,
( spl0_670
<=> ! [X13] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f393,axiom,
! [X13] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6713,plain,
spl0_669,
inference(avatar_split_clause,[],[f386,f6711]) ).
fof(f6711,plain,
( spl0_669
<=> ! [X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f386,axiom,
! [X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6709,plain,
spl0_668,
inference(avatar_split_clause,[],[f274,f6707]) ).
fof(f274,axiom,
! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6705,plain,
spl0_667,
inference(avatar_split_clause,[],[f234,f6703]) ).
fof(f234,axiom,
! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6701,plain,
spl0_666,
inference(avatar_split_clause,[],[f228,f6699]) ).
fof(f228,axiom,
! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6697,plain,
~ spl0_665,
inference(avatar_split_clause,[],[f159,f6694]) ).
fof(f159,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f6692,plain,
spl0_664,
inference(avatar_split_clause,[],[f146,f6690]) ).
fof(f6690,plain,
( spl0_664
<=> ! [X8,X3] : c_Fun_Oid(X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f146,axiom,
! [X3,X8] : c_Fun_Oid(X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6688,plain,
spl0_663,
inference(avatar_split_clause,[],[f145,f6686]) ).
fof(f145,axiom,
! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6684,plain,
spl0_662,
inference(avatar_split_clause,[],[f128,f6682]) ).
fof(f6682,plain,
( spl0_662
<=> ! [X3] : c_0 = c_Finite__Set_Ocard(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f128,axiom,
! [X3] : c_0 = c_Finite__Set_Ocard(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6680,plain,
spl0_661,
inference(avatar_split_clause,[],[f105,f6677]) ).
fof(f6677,plain,
( spl0_661
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f105,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f6675,plain,
spl0_660,
inference(avatar_split_clause,[],[f104,f6672]) ).
fof(f6672,plain,
( spl0_660
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f104,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f6670,plain,
spl0_659,
inference(avatar_split_clause,[],[f34,f6667]) ).
fof(f6667,plain,
( spl0_659
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f34,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f6665,plain,
spl0_658,
inference(avatar_split_clause,[],[f23,f6663]) ).
fof(f6663,plain,
( spl0_658
<=> ! [X3,X14] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X14,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f23,axiom,
! [X3,X14] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X14,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f6661,plain,
spl0_657,
inference(avatar_split_clause,[],[f22,f6659]) ).
fof(f6659,plain,
( spl0_657
<=> ! [X3] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f22,axiom,
! [X3] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6657,plain,
spl0_656,
inference(avatar_split_clause,[],[f15,f6655]) ).
fof(f6655,plain,
( spl0_656
<=> ! [X10] : c_1 = c_Binomial_Obinomial(X10,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f15,axiom,
! [X10] : c_1 = c_Binomial_Obinomial(X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6653,plain,
spl0_655,
inference(avatar_split_clause,[],[f14,f6651]) ).
fof(f6651,plain,
( spl0_655
<=> ! [X10] : c_Binomial_Obinomial(X10,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f14,axiom,
! [X10] : c_Binomial_Obinomial(X10,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f5899,plain,
( ~ spl0_654
| ~ spl0_110
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f5879,f3710,f3700,f5896]) ).
fof(f5896,plain,
( spl0_654
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f3710,plain,
( spl0_112
<=> ! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f5879,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_110
| ~ spl0_112 ),
inference(superposition,[],[f3711,f3702]) ).
fof(f3711,plain,
( ! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3710]) ).
fof(f5884,plain,
( ~ spl0_653
| ~ spl0_109
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f5878,f3710,f3695,f5881]) ).
fof(f5878,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_109
| ~ spl0_112 ),
inference(superposition,[],[f3711,f3697]) ).
fof(f5877,plain,
spl0_652,
inference(avatar_split_clause,[],[f2988,f5874]) ).
fof(f2988,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f336,f314]) ).
fof(f336,axiom,
! [X11] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f5872,plain,
spl0_651,
inference(avatar_split_clause,[],[f2969,f5869]) ).
fof(f5869,plain,
( spl0_651
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2969,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f227,f224]) ).
fof(f227,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f5867,plain,
spl0_650,
inference(avatar_split_clause,[],[f2968,f5865]) ).
fof(f5865,plain,
( spl0_650
<=> ! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2968,plain,
! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat),
inference(forward_demodulation,[],[f2753,f2749]) ).
fof(f2753,plain,
! [X9] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X9,tc_nat),
inference(definition_unfolding,[],[f1601,f1394]) ).
fof(f1601,axiom,
! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5863,plain,
spl0_649,
inference(avatar_split_clause,[],[f2966,f5860]) ).
fof(f2966,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2751,f2749]) ).
fof(f2751,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f194,f1394]) ).
fof(f194,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5858,plain,
spl0_648,
inference(avatar_split_clause,[],[f2736,f5856]) ).
fof(f5856,plain,
( spl0_648
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2736,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5854,plain,
spl0_647,
inference(avatar_split_clause,[],[f2735,f5852]) ).
fof(f5852,plain,
( spl0_647
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2735,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5850,plain,
spl0_646,
inference(avatar_split_clause,[],[f2734,f5848]) ).
fof(f5848,plain,
( spl0_646
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2734,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5846,plain,
spl0_645,
inference(avatar_split_clause,[],[f2733,f5844]) ).
fof(f5844,plain,
( spl0_645
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f2733,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5842,plain,
spl0_644,
inference(avatar_split_clause,[],[f2732,f5840]) ).
fof(f5840,plain,
( spl0_644
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2732,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5838,plain,
spl0_643,
inference(avatar_split_clause,[],[f2731,f5836]) ).
fof(f5836,plain,
( spl0_643
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2731,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5834,plain,
spl0_642,
inference(avatar_split_clause,[],[f2730,f5832]) ).
fof(f5832,plain,
( spl0_642
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f2730,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5830,plain,
spl0_641,
inference(avatar_split_clause,[],[f2725,f5828]) ).
fof(f5828,plain,
( spl0_641
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2725,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5826,plain,
spl0_640,
inference(avatar_split_clause,[],[f2724,f5824]) ).
fof(f5824,plain,
( spl0_640
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2724,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5822,plain,
spl0_639,
inference(avatar_split_clause,[],[f2723,f5820]) ).
fof(f5820,plain,
( spl0_639
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2723,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5818,plain,
spl0_638,
inference(avatar_split_clause,[],[f2722,f5816]) ).
fof(f5816,plain,
( spl0_638
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2722,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5814,plain,
spl0_637,
inference(avatar_split_clause,[],[f2721,f5812]) ).
fof(f5812,plain,
( spl0_637
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2721,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5810,plain,
spl0_636,
inference(avatar_split_clause,[],[f2720,f5808]) ).
fof(f5808,plain,
( spl0_636
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2720,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5806,plain,
spl0_635,
inference(avatar_split_clause,[],[f2717,f5804]) ).
fof(f5804,plain,
( spl0_635
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f2717,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5802,plain,
spl0_634,
inference(avatar_split_clause,[],[f2716,f5800]) ).
fof(f5800,plain,
( spl0_634
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f2716,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5798,plain,
spl0_633,
inference(avatar_split_clause,[],[f2715,f5796]) ).
fof(f5796,plain,
( spl0_633
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f2715,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5794,plain,
spl0_632,
inference(avatar_split_clause,[],[f2712,f5792]) ).
fof(f5792,plain,
( spl0_632
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2712,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5790,plain,
spl0_631,
inference(avatar_split_clause,[],[f2709,f5788]) ).
fof(f5788,plain,
( spl0_631
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2709,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5786,plain,
spl0_630,
inference(avatar_split_clause,[],[f2708,f5784]) ).
fof(f5784,plain,
( spl0_630
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f2708,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5782,plain,
spl0_629,
inference(avatar_split_clause,[],[f2707,f5780]) ).
fof(f5780,plain,
( spl0_629
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2707,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5778,plain,
spl0_628,
inference(avatar_split_clause,[],[f2706,f5776]) ).
fof(f5776,plain,
( spl0_628
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2706,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5774,plain,
spl0_627,
inference(avatar_split_clause,[],[f2703,f5772]) ).
fof(f5772,plain,
( spl0_627
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2703,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5770,plain,
spl0_626,
inference(avatar_split_clause,[],[f2702,f5768]) ).
fof(f5768,plain,
( spl0_626
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2702,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5766,plain,
spl0_625,
inference(avatar_split_clause,[],[f2697,f5764]) ).
fof(f5764,plain,
( spl0_625
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2697,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5762,plain,
spl0_624,
inference(avatar_split_clause,[],[f2694,f5760]) ).
fof(f5760,plain,
( spl0_624
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2694,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5758,plain,
spl0_623,
inference(avatar_split_clause,[],[f2693,f5756]) ).
fof(f5756,plain,
( spl0_623
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2693,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5754,plain,
spl0_622,
inference(avatar_split_clause,[],[f2692,f5752]) ).
fof(f5752,plain,
( spl0_622
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2692,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5750,plain,
spl0_621,
inference(avatar_split_clause,[],[f2690,f5748]) ).
fof(f5748,plain,
( spl0_621
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2690,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5746,plain,
spl0_620,
inference(avatar_split_clause,[],[f2684,f5744]) ).
fof(f5744,plain,
( spl0_620
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2684,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5742,plain,
spl0_619,
inference(avatar_split_clause,[],[f2676,f5740]) ).
fof(f5740,plain,
( spl0_619
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2676,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5738,plain,
spl0_618,
inference(avatar_split_clause,[],[f2675,f5736]) ).
fof(f5736,plain,
( spl0_618
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2675,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5734,plain,
spl0_617,
inference(avatar_split_clause,[],[f2674,f5732]) ).
fof(f5732,plain,
( spl0_617
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2674,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5730,plain,
spl0_616,
inference(avatar_split_clause,[],[f2673,f5728]) ).
fof(f5728,plain,
( spl0_616
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2673,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5726,plain,
spl0_615,
inference(avatar_split_clause,[],[f2672,f5724]) ).
fof(f5724,plain,
( spl0_615
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2672,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5722,plain,
spl0_614,
inference(avatar_split_clause,[],[f2670,f5720]) ).
fof(f5720,plain,
( spl0_614
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2670,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5718,plain,
spl0_613,
inference(avatar_split_clause,[],[f2669,f5716]) ).
fof(f5716,plain,
( spl0_613
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2669,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5714,plain,
spl0_612,
inference(avatar_split_clause,[],[f2668,f5712]) ).
fof(f5712,plain,
( spl0_612
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2668,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5710,plain,
spl0_611,
inference(avatar_split_clause,[],[f2667,f5708]) ).
fof(f5708,plain,
( spl0_611
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2667,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5706,plain,
spl0_610,
inference(avatar_split_clause,[],[f2666,f5704]) ).
fof(f5704,plain,
( spl0_610
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2666,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5702,plain,
spl0_609,
inference(avatar_split_clause,[],[f2661,f5700]) ).
fof(f5700,plain,
( spl0_609
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2661,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5698,plain,
spl0_608,
inference(avatar_split_clause,[],[f2660,f5696]) ).
fof(f5696,plain,
( spl0_608
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2660,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5694,plain,
spl0_607,
inference(avatar_split_clause,[],[f2659,f5692]) ).
fof(f5692,plain,
( spl0_607
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2659,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5690,plain,
spl0_606,
inference(avatar_split_clause,[],[f2657,f5688]) ).
fof(f5688,plain,
( spl0_606
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2657,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5686,plain,
spl0_605,
inference(avatar_split_clause,[],[f2655,f5684]) ).
fof(f5684,plain,
( spl0_605
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2655,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5682,plain,
spl0_604,
inference(avatar_split_clause,[],[f2650,f5680]) ).
fof(f5680,plain,
( spl0_604
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2650,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5678,plain,
spl0_603,
inference(avatar_split_clause,[],[f2649,f5676]) ).
fof(f5676,plain,
( spl0_603
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2649,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5674,plain,
spl0_602,
inference(avatar_split_clause,[],[f2648,f5672]) ).
fof(f5672,plain,
( spl0_602
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2648,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5670,plain,
spl0_601,
inference(avatar_split_clause,[],[f2647,f5668]) ).
fof(f5668,plain,
( spl0_601
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2647,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5666,plain,
spl0_600,
inference(avatar_split_clause,[],[f2645,f5664]) ).
fof(f5664,plain,
( spl0_600
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2645,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5662,plain,
spl0_599,
inference(avatar_split_clause,[],[f2644,f5660]) ).
fof(f5660,plain,
( spl0_599
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2644,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5658,plain,
spl0_598,
inference(avatar_split_clause,[],[f2639,f5656]) ).
fof(f5656,plain,
( spl0_598
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2639,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5654,plain,
spl0_597,
inference(avatar_split_clause,[],[f2636,f5652]) ).
fof(f5652,plain,
( spl0_597
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2636,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5650,plain,
spl0_596,
inference(avatar_split_clause,[],[f2635,f5648]) ).
fof(f5648,plain,
( spl0_596
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2635,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5646,plain,
spl0_595,
inference(avatar_split_clause,[],[f2634,f5644]) ).
fof(f5644,plain,
( spl0_595
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2634,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5642,plain,
spl0_594,
inference(avatar_split_clause,[],[f2633,f5640]) ).
fof(f5640,plain,
( spl0_594
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2633,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5638,plain,
spl0_593,
inference(avatar_split_clause,[],[f2630,f5636]) ).
fof(f5636,plain,
( spl0_593
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2630,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5634,plain,
spl0_592,
inference(avatar_split_clause,[],[f2629,f5632]) ).
fof(f5632,plain,
( spl0_592
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2629,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5630,plain,
spl0_591,
inference(avatar_split_clause,[],[f2628,f5628]) ).
fof(f5628,plain,
( spl0_591
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2628,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5626,plain,
spl0_590,
inference(avatar_split_clause,[],[f2627,f5624]) ).
fof(f5624,plain,
( spl0_590
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2627,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5622,plain,
spl0_589,
inference(avatar_split_clause,[],[f2626,f5620]) ).
fof(f5620,plain,
( spl0_589
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2626,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5618,plain,
spl0_588,
inference(avatar_split_clause,[],[f2625,f5616]) ).
fof(f5616,plain,
( spl0_588
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2625,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5614,plain,
spl0_587,
inference(avatar_split_clause,[],[f2624,f5612]) ).
fof(f5612,plain,
( spl0_587
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2624,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5610,plain,
spl0_586,
inference(avatar_split_clause,[],[f2623,f5608]) ).
fof(f5608,plain,
( spl0_586
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2623,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5606,plain,
spl0_585,
inference(avatar_split_clause,[],[f2621,f5604]) ).
fof(f5604,plain,
( spl0_585
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2621,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5602,plain,
spl0_584,
inference(avatar_split_clause,[],[f2620,f5600]) ).
fof(f5600,plain,
( spl0_584
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2620,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5598,plain,
spl0_583,
inference(avatar_split_clause,[],[f2619,f5596]) ).
fof(f5596,plain,
( spl0_583
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2619,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5594,plain,
spl0_582,
inference(avatar_split_clause,[],[f2618,f5592]) ).
fof(f5592,plain,
( spl0_582
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2618,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5590,plain,
spl0_581,
inference(avatar_split_clause,[],[f2617,f5588]) ).
fof(f5588,plain,
( spl0_581
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2617,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5586,plain,
spl0_580,
inference(avatar_split_clause,[],[f2612,f5584]) ).
fof(f5584,plain,
( spl0_580
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2612,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5582,plain,
spl0_579,
inference(avatar_split_clause,[],[f2611,f5580]) ).
fof(f5580,plain,
( spl0_579
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2611,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5578,plain,
spl0_578,
inference(avatar_split_clause,[],[f2610,f5576]) ).
fof(f5576,plain,
( spl0_578
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2610,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5574,plain,
spl0_577,
inference(avatar_split_clause,[],[f2607,f5572]) ).
fof(f5572,plain,
( spl0_577
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2607,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5570,plain,
spl0_576,
inference(avatar_split_clause,[],[f2604,f5568]) ).
fof(f5568,plain,
( spl0_576
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2604,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5566,plain,
spl0_575,
inference(avatar_split_clause,[],[f2603,f5564]) ).
fof(f5564,plain,
( spl0_575
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2603,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5562,plain,
spl0_574,
inference(avatar_split_clause,[],[f2601,f5560]) ).
fof(f5560,plain,
( spl0_574
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2601,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5558,plain,
spl0_573,
inference(avatar_split_clause,[],[f2600,f5556]) ).
fof(f5556,plain,
( spl0_573
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2600,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5554,plain,
spl0_572,
inference(avatar_split_clause,[],[f2599,f5552]) ).
fof(f5552,plain,
( spl0_572
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2599,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5550,plain,
spl0_571,
inference(avatar_split_clause,[],[f2598,f5548]) ).
fof(f5548,plain,
( spl0_571
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2598,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5546,plain,
spl0_570,
inference(avatar_split_clause,[],[f2595,f5544]) ).
fof(f5544,plain,
( spl0_570
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2595,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5542,plain,
spl0_569,
inference(avatar_split_clause,[],[f2594,f5540]) ).
fof(f5540,plain,
( spl0_569
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2594,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5538,plain,
spl0_568,
inference(avatar_split_clause,[],[f2566,f5536]) ).
fof(f5536,plain,
( spl0_568
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2566,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5534,plain,
spl0_567,
inference(avatar_split_clause,[],[f2564,f5532]) ).
fof(f5532,plain,
( spl0_567
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2564,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5530,plain,
spl0_566,
inference(avatar_split_clause,[],[f2561,f5528]) ).
fof(f5528,plain,
( spl0_566
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2561,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5526,plain,
spl0_565,
inference(avatar_split_clause,[],[f2560,f5524]) ).
fof(f5524,plain,
( spl0_565
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2560,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5522,plain,
spl0_564,
inference(avatar_split_clause,[],[f2559,f5520]) ).
fof(f5520,plain,
( spl0_564
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2559,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5518,plain,
spl0_563,
inference(avatar_split_clause,[],[f2558,f5516]) ).
fof(f5516,plain,
( spl0_563
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2558,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5514,plain,
spl0_562,
inference(avatar_split_clause,[],[f2557,f5512]) ).
fof(f5512,plain,
( spl0_562
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2557,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5510,plain,
spl0_561,
inference(avatar_split_clause,[],[f2556,f5508]) ).
fof(f5508,plain,
( spl0_561
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2556,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5506,plain,
spl0_560,
inference(avatar_split_clause,[],[f2554,f5504]) ).
fof(f5504,plain,
( spl0_560
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2554,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5502,plain,
spl0_559,
inference(avatar_split_clause,[],[f2553,f5500]) ).
fof(f5500,plain,
( spl0_559
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2553,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5498,plain,
spl0_558,
inference(avatar_split_clause,[],[f2551,f5496]) ).
fof(f5496,plain,
( spl0_558
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2551,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5494,plain,
spl0_557,
inference(avatar_split_clause,[],[f2548,f5492]) ).
fof(f5492,plain,
( spl0_557
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2548,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5490,plain,
spl0_556,
inference(avatar_split_clause,[],[f2547,f5488]) ).
fof(f5488,plain,
( spl0_556
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2547,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5486,plain,
spl0_555,
inference(avatar_split_clause,[],[f2545,f5484]) ).
fof(f5484,plain,
( spl0_555
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2545,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5482,plain,
spl0_554,
inference(avatar_split_clause,[],[f2544,f5480]) ).
fof(f5480,plain,
( spl0_554
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2544,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5478,plain,
spl0_553,
inference(avatar_split_clause,[],[f2543,f5476]) ).
fof(f5476,plain,
( spl0_553
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2543,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5474,plain,
spl0_552,
inference(avatar_split_clause,[],[f2542,f5472]) ).
fof(f5472,plain,
( spl0_552
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2542,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5470,plain,
spl0_551,
inference(avatar_split_clause,[],[f2541,f5468]) ).
fof(f5468,plain,
( spl0_551
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2541,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5466,plain,
spl0_550,
inference(avatar_split_clause,[],[f2540,f5464]) ).
fof(f5464,plain,
( spl0_550
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2540,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5462,plain,
spl0_549,
inference(avatar_split_clause,[],[f2539,f5460]) ).
fof(f5460,plain,
( spl0_549
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2539,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5458,plain,
spl0_548,
inference(avatar_split_clause,[],[f2538,f5456]) ).
fof(f5456,plain,
( spl0_548
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2538,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5454,plain,
spl0_547,
inference(avatar_split_clause,[],[f2534,f5452]) ).
fof(f5452,plain,
( spl0_547
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2534,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5450,plain,
spl0_546,
inference(avatar_split_clause,[],[f2533,f5448]) ).
fof(f5448,plain,
( spl0_546
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2533,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5446,plain,
spl0_545,
inference(avatar_split_clause,[],[f2532,f5444]) ).
fof(f5444,plain,
( spl0_545
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2532,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5442,plain,
spl0_544,
inference(avatar_split_clause,[],[f2531,f5440]) ).
fof(f5440,plain,
( spl0_544
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2531,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5438,plain,
spl0_543,
inference(avatar_split_clause,[],[f2526,f5436]) ).
fof(f5436,plain,
( spl0_543
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2526,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5434,plain,
spl0_542,
inference(avatar_split_clause,[],[f2524,f5432]) ).
fof(f5432,plain,
( spl0_542
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2524,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5430,plain,
spl0_541,
inference(avatar_split_clause,[],[f2523,f5428]) ).
fof(f5428,plain,
( spl0_541
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2523,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5426,plain,
spl0_540,
inference(avatar_split_clause,[],[f2522,f5424]) ).
fof(f5424,plain,
( spl0_540
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2522,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5422,plain,
spl0_539,
inference(avatar_split_clause,[],[f2521,f5420]) ).
fof(f5420,plain,
( spl0_539
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2521,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5418,plain,
spl0_538,
inference(avatar_split_clause,[],[f2519,f5416]) ).
fof(f5416,plain,
( spl0_538
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2519,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5414,plain,
spl0_537,
inference(avatar_split_clause,[],[f2518,f5412]) ).
fof(f5412,plain,
( spl0_537
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2518,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5410,plain,
spl0_536,
inference(avatar_split_clause,[],[f2517,f5408]) ).
fof(f5408,plain,
( spl0_536
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2517,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5406,plain,
spl0_535,
inference(avatar_split_clause,[],[f2516,f5404]) ).
fof(f5404,plain,
( spl0_535
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2516,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5402,plain,
spl0_534,
inference(avatar_split_clause,[],[f2515,f5400]) ).
fof(f5400,plain,
( spl0_534
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2515,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5398,plain,
spl0_533,
inference(avatar_split_clause,[],[f2514,f5396]) ).
fof(f5396,plain,
( spl0_533
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2514,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5394,plain,
spl0_532,
inference(avatar_split_clause,[],[f2513,f5392]) ).
fof(f5392,plain,
( spl0_532
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2513,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5390,plain,
spl0_531,
inference(avatar_split_clause,[],[f2512,f5388]) ).
fof(f5388,plain,
( spl0_531
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2512,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5386,plain,
spl0_530,
inference(avatar_split_clause,[],[f2511,f5384]) ).
fof(f5384,plain,
( spl0_530
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2511,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5382,plain,
spl0_529,
inference(avatar_split_clause,[],[f2510,f5380]) ).
fof(f5380,plain,
( spl0_529
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2510,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5378,plain,
spl0_528,
inference(avatar_split_clause,[],[f2509,f5376]) ).
fof(f5376,plain,
( spl0_528
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2509,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5374,plain,
spl0_527,
inference(avatar_split_clause,[],[f2508,f5372]) ).
fof(f5372,plain,
( spl0_527
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2508,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5370,plain,
spl0_526,
inference(avatar_split_clause,[],[f2507,f5368]) ).
fof(f5368,plain,
( spl0_526
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2507,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5366,plain,
spl0_525,
inference(avatar_split_clause,[],[f2506,f5364]) ).
fof(f5364,plain,
( spl0_525
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2506,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5362,plain,
spl0_524,
inference(avatar_split_clause,[],[f2505,f5360]) ).
fof(f5360,plain,
( spl0_524
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2505,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5358,plain,
spl0_523,
inference(avatar_split_clause,[],[f2504,f5356]) ).
fof(f5356,plain,
( spl0_523
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2504,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5354,plain,
spl0_522,
inference(avatar_split_clause,[],[f2503,f5352]) ).
fof(f5352,plain,
( spl0_522
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2503,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5350,plain,
spl0_521,
inference(avatar_split_clause,[],[f2502,f5348]) ).
fof(f5348,plain,
( spl0_521
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2502,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5346,plain,
spl0_520,
inference(avatar_split_clause,[],[f2501,f5344]) ).
fof(f5344,plain,
( spl0_520
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2501,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5342,plain,
spl0_519,
inference(avatar_split_clause,[],[f2500,f5340]) ).
fof(f5340,plain,
( spl0_519
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2500,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5338,plain,
spl0_518,
inference(avatar_split_clause,[],[f2499,f5336]) ).
fof(f5336,plain,
( spl0_518
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2499,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5334,plain,
spl0_517,
inference(avatar_split_clause,[],[f2498,f5332]) ).
fof(f5332,plain,
( spl0_517
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2498,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5330,plain,
spl0_516,
inference(avatar_split_clause,[],[f2497,f5328]) ).
fof(f5328,plain,
( spl0_516
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2497,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5326,plain,
spl0_515,
inference(avatar_split_clause,[],[f2496,f5324]) ).
fof(f5324,plain,
( spl0_515
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2496,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5322,plain,
spl0_514,
inference(avatar_split_clause,[],[f2495,f5320]) ).
fof(f5320,plain,
( spl0_514
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2495,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5318,plain,
spl0_513,
inference(avatar_split_clause,[],[f2494,f5316]) ).
fof(f5316,plain,
( spl0_513
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2494,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5314,plain,
spl0_512,
inference(avatar_split_clause,[],[f2493,f5312]) ).
fof(f5312,plain,
( spl0_512
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2493,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5310,plain,
spl0_511,
inference(avatar_split_clause,[],[f2492,f5308]) ).
fof(f5308,plain,
( spl0_511
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2492,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5306,plain,
spl0_510,
inference(avatar_split_clause,[],[f2491,f5304]) ).
fof(f5304,plain,
( spl0_510
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2491,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5302,plain,
spl0_509,
inference(avatar_split_clause,[],[f2490,f5300]) ).
fof(f5300,plain,
( spl0_509
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2490,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5298,plain,
spl0_508,
inference(avatar_split_clause,[],[f2489,f5296]) ).
fof(f5296,plain,
( spl0_508
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2489,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5294,plain,
spl0_507,
inference(avatar_split_clause,[],[f2488,f5292]) ).
fof(f5292,plain,
( spl0_507
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2488,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5290,plain,
spl0_506,
inference(avatar_split_clause,[],[f2487,f5288]) ).
fof(f5288,plain,
( spl0_506
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2487,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5286,plain,
spl0_505,
inference(avatar_split_clause,[],[f2486,f5284]) ).
fof(f5284,plain,
( spl0_505
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2486,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5282,plain,
spl0_504,
inference(avatar_split_clause,[],[f2485,f5280]) ).
fof(f5280,plain,
( spl0_504
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2485,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5278,plain,
spl0_503,
inference(avatar_split_clause,[],[f2482,f5276]) ).
fof(f5276,plain,
( spl0_503
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2482,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5274,plain,
spl0_502,
inference(avatar_split_clause,[],[f2480,f5272]) ).
fof(f5272,plain,
( spl0_502
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2480,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5270,plain,
spl0_501,
inference(avatar_split_clause,[],[f2479,f5268]) ).
fof(f5268,plain,
( spl0_501
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2479,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5266,plain,
spl0_500,
inference(avatar_split_clause,[],[f2477,f5264]) ).
fof(f5264,plain,
( spl0_500
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2477,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5262,plain,
spl0_499,
inference(avatar_split_clause,[],[f2474,f5260]) ).
fof(f5260,plain,
( spl0_499
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2474,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5258,plain,
spl0_498,
inference(avatar_split_clause,[],[f2473,f5256]) ).
fof(f5256,plain,
( spl0_498
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2473,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5254,plain,
spl0_497,
inference(avatar_split_clause,[],[f2472,f5252]) ).
fof(f5252,plain,
( spl0_497
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2472,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5250,plain,
spl0_496,
inference(avatar_split_clause,[],[f2470,f5248]) ).
fof(f5248,plain,
( spl0_496
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2470,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5246,plain,
spl0_495,
inference(avatar_split_clause,[],[f2469,f5244]) ).
fof(f5244,plain,
( spl0_495
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2469,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5242,plain,
spl0_494,
inference(avatar_split_clause,[],[f2468,f5240]) ).
fof(f5240,plain,
( spl0_494
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2468,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5238,plain,
spl0_493,
inference(avatar_split_clause,[],[f2465,f5236]) ).
fof(f5236,plain,
( spl0_493
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2465,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5234,plain,
spl0_492,
inference(avatar_split_clause,[],[f2464,f5232]) ).
fof(f5232,plain,
( spl0_492
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2464,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5230,plain,
spl0_491,
inference(avatar_split_clause,[],[f2463,f5228]) ).
fof(f5228,plain,
( spl0_491
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2463,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5226,plain,
spl0_490,
inference(avatar_split_clause,[],[f2462,f5224]) ).
fof(f5224,plain,
( spl0_490
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2462,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5222,plain,
spl0_489,
inference(avatar_split_clause,[],[f2460,f5220]) ).
fof(f5220,plain,
( spl0_489
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2460,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5218,plain,
spl0_488,
inference(avatar_split_clause,[],[f2459,f5216]) ).
fof(f5216,plain,
( spl0_488
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2459,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5214,plain,
spl0_487,
inference(avatar_split_clause,[],[f2458,f5212]) ).
fof(f5212,plain,
( spl0_487
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2458,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5210,plain,
spl0_486,
inference(avatar_split_clause,[],[f2457,f5208]) ).
fof(f5208,plain,
( spl0_486
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2457,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5206,plain,
spl0_485,
inference(avatar_split_clause,[],[f2456,f5204]) ).
fof(f5204,plain,
( spl0_485
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Olordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2456,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Olordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5202,plain,
spl0_484,
inference(avatar_split_clause,[],[f2455,f5200]) ).
fof(f5200,plain,
( spl0_484
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2455,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5198,plain,
spl0_483,
inference(avatar_split_clause,[],[f2454,f5196]) ).
fof(f5196,plain,
( spl0_483
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2454,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5194,plain,
spl0_482,
inference(avatar_split_clause,[],[f2453,f5192]) ).
fof(f5192,plain,
( spl0_482
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2453,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5190,plain,
spl0_481,
inference(avatar_split_clause,[],[f2452,f5188]) ).
fof(f5188,plain,
( spl0_481
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2452,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5186,plain,
spl0_480,
inference(avatar_split_clause,[],[f2451,f5184]) ).
fof(f5184,plain,
( spl0_480
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2451,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5182,plain,
spl0_479,
inference(avatar_split_clause,[],[f2450,f5180]) ).
fof(f5180,plain,
( spl0_479
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2450,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5178,plain,
spl0_478,
inference(avatar_split_clause,[],[f2449,f5176]) ).
fof(f5176,plain,
( spl0_478
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2449,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5174,plain,
spl0_477,
inference(avatar_split_clause,[],[f2448,f5172]) ).
fof(f5172,plain,
( spl0_477
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2448,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5170,plain,
spl0_476,
inference(avatar_split_clause,[],[f2447,f5168]) ).
fof(f5168,plain,
( spl0_476
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2447,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5166,plain,
spl0_475,
inference(avatar_split_clause,[],[f2446,f5164]) ).
fof(f5164,plain,
( spl0_475
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2446,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5162,plain,
spl0_474,
inference(avatar_split_clause,[],[f2445,f5160]) ).
fof(f5160,plain,
( spl0_474
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2445,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5158,plain,
spl0_473,
inference(avatar_split_clause,[],[f2444,f5156]) ).
fof(f5156,plain,
( spl0_473
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2444,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5154,plain,
spl0_472,
inference(avatar_split_clause,[],[f2442,f5152]) ).
fof(f5152,plain,
( spl0_472
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2442,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5150,plain,
spl0_471,
inference(avatar_split_clause,[],[f2441,f5148]) ).
fof(f5148,plain,
( spl0_471
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2441,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5146,plain,
spl0_470,
inference(avatar_split_clause,[],[f2440,f5144]) ).
fof(f5144,plain,
( spl0_470
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2440,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5142,plain,
spl0_469,
inference(avatar_split_clause,[],[f2439,f5140]) ).
fof(f5140,plain,
( spl0_469
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2439,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5138,plain,
spl0_468,
inference(avatar_split_clause,[],[f2438,f5136]) ).
fof(f5136,plain,
( spl0_468
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2438,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5134,plain,
spl0_467,
inference(avatar_split_clause,[],[f2433,f5132]) ).
fof(f5132,plain,
( spl0_467
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2433,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5130,plain,
spl0_466,
inference(avatar_split_clause,[],[f2432,f5128]) ).
fof(f5128,plain,
( spl0_466
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2432,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5126,plain,
spl0_465,
inference(avatar_split_clause,[],[f2431,f5124]) ).
fof(f5124,plain,
( spl0_465
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2431,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5122,plain,
spl0_464,
inference(avatar_split_clause,[],[f2430,f5120]) ).
fof(f5120,plain,
( spl0_464
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2430,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5118,plain,
spl0_463,
inference(avatar_split_clause,[],[f2429,f5116]) ).
fof(f5116,plain,
( spl0_463
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2429,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5114,plain,
spl0_462,
inference(avatar_split_clause,[],[f2428,f5112]) ).
fof(f5112,plain,
( spl0_462
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2428,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5110,plain,
spl0_461,
inference(avatar_split_clause,[],[f2427,f5108]) ).
fof(f5108,plain,
( spl0_461
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2427,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5106,plain,
spl0_460,
inference(avatar_split_clause,[],[f2426,f5104]) ).
fof(f5104,plain,
( spl0_460
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oidom(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2426,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oidom(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5102,plain,
spl0_459,
inference(avatar_split_clause,[],[f2424,f5100]) ).
fof(f5100,plain,
( spl0_459
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semidom(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2424,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semidom(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5098,plain,
spl0_458,
inference(avatar_split_clause,[],[f2423,f5096]) ).
fof(f5096,plain,
( spl0_458
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2423,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5094,plain,
spl0_457,
inference(avatar_split_clause,[],[f2422,f5092]) ).
fof(f5092,plain,
( spl0_457
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2422,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5090,plain,
spl0_456,
inference(avatar_split_clause,[],[f2421,f5088]) ).
fof(f5088,plain,
( spl0_456
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2421,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5086,plain,
spl0_455,
inference(avatar_split_clause,[],[f2420,f5084]) ).
fof(f5084,plain,
( spl0_455
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2420,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5082,plain,
spl0_454,
inference(avatar_split_clause,[],[f2419,f5080]) ).
fof(f5080,plain,
( spl0_454
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2419,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5078,plain,
spl0_453,
inference(avatar_split_clause,[],[f2417,f5076]) ).
fof(f5076,plain,
( spl0_453
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2417,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5074,plain,
spl0_452,
inference(avatar_split_clause,[],[f2416,f5072]) ).
fof(f5072,plain,
( spl0_452
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Olordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2416,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Olordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5070,plain,
spl0_451,
inference(avatar_split_clause,[],[f2415,f5068]) ).
fof(f5068,plain,
( spl0_451
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__ring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2415,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__ring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5066,plain,
spl0_450,
inference(avatar_split_clause,[],[f2414,f5064]) ).
fof(f5064,plain,
( spl0_450
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2414,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5062,plain,
spl0_449,
inference(avatar_split_clause,[],[f2413,f5060]) ).
fof(f5060,plain,
( spl0_449
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2413,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5058,plain,
spl0_448,
inference(avatar_split_clause,[],[f2412,f5056]) ).
fof(f5056,plain,
( spl0_448
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2412,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5054,plain,
spl0_447,
inference(avatar_split_clause,[],[f2411,f5052]) ).
fof(f5052,plain,
( spl0_447
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2411,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5050,plain,
spl0_446,
inference(avatar_split_clause,[],[f2410,f5048]) ).
fof(f5048,plain,
( spl0_446
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2410,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5046,plain,
spl0_445,
inference(avatar_split_clause,[],[f2409,f5044]) ).
fof(f5044,plain,
( spl0_445
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2409,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5042,plain,
spl0_444,
inference(avatar_split_clause,[],[f2408,f5040]) ).
fof(f5040,plain,
( spl0_444
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2408,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5038,plain,
spl0_443,
inference(avatar_split_clause,[],[f2407,f5036]) ).
fof(f5036,plain,
( spl0_443
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2407,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5034,plain,
spl0_442,
inference(avatar_split_clause,[],[f2406,f5032]) ).
fof(f5032,plain,
( spl0_442
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2406,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5030,plain,
spl0_441,
inference(avatar_split_clause,[],[f2405,f5028]) ).
fof(f5028,plain,
( spl0_441
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2405,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5026,plain,
spl0_440,
inference(avatar_split_clause,[],[f2404,f5024]) ).
fof(f5024,plain,
( spl0_440
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2404,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5022,plain,
spl0_439,
inference(avatar_split_clause,[],[f2403,f5020]) ).
fof(f5020,plain,
( spl0_439
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2403,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5018,plain,
spl0_438,
inference(avatar_split_clause,[],[f2402,f5016]) ).
fof(f5016,plain,
( spl0_438
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2402,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5014,plain,
spl0_437,
inference(avatar_split_clause,[],[f2401,f5012]) ).
fof(f5012,plain,
( spl0_437
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2401,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5010,plain,
spl0_436,
inference(avatar_split_clause,[],[f2400,f5008]) ).
fof(f5008,plain,
( spl0_436
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2400,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5006,plain,
spl0_435,
inference(avatar_split_clause,[],[f2399,f5004]) ).
fof(f5004,plain,
( spl0_435
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2399,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5002,plain,
spl0_434,
inference(avatar_split_clause,[],[f2398,f5000]) ).
fof(f5000,plain,
( spl0_434
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2398,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f4998,plain,
spl0_433,
inference(avatar_split_clause,[],[f2397,f4996]) ).
fof(f4996,plain,
( spl0_433
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2397,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f4994,plain,
spl0_432,
inference(avatar_split_clause,[],[f2396,f4992]) ).
fof(f4992,plain,
( spl0_432
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2396,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f4990,plain,
spl0_431,
inference(avatar_split_clause,[],[f2393,f4988]) ).
fof(f4988,plain,
( spl0_431
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2393,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f4986,plain,
spl0_430,
inference(avatar_split_clause,[],[f2391,f4984]) ).
fof(f4984,plain,
( spl0_430
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2391,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f4982,plain,
spl0_429,
inference(avatar_split_clause,[],[f2389,f4980]) ).
fof(f4980,plain,
( spl0_429
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2389,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f4978,plain,
spl0_428,
inference(avatar_split_clause,[],[f2386,f4976]) ).
fof(f4976,plain,
( spl0_428
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2386,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f4974,plain,
spl0_427,
inference(avatar_split_clause,[],[f2385,f4972]) ).
fof(f4972,plain,
( spl0_427
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2385,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f4970,plain,
spl0_426,
inference(avatar_split_clause,[],[f2384,f4968]) ).
fof(f4968,plain,
( spl0_426
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2384,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f4966,plain,
spl0_425,
inference(avatar_split_clause,[],[f2383,f4964]) ).
fof(f4964,plain,
( spl0_425
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2383,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f4962,plain,
spl0_424,
inference(avatar_split_clause,[],[f2381,f4960]) ).
fof(f4960,plain,
( spl0_424
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2381,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f4958,plain,
spl0_423,
inference(avatar_split_clause,[],[f2380,f4956]) ).
fof(f4956,plain,
( spl0_423
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2380,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f4954,plain,
spl0_422,
inference(avatar_split_clause,[],[f2379,f4952]) ).
fof(f4952,plain,
( spl0_422
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2379,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4950,plain,
spl0_421,
inference(avatar_split_clause,[],[f2378,f4948]) ).
fof(f4948,plain,
( spl0_421
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2378,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4946,plain,
spl0_420,
inference(avatar_split_clause,[],[f2377,f4944]) ).
fof(f4944,plain,
( spl0_420
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2377,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4942,plain,
spl0_419,
inference(avatar_split_clause,[],[f2376,f4940]) ).
fof(f4940,plain,
( spl0_419
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2376,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4938,plain,
spl0_418,
inference(avatar_split_clause,[],[f2375,f4936]) ).
fof(f4936,plain,
( spl0_418
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2375,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4934,plain,
spl0_417,
inference(avatar_split_clause,[],[f2374,f4932]) ).
fof(f4932,plain,
( spl0_417
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2374,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4930,plain,
spl0_416,
inference(avatar_split_clause,[],[f2373,f4928]) ).
fof(f4928,plain,
( spl0_416
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2373,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4926,plain,
spl0_415,
inference(avatar_split_clause,[],[f2309,f4924]) ).
fof(f4924,plain,
( spl0_415
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2309,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4922,plain,
spl0_414,
inference(avatar_split_clause,[],[f2306,f4920]) ).
fof(f4920,plain,
( spl0_414
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2306,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4918,plain,
spl0_413,
inference(avatar_split_clause,[],[f2305,f4916]) ).
fof(f4916,plain,
( spl0_413
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2305,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4914,plain,
spl0_412,
inference(avatar_split_clause,[],[f2304,f4912]) ).
fof(f4912,plain,
( spl0_412
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2304,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4910,plain,
spl0_411,
inference(avatar_split_clause,[],[f2303,f4908]) ).
fof(f4908,plain,
( spl0_411
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2303,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4906,plain,
spl0_410,
inference(avatar_split_clause,[],[f2302,f4904]) ).
fof(f4904,plain,
( spl0_410
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2302,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4902,plain,
spl0_409,
inference(avatar_split_clause,[],[f2301,f4900]) ).
fof(f4900,plain,
( spl0_409
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2301,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4898,plain,
spl0_408,
inference(avatar_split_clause,[],[f2300,f4896]) ).
fof(f4896,plain,
( spl0_408
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2300,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4894,plain,
spl0_407,
inference(avatar_split_clause,[],[f2299,f4892]) ).
fof(f4892,plain,
( spl0_407
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2299,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4890,plain,
spl0_406,
inference(avatar_split_clause,[],[f2298,f4888]) ).
fof(f4888,plain,
( spl0_406
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2298,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4886,plain,
spl0_405,
inference(avatar_split_clause,[],[f2297,f4884]) ).
fof(f4884,plain,
( spl0_405
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2297,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4882,plain,
spl0_404,
inference(avatar_split_clause,[],[f2296,f4880]) ).
fof(f4880,plain,
( spl0_404
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2296,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4878,plain,
spl0_403,
inference(avatar_split_clause,[],[f2295,f4876]) ).
fof(f4876,plain,
( spl0_403
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2295,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4874,plain,
spl0_402,
inference(avatar_split_clause,[],[f2293,f4872]) ).
fof(f4872,plain,
( spl0_402
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2293,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4870,plain,
spl0_401,
inference(avatar_split_clause,[],[f2292,f4868]) ).
fof(f4868,plain,
( spl0_401
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2292,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4866,plain,
spl0_400,
inference(avatar_split_clause,[],[f2291,f4864]) ).
fof(f4864,plain,
( spl0_400
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2291,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4862,plain,
spl0_399,
inference(avatar_split_clause,[],[f2290,f4860]) ).
fof(f4860,plain,
( spl0_399
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2290,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4858,plain,
spl0_398,
inference(avatar_split_clause,[],[f2289,f4856]) ).
fof(f4856,plain,
( spl0_398
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2289,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4854,plain,
spl0_397,
inference(avatar_split_clause,[],[f2288,f4852]) ).
fof(f4852,plain,
( spl0_397
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2288,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4850,plain,
spl0_396,
inference(avatar_split_clause,[],[f2287,f4848]) ).
fof(f4848,plain,
( spl0_396
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2287,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4846,plain,
spl0_395,
inference(avatar_split_clause,[],[f2286,f4844]) ).
fof(f4844,plain,
( spl0_395
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2286,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4842,plain,
spl0_394,
inference(avatar_split_clause,[],[f2283,f4840]) ).
fof(f4840,plain,
( spl0_394
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2283,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4838,plain,
spl0_393,
inference(avatar_split_clause,[],[f2282,f4836]) ).
fof(f4836,plain,
( spl0_393
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2282,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4834,plain,
spl0_392,
inference(avatar_split_clause,[],[f2281,f4832]) ).
fof(f4832,plain,
( spl0_392
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2281,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4830,plain,
spl0_391,
inference(avatar_split_clause,[],[f2280,f4828]) ).
fof(f4828,plain,
( spl0_391
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2280,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4826,plain,
spl0_390,
inference(avatar_split_clause,[],[f2279,f4824]) ).
fof(f4824,plain,
( spl0_390
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2279,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4822,plain,
spl0_389,
inference(avatar_split_clause,[],[f2278,f4820]) ).
fof(f4820,plain,
( spl0_389
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2278,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4818,plain,
spl0_388,
inference(avatar_split_clause,[],[f2277,f4816]) ).
fof(f4816,plain,
( spl0_388
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2277,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4814,plain,
spl0_387,
inference(avatar_split_clause,[],[f2275,f4812]) ).
fof(f4812,plain,
( spl0_387
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2275,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4810,plain,
spl0_386,
inference(avatar_split_clause,[],[f2274,f4808]) ).
fof(f4808,plain,
( spl0_386
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2274,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4806,plain,
spl0_385,
inference(avatar_split_clause,[],[f2273,f4804]) ).
fof(f4804,plain,
( spl0_385
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2273,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4802,plain,
spl0_384,
inference(avatar_split_clause,[],[f2272,f4800]) ).
fof(f4800,plain,
( spl0_384
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2272,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4798,plain,
spl0_383,
inference(avatar_split_clause,[],[f2271,f4796]) ).
fof(f4796,plain,
( spl0_383
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2271,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4794,plain,
spl0_382,
inference(avatar_split_clause,[],[f2270,f4792]) ).
fof(f4792,plain,
( spl0_382
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2270,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4790,plain,
spl0_381,
inference(avatar_split_clause,[],[f2269,f4788]) ).
fof(f4788,plain,
( spl0_381
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2269,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4786,plain,
spl0_380,
inference(avatar_split_clause,[],[f2268,f4784]) ).
fof(f4784,plain,
( spl0_380
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2268,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4782,plain,
spl0_379,
inference(avatar_split_clause,[],[f2265,f4780]) ).
fof(f4780,plain,
( spl0_379
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2265,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4778,plain,
spl0_378,
inference(avatar_split_clause,[],[f2263,f4776]) ).
fof(f4776,plain,
( spl0_378
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2263,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4774,plain,
spl0_377,
inference(avatar_split_clause,[],[f2262,f4772]) ).
fof(f4772,plain,
( spl0_377
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2262,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4770,plain,
spl0_376,
inference(avatar_split_clause,[],[f2260,f4768]) ).
fof(f4768,plain,
( spl0_376
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2260,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4766,plain,
spl0_375,
inference(avatar_split_clause,[],[f2257,f4764]) ).
fof(f4764,plain,
( spl0_375
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2257,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4762,plain,
spl0_374,
inference(avatar_split_clause,[],[f2256,f4760]) ).
fof(f4760,plain,
( spl0_374
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2256,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4758,plain,
spl0_373,
inference(avatar_split_clause,[],[f2255,f4756]) ).
fof(f4756,plain,
( spl0_373
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2255,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4754,plain,
spl0_372,
inference(avatar_split_clause,[],[f2254,f4752]) ).
fof(f4752,plain,
( spl0_372
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2254,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4750,plain,
spl0_371,
inference(avatar_split_clause,[],[f2253,f4748]) ).
fof(f4748,plain,
( spl0_371
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2253,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4746,plain,
spl0_370,
inference(avatar_split_clause,[],[f2252,f4744]) ).
fof(f4744,plain,
( spl0_370
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2252,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4742,plain,
spl0_369,
inference(avatar_split_clause,[],[f2251,f4740]) ).
fof(f4740,plain,
( spl0_369
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2251,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4738,plain,
spl0_368,
inference(avatar_split_clause,[],[f2250,f4736]) ).
fof(f4736,plain,
( spl0_368
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2250,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4734,plain,
spl0_367,
inference(avatar_split_clause,[],[f2249,f4732]) ).
fof(f4732,plain,
( spl0_367
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2249,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4730,plain,
spl0_366,
inference(avatar_split_clause,[],[f2248,f4728]) ).
fof(f4728,plain,
( spl0_366
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2248,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4726,plain,
spl0_365,
inference(avatar_split_clause,[],[f2247,f4724]) ).
fof(f4724,plain,
( spl0_365
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2247,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4722,plain,
spl0_364,
inference(avatar_split_clause,[],[f2245,f4720]) ).
fof(f4720,plain,
( spl0_364
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2245,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4718,plain,
spl0_363,
inference(avatar_split_clause,[],[f2243,f4716]) ).
fof(f4716,plain,
( spl0_363
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2243,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4714,plain,
spl0_362,
inference(avatar_split_clause,[],[f2240,f4712]) ).
fof(f4712,plain,
( spl0_362
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2240,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4710,plain,
spl0_361,
inference(avatar_split_clause,[],[f2238,f4708]) ).
fof(f4708,plain,
( spl0_361
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2238,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4706,plain,
spl0_360,
inference(avatar_split_clause,[],[f2236,f4704]) ).
fof(f4704,plain,
( spl0_360
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2236,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4702,plain,
spl0_359,
inference(avatar_split_clause,[],[f2233,f4700]) ).
fof(f4700,plain,
( spl0_359
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2233,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4698,plain,
spl0_358,
inference(avatar_split_clause,[],[f2232,f4696]) ).
fof(f4696,plain,
( spl0_358
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2232,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4694,plain,
spl0_357,
inference(avatar_split_clause,[],[f2231,f4692]) ).
fof(f4692,plain,
( spl0_357
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2231,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4690,plain,
spl0_356,
inference(avatar_split_clause,[],[f2230,f4688]) ).
fof(f4688,plain,
( spl0_356
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2230,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4686,plain,
spl0_355,
inference(avatar_split_clause,[],[f2228,f4684]) ).
fof(f4684,plain,
( spl0_355
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2228,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4682,plain,
spl0_354,
inference(avatar_split_clause,[],[f2227,f4680]) ).
fof(f4680,plain,
( spl0_354
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2227,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4678,plain,
spl0_353,
inference(avatar_split_clause,[],[f2226,f4676]) ).
fof(f4676,plain,
( spl0_353
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2226,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4674,plain,
spl0_352,
inference(avatar_split_clause,[],[f2225,f4672]) ).
fof(f4672,plain,
( spl0_352
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2225,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4670,plain,
spl0_351,
inference(avatar_split_clause,[],[f2224,f4668]) ).
fof(f4668,plain,
( spl0_351
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2224,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4666,plain,
spl0_350,
inference(avatar_split_clause,[],[f2223,f4664]) ).
fof(f4664,plain,
( spl0_350
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2223,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4662,plain,
spl0_349,
inference(avatar_split_clause,[],[f2222,f4660]) ).
fof(f4660,plain,
( spl0_349
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2222,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4658,plain,
spl0_348,
inference(avatar_split_clause,[],[f2221,f4656]) ).
fof(f4656,plain,
( spl0_348
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2221,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4654,plain,
spl0_347,
inference(avatar_split_clause,[],[f2220,f4652]) ).
fof(f4652,plain,
( spl0_347
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2220,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4650,plain,
spl0_346,
inference(avatar_split_clause,[],[f2184,f4648]) ).
fof(f4648,plain,
( spl0_346
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2184,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4646,plain,
spl0_345,
inference(avatar_split_clause,[],[f2183,f4644]) ).
fof(f4644,plain,
( spl0_345
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2183,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4642,plain,
spl0_344,
inference(avatar_split_clause,[],[f2182,f4640]) ).
fof(f4640,plain,
( spl0_344
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2182,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4638,plain,
spl0_343,
inference(avatar_split_clause,[],[f2181,f4636]) ).
fof(f4636,plain,
( spl0_343
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2181,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4634,plain,
spl0_342,
inference(avatar_split_clause,[],[f2180,f4632]) ).
fof(f4632,plain,
( spl0_342
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2180,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4630,plain,
spl0_341,
inference(avatar_split_clause,[],[f2178,f4628]) ).
fof(f4628,plain,
( spl0_341
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2178,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4626,plain,
spl0_340,
inference(avatar_split_clause,[],[f2177,f4624]) ).
fof(f4624,plain,
( spl0_340
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2177,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4622,plain,
spl0_339,
inference(avatar_split_clause,[],[f2176,f4620]) ).
fof(f4620,plain,
( spl0_339
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2176,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4618,plain,
spl0_338,
inference(avatar_split_clause,[],[f2175,f4616]) ).
fof(f4616,plain,
( spl0_338
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2175,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4614,plain,
spl0_337,
inference(avatar_split_clause,[],[f2174,f4612]) ).
fof(f4612,plain,
( spl0_337
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2174,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4610,plain,
spl0_336,
inference(avatar_split_clause,[],[f2173,f4608]) ).
fof(f4608,plain,
( spl0_336
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2173,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4606,plain,
spl0_335,
inference(avatar_split_clause,[],[f2172,f4604]) ).
fof(f4604,plain,
( spl0_335
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2172,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4602,plain,
spl0_334,
inference(avatar_split_clause,[],[f2169,f4600]) ).
fof(f4600,plain,
( spl0_334
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2169,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4598,plain,
spl0_333,
inference(avatar_split_clause,[],[f2168,f4596]) ).
fof(f4596,plain,
( spl0_333
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2168,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4594,plain,
spl0_332,
inference(avatar_split_clause,[],[f2163,f4592]) ).
fof(f4592,plain,
( spl0_332
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2163,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4590,plain,
spl0_331,
inference(avatar_split_clause,[],[f2162,f4588]) ).
fof(f4588,plain,
( spl0_331
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2162,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4586,plain,
spl0_330,
inference(avatar_split_clause,[],[f2159,f4584]) ).
fof(f4584,plain,
( spl0_330
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2159,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4582,plain,
spl0_329,
inference(avatar_split_clause,[],[f2158,f4580]) ).
fof(f4580,plain,
( spl0_329
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2158,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4578,plain,
spl0_328,
inference(avatar_split_clause,[],[f2156,f4576]) ).
fof(f4576,plain,
( spl0_328
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2156,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4574,plain,
spl0_327,
inference(avatar_split_clause,[],[f2155,f4572]) ).
fof(f4572,plain,
( spl0_327
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2155,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4570,plain,
spl0_326,
inference(avatar_split_clause,[],[f2154,f4568]) ).
fof(f4568,plain,
( spl0_326
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2154,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4566,plain,
spl0_325,
inference(avatar_split_clause,[],[f2153,f4564]) ).
fof(f4564,plain,
( spl0_325
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2153,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4562,plain,
spl0_324,
inference(avatar_split_clause,[],[f2152,f4560]) ).
fof(f4560,plain,
( spl0_324
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2152,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4558,plain,
spl0_323,
inference(avatar_split_clause,[],[f2151,f4556]) ).
fof(f4556,plain,
( spl0_323
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2151,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4554,plain,
spl0_322,
inference(avatar_split_clause,[],[f2147,f4552]) ).
fof(f4552,plain,
( spl0_322
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2147,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4550,plain,
spl0_321,
inference(avatar_split_clause,[],[f2145,f4548]) ).
fof(f4548,plain,
( spl0_321
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2145,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4546,plain,
spl0_320,
inference(avatar_split_clause,[],[f2142,f4544]) ).
fof(f4544,plain,
( spl0_320
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2142,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4542,plain,
spl0_319,
inference(avatar_split_clause,[],[f2139,f4540]) ).
fof(f4540,plain,
( spl0_319
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2139,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4538,plain,
spl0_318,
inference(avatar_split_clause,[],[f2138,f4536]) ).
fof(f4536,plain,
( spl0_318
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2138,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4534,plain,
spl0_317,
inference(avatar_split_clause,[],[f2136,f4532]) ).
fof(f4532,plain,
( spl0_317
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2136,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4530,plain,
spl0_316,
inference(avatar_split_clause,[],[f2135,f4528]) ).
fof(f4528,plain,
( spl0_316
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2135,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4526,plain,
spl0_315,
inference(avatar_split_clause,[],[f2134,f4524]) ).
fof(f4524,plain,
( spl0_315
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2134,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4522,plain,
spl0_314,
inference(avatar_split_clause,[],[f2131,f4520]) ).
fof(f4520,plain,
( spl0_314
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2131,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4518,plain,
spl0_313,
inference(avatar_split_clause,[],[f2130,f4516]) ).
fof(f4516,plain,
( spl0_313
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2130,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4514,plain,
spl0_312,
inference(avatar_split_clause,[],[f2128,f4512]) ).
fof(f4512,plain,
( spl0_312
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2128,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4510,plain,
spl0_311,
inference(avatar_split_clause,[],[f2122,f4508]) ).
fof(f4508,plain,
( spl0_311
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2122,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4506,plain,
spl0_310,
inference(avatar_split_clause,[],[f2121,f4504]) ).
fof(f4504,plain,
( spl0_310
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2121,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4502,plain,
spl0_309,
inference(avatar_split_clause,[],[f2119,f4500]) ).
fof(f4500,plain,
( spl0_309
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2119,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4498,plain,
spl0_308,
inference(avatar_split_clause,[],[f2118,f4496]) ).
fof(f4496,plain,
( spl0_308
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2118,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4494,plain,
spl0_307,
inference(avatar_split_clause,[],[f2111,f4492]) ).
fof(f4492,plain,
( spl0_307
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2111,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4490,plain,
spl0_306,
inference(avatar_split_clause,[],[f2110,f4488]) ).
fof(f4488,plain,
( spl0_306
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2110,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4486,plain,
spl0_305,
inference(avatar_split_clause,[],[f2108,f4484]) ).
fof(f4484,plain,
( spl0_305
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2108,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4482,plain,
spl0_304,
inference(avatar_split_clause,[],[f2107,f4480]) ).
fof(f4480,plain,
( spl0_304
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2107,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4478,plain,
spl0_303,
inference(avatar_split_clause,[],[f2106,f4476]) ).
fof(f4476,plain,
( spl0_303
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2106,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4474,plain,
spl0_302,
inference(avatar_split_clause,[],[f2104,f4472]) ).
fof(f4472,plain,
( spl0_302
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2104,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4470,plain,
spl0_301,
inference(avatar_split_clause,[],[f2103,f4468]) ).
fof(f4468,plain,
( spl0_301
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2103,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4466,plain,
spl0_300,
inference(avatar_split_clause,[],[f2102,f4464]) ).
fof(f4464,plain,
( spl0_300
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2102,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4462,plain,
spl0_299,
inference(avatar_split_clause,[],[f2101,f4460]) ).
fof(f4460,plain,
( spl0_299
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2101,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4458,plain,
spl0_298,
inference(avatar_split_clause,[],[f2100,f4456]) ).
fof(f4456,plain,
( spl0_298
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2100,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4454,plain,
spl0_297,
inference(avatar_split_clause,[],[f2099,f4452]) ).
fof(f4452,plain,
( spl0_297
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2099,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4450,plain,
spl0_296,
inference(avatar_split_clause,[],[f2098,f4448]) ).
fof(f4448,plain,
( spl0_296
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2098,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4446,plain,
spl0_295,
inference(avatar_split_clause,[],[f2097,f4444]) ).
fof(f4444,plain,
( spl0_295
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2097,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4442,plain,
spl0_294,
inference(avatar_split_clause,[],[f2096,f4440]) ).
fof(f4440,plain,
( spl0_294
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2096,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4438,plain,
spl0_293,
inference(avatar_split_clause,[],[f2095,f4436]) ).
fof(f4436,plain,
( spl0_293
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2095,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4434,plain,
spl0_292,
inference(avatar_split_clause,[],[f2092,f4432]) ).
fof(f4432,plain,
( spl0_292
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2092,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4430,plain,
spl0_291,
inference(avatar_split_clause,[],[f2090,f4428]) ).
fof(f4428,plain,
( spl0_291
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2090,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4426,plain,
spl0_290,
inference(avatar_split_clause,[],[f2088,f4424]) ).
fof(f4424,plain,
( spl0_290
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2088,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4422,plain,
spl0_289,
inference(avatar_split_clause,[],[f2085,f4420]) ).
fof(f4420,plain,
( spl0_289
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2085,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4418,plain,
spl0_288,
inference(avatar_split_clause,[],[f2084,f4416]) ).
fof(f4416,plain,
( spl0_288
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2084,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4414,plain,
spl0_287,
inference(avatar_split_clause,[],[f2083,f4412]) ).
fof(f4412,plain,
( spl0_287
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2083,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4410,plain,
spl0_286,
inference(avatar_split_clause,[],[f2080,f4408]) ).
fof(f4408,plain,
( spl0_286
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2080,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4406,plain,
spl0_285,
inference(avatar_split_clause,[],[f2077,f4404]) ).
fof(f4404,plain,
( spl0_285
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2077,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4402,plain,
spl0_284,
inference(avatar_split_clause,[],[f2076,f4400]) ).
fof(f4400,plain,
( spl0_284
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2076,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4398,plain,
spl0_283,
inference(avatar_split_clause,[],[f2074,f4396]) ).
fof(f4396,plain,
( spl0_283
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2074,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4394,plain,
spl0_282,
inference(avatar_split_clause,[],[f2073,f4392]) ).
fof(f4392,plain,
( spl0_282
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2073,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4390,plain,
spl0_281,
inference(avatar_split_clause,[],[f2072,f4388]) ).
fof(f4388,plain,
( spl0_281
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2072,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4386,plain,
spl0_280,
inference(avatar_split_clause,[],[f2071,f4384]) ).
fof(f4384,plain,
( spl0_280
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2071,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4382,plain,
spl0_279,
inference(avatar_split_clause,[],[f2070,f4380]) ).
fof(f4380,plain,
( spl0_279
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2070,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4378,plain,
spl0_278,
inference(avatar_split_clause,[],[f2068,f4376]) ).
fof(f4376,plain,
( spl0_278
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2068,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4374,plain,
spl0_277,
inference(avatar_split_clause,[],[f2065,f4372]) ).
fof(f4372,plain,
( spl0_277
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2065,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4370,plain,
spl0_276,
inference(avatar_split_clause,[],[f2064,f4368]) ).
fof(f4368,plain,
( spl0_276
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2064,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4366,plain,
spl0_275,
inference(avatar_split_clause,[],[f2060,f4364]) ).
fof(f4364,plain,
( spl0_275
<=> ! [X92] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2060,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4362,plain,
spl0_274,
inference(avatar_split_clause,[],[f2058,f4360]) ).
fof(f4360,plain,
( spl0_274
<=> ! [X92] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2058,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4358,plain,
spl0_273,
inference(avatar_split_clause,[],[f2050,f4356]) ).
fof(f4356,plain,
( spl0_273
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2050,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4354,plain,
spl0_272,
inference(avatar_split_clause,[],[f2049,f4352]) ).
fof(f4352,plain,
( spl0_272
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2049,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4350,plain,
spl0_271,
inference(avatar_split_clause,[],[f2048,f4348]) ).
fof(f4348,plain,
( spl0_271
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2048,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4346,plain,
spl0_270,
inference(avatar_split_clause,[],[f2047,f4344]) ).
fof(f4344,plain,
( spl0_270
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2047,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4342,plain,
spl0_269,
inference(avatar_split_clause,[],[f2046,f4340]) ).
fof(f4340,plain,
( spl0_269
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2046,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4338,plain,
spl0_268,
inference(avatar_split_clause,[],[f2045,f4336]) ).
fof(f4336,plain,
( spl0_268
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2045,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4334,plain,
spl0_267,
inference(avatar_split_clause,[],[f2044,f4332]) ).
fof(f4332,plain,
( spl0_267
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2044,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4330,plain,
spl0_266,
inference(avatar_split_clause,[],[f2043,f4328]) ).
fof(f4328,plain,
( spl0_266
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2043,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4326,plain,
spl0_265,
inference(avatar_split_clause,[],[f2042,f4324]) ).
fof(f4324,plain,
( spl0_265
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2042,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4322,plain,
spl0_264,
inference(avatar_split_clause,[],[f2041,f4320]) ).
fof(f4320,plain,
( spl0_264
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2041,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4318,plain,
spl0_263,
inference(avatar_split_clause,[],[f2040,f4316]) ).
fof(f4316,plain,
( spl0_263
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2040,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4314,plain,
spl0_262,
inference(avatar_split_clause,[],[f2039,f4312]) ).
fof(f4312,plain,
( spl0_262
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2039,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4310,plain,
spl0_261,
inference(avatar_split_clause,[],[f2038,f4308]) ).
fof(f4308,plain,
( spl0_261
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2038,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4306,plain,
spl0_260,
inference(avatar_split_clause,[],[f2037,f4304]) ).
fof(f4304,plain,
( spl0_260
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2037,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4302,plain,
spl0_259,
inference(avatar_split_clause,[],[f2036,f4300]) ).
fof(f4300,plain,
( spl0_259
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2036,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4298,plain,
spl0_258,
inference(avatar_split_clause,[],[f2035,f4296]) ).
fof(f4296,plain,
( spl0_258
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2035,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4294,plain,
spl0_257,
inference(avatar_split_clause,[],[f2034,f4292]) ).
fof(f4292,plain,
( spl0_257
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2034,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4290,plain,
spl0_256,
inference(avatar_split_clause,[],[f2031,f4288]) ).
fof(f4288,plain,
( spl0_256
<=> ! [X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2031,axiom,
! [X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4286,plain,
spl0_255,
inference(avatar_split_clause,[],[f2030,f4284]) ).
fof(f4284,plain,
( spl0_255
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2030,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4282,plain,
spl0_254,
inference(avatar_split_clause,[],[f2029,f4280]) ).
fof(f4280,plain,
( spl0_254
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2029,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4278,plain,
spl0_253,
inference(avatar_split_clause,[],[f2028,f4276]) ).
fof(f4276,plain,
( spl0_253
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2028,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4274,plain,
spl0_252,
inference(avatar_split_clause,[],[f2027,f4272]) ).
fof(f4272,plain,
( spl0_252
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2027,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4270,plain,
spl0_251,
inference(avatar_split_clause,[],[f2026,f4268]) ).
fof(f4268,plain,
( spl0_251
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2026,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4266,plain,
spl0_250,
inference(avatar_split_clause,[],[f2023,f4264]) ).
fof(f4264,plain,
( spl0_250
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2023,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4262,plain,
spl0_249,
inference(avatar_split_clause,[],[f2022,f4260]) ).
fof(f4260,plain,
( spl0_249
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2022,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4258,plain,
spl0_248,
inference(avatar_split_clause,[],[f2018,f4256]) ).
fof(f4256,plain,
( spl0_248
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2018,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4254,plain,
spl0_247,
inference(avatar_split_clause,[],[f2017,f4252]) ).
fof(f4252,plain,
( spl0_247
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2017,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4250,plain,
spl0_246,
inference(avatar_split_clause,[],[f2016,f4248]) ).
fof(f4248,plain,
( spl0_246
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2016,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4246,plain,
spl0_245,
inference(avatar_split_clause,[],[f2013,f4244]) ).
fof(f4244,plain,
( spl0_245
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2013,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4242,plain,
spl0_244,
inference(avatar_split_clause,[],[f2011,f4240]) ).
fof(f4240,plain,
( spl0_244
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2011,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4238,plain,
spl0_243,
inference(avatar_split_clause,[],[f2010,f4236]) ).
fof(f4236,plain,
( spl0_243
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2010,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4234,plain,
spl0_242,
inference(avatar_split_clause,[],[f2009,f4232]) ).
fof(f4232,plain,
( spl0_242
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2009,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4230,plain,
spl0_241,
inference(avatar_split_clause,[],[f2008,f4228]) ).
fof(f4228,plain,
( spl0_241
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2008,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4226,plain,
spl0_240,
inference(avatar_split_clause,[],[f2007,f4224]) ).
fof(f4224,plain,
( spl0_240
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2007,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4222,plain,
spl0_239,
inference(avatar_split_clause,[],[f2003,f4220]) ).
fof(f4220,plain,
( spl0_239
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2003,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4218,plain,
spl0_238,
inference(avatar_split_clause,[],[f2002,f4216]) ).
fof(f4216,plain,
( spl0_238
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2002,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4214,plain,
spl0_237,
inference(avatar_split_clause,[],[f2001,f4212]) ).
fof(f4212,plain,
( spl0_237
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2001,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4210,plain,
spl0_236,
inference(avatar_split_clause,[],[f1998,f4208]) ).
fof(f4208,plain,
( spl0_236
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1998,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4206,plain,
spl0_235,
inference(avatar_split_clause,[],[f1996,f4204]) ).
fof(f4204,plain,
( spl0_235
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1996,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4202,plain,
spl0_234,
inference(avatar_split_clause,[],[f1994,f4200]) ).
fof(f4200,plain,
( spl0_234
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1994,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4198,plain,
spl0_233,
inference(avatar_split_clause,[],[f1993,f4196]) ).
fof(f4196,plain,
( spl0_233
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1993,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4194,plain,
spl0_232,
inference(avatar_split_clause,[],[f1992,f4192]) ).
fof(f4192,plain,
( spl0_232
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1992,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4190,plain,
spl0_231,
inference(avatar_split_clause,[],[f1991,f4188]) ).
fof(f4188,plain,
( spl0_231
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1991,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4186,plain,
spl0_230,
inference(avatar_split_clause,[],[f1990,f4184]) ).
fof(f4184,plain,
( spl0_230
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1990,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4182,plain,
spl0_229,
inference(avatar_split_clause,[],[f1988,f4180]) ).
fof(f4180,plain,
( spl0_229
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1988,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4178,plain,
spl0_228,
inference(avatar_split_clause,[],[f1987,f4176]) ).
fof(f4176,plain,
( spl0_228
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1987,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4174,plain,
spl0_227,
inference(avatar_split_clause,[],[f1984,f4172]) ).
fof(f4172,plain,
( spl0_227
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1984,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4170,plain,
spl0_226,
inference(avatar_split_clause,[],[f1982,f4168]) ).
fof(f4168,plain,
( spl0_226
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1982,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4166,plain,
spl0_225,
inference(avatar_split_clause,[],[f1981,f4164]) ).
fof(f4164,plain,
( spl0_225
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1981,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4162,plain,
spl0_224,
inference(avatar_split_clause,[],[f1980,f4160]) ).
fof(f4160,plain,
( spl0_224
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1980,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4158,plain,
spl0_223,
inference(avatar_split_clause,[],[f1979,f4156]) ).
fof(f4156,plain,
( spl0_223
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1979,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4154,plain,
spl0_222,
inference(avatar_split_clause,[],[f1978,f4152]) ).
fof(f4152,plain,
( spl0_222
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1978,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4150,plain,
spl0_221,
inference(avatar_split_clause,[],[f1977,f4148]) ).
fof(f4148,plain,
( spl0_221
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1977,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4146,plain,
spl0_220,
inference(avatar_split_clause,[],[f1976,f4144]) ).
fof(f4144,plain,
( spl0_220
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1976,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4142,plain,
spl0_219,
inference(avatar_split_clause,[],[f1975,f4140]) ).
fof(f4140,plain,
( spl0_219
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1975,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4138,plain,
spl0_218,
inference(avatar_split_clause,[],[f1974,f4136]) ).
fof(f4136,plain,
( spl0_218
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1974,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4134,plain,
spl0_217,
inference(avatar_split_clause,[],[f1971,f4132]) ).
fof(f4132,plain,
( spl0_217
<=> ! [X92] :
( ~ class_OrderedGroup_Omonoid__mult(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1971,axiom,
! [X92] :
( ~ class_OrderedGroup_Omonoid__mult(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4130,plain,
spl0_216,
inference(avatar_split_clause,[],[f1970,f4128]) ).
fof(f4128,plain,
( spl0_216
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1970,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4126,plain,
spl0_215,
inference(avatar_split_clause,[],[f1969,f4124]) ).
fof(f4124,plain,
( spl0_215
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1969,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4122,plain,
spl0_214,
inference(avatar_split_clause,[],[f1968,f4120]) ).
fof(f4120,plain,
( spl0_214
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1968,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4118,plain,
spl0_213,
inference(avatar_split_clause,[],[f1967,f4116]) ).
fof(f4116,plain,
( spl0_213
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1967,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4114,plain,
spl0_212,
inference(avatar_split_clause,[],[f1966,f4112]) ).
fof(f4112,plain,
( spl0_212
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1966,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4110,plain,
spl0_211,
inference(avatar_split_clause,[],[f1964,f4108]) ).
fof(f4108,plain,
( spl0_211
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1964,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4106,plain,
spl0_210,
inference(avatar_split_clause,[],[f1962,f4104]) ).
fof(f4104,plain,
( spl0_210
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1962,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4102,plain,
spl0_209,
inference(avatar_split_clause,[],[f1961,f4100]) ).
fof(f4100,plain,
( spl0_209
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1961,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4098,plain,
spl0_208,
inference(avatar_split_clause,[],[f1960,f4096]) ).
fof(f4096,plain,
( spl0_208
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1960,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4094,plain,
spl0_207,
inference(avatar_split_clause,[],[f1959,f4092]) ).
fof(f4092,plain,
( spl0_207
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1959,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4090,plain,
spl0_206,
inference(avatar_split_clause,[],[f1956,f4088]) ).
fof(f4088,plain,
( spl0_206
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1956,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4086,plain,
spl0_205,
inference(avatar_split_clause,[],[f1954,f4084]) ).
fof(f4084,plain,
( spl0_205
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1954,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4082,plain,
spl0_204,
inference(avatar_split_clause,[],[f1953,f4080]) ).
fof(f4080,plain,
( spl0_204
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1953,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4078,plain,
spl0_203,
inference(avatar_split_clause,[],[f1952,f4076]) ).
fof(f4076,plain,
( spl0_203
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1952,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4074,plain,
spl0_202,
inference(avatar_split_clause,[],[f1951,f4072]) ).
fof(f4072,plain,
( spl0_202
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1951,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4070,plain,
spl0_201,
inference(avatar_split_clause,[],[f1950,f4068]) ).
fof(f4068,plain,
( spl0_201
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1950,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4066,plain,
spl0_200,
inference(avatar_split_clause,[],[f1949,f4064]) ).
fof(f4064,plain,
( spl0_200
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1949,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4062,plain,
spl0_199,
inference(avatar_split_clause,[],[f1948,f4060]) ).
fof(f4060,plain,
( spl0_199
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1948,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4058,plain,
spl0_198,
inference(avatar_split_clause,[],[f1947,f4056]) ).
fof(f4056,plain,
( spl0_198
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1947,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4054,plain,
spl0_197,
inference(avatar_split_clause,[],[f1945,f4052]) ).
fof(f4052,plain,
( spl0_197
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1945,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4050,plain,
spl0_196,
inference(avatar_split_clause,[],[f1943,f4048]) ).
fof(f4048,plain,
( spl0_196
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1943,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4046,plain,
spl0_195,
inference(avatar_split_clause,[],[f1942,f4044]) ).
fof(f4044,plain,
( spl0_195
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1942,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4042,plain,
spl0_194,
inference(avatar_split_clause,[],[f1941,f4040]) ).
fof(f4040,plain,
( spl0_194
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1941,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4038,plain,
spl0_193,
inference(avatar_split_clause,[],[f1940,f4036]) ).
fof(f4036,plain,
( spl0_193
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1940,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4034,plain,
spl0_192,
inference(avatar_split_clause,[],[f1937,f4032]) ).
fof(f4032,plain,
( spl0_192
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1937,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4030,plain,
spl0_191,
inference(avatar_split_clause,[],[f1935,f4028]) ).
fof(f4028,plain,
( spl0_191
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1935,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4026,plain,
spl0_190,
inference(avatar_split_clause,[],[f1934,f4024]) ).
fof(f4024,plain,
( spl0_190
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1934,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4022,plain,
spl0_189,
inference(avatar_split_clause,[],[f1933,f4020]) ).
fof(f4020,plain,
( spl0_189
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1933,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4018,plain,
spl0_188,
inference(avatar_split_clause,[],[f1932,f4016]) ).
fof(f4016,plain,
( spl0_188
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1932,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4014,plain,
spl0_187,
inference(avatar_split_clause,[],[f1931,f4012]) ).
fof(f4012,plain,
( spl0_187
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1931,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4010,plain,
spl0_186,
inference(avatar_split_clause,[],[f1930,f4008]) ).
fof(f4008,plain,
( spl0_186
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1930,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4006,plain,
spl0_185,
inference(avatar_split_clause,[],[f1929,f4004]) ).
fof(f4004,plain,
( spl0_185
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1929,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4002,plain,
spl0_184,
inference(avatar_split_clause,[],[f1927,f4000]) ).
fof(f4000,plain,
( spl0_184
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1927,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f3998,plain,
spl0_183,
inference(avatar_split_clause,[],[f1925,f3996]) ).
fof(f3996,plain,
( spl0_183
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1925,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f3994,plain,
spl0_182,
inference(avatar_split_clause,[],[f1924,f3992]) ).
fof(f3992,plain,
( spl0_182
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1924,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f3990,plain,
spl0_181,
inference(avatar_split_clause,[],[f1923,f3988]) ).
fof(f3988,plain,
( spl0_181
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1923,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f3986,plain,
spl0_180,
inference(avatar_split_clause,[],[f1922,f3984]) ).
fof(f3984,plain,
( spl0_180
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1922,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f3982,plain,
spl0_179,
inference(avatar_split_clause,[],[f1921,f3980]) ).
fof(f3980,plain,
( spl0_179
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1921,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f3978,plain,
spl0_178,
inference(avatar_split_clause,[],[f1920,f3976]) ).
fof(f3976,plain,
( spl0_178
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1920,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f3974,plain,
spl0_177,
inference(avatar_split_clause,[],[f1917,f3972]) ).
fof(f3972,plain,
( spl0_177
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1917,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f3970,plain,
spl0_176,
inference(avatar_split_clause,[],[f1915,f3968]) ).
fof(f3968,plain,
( spl0_176
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1915,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f3966,plain,
spl0_175,
inference(avatar_split_clause,[],[f1914,f3964]) ).
fof(f3964,plain,
( spl0_175
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1914,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f3962,plain,
spl0_174,
inference(avatar_split_clause,[],[f1913,f3960]) ).
fof(f3960,plain,
( spl0_174
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1913,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f3958,plain,
spl0_173,
inference(avatar_split_clause,[],[f1912,f3956]) ).
fof(f3956,plain,
( spl0_173
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1912,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f3954,plain,
spl0_172,
inference(avatar_split_clause,[],[f1911,f3952]) ).
fof(f3952,plain,
( spl0_172
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1911,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3950,plain,
spl0_171,
inference(avatar_split_clause,[],[f1910,f3948]) ).
fof(f3948,plain,
( spl0_171
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1910,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3946,plain,
spl0_170,
inference(avatar_split_clause,[],[f1909,f3944]) ).
fof(f3944,plain,
( spl0_170
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1909,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3942,plain,
spl0_169,
inference(avatar_split_clause,[],[f1907,f3940]) ).
fof(f3940,plain,
( spl0_169
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1907,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3938,plain,
spl0_168,
inference(avatar_split_clause,[],[f1905,f3936]) ).
fof(f3936,plain,
( spl0_168
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1905,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3934,plain,
spl0_167,
inference(avatar_split_clause,[],[f1904,f3932]) ).
fof(f3932,plain,
( spl0_167
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1904,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3930,plain,
spl0_166,
inference(avatar_split_clause,[],[f1903,f3928]) ).
fof(f3928,plain,
( spl0_166
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1903,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3926,plain,
spl0_165,
inference(avatar_split_clause,[],[f1900,f3924]) ).
fof(f3924,plain,
( spl0_165
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1900,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3922,plain,
spl0_164,
inference(avatar_split_clause,[],[f1898,f3920]) ).
fof(f3920,plain,
( spl0_164
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1898,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3918,plain,
spl0_163,
inference(avatar_split_clause,[],[f1897,f3916]) ).
fof(f3916,plain,
( spl0_163
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1897,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3914,plain,
spl0_162,
inference(avatar_split_clause,[],[f1896,f3912]) ).
fof(f3912,plain,
( spl0_162
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1896,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3910,plain,
spl0_161,
inference(avatar_split_clause,[],[f1895,f3908]) ).
fof(f3908,plain,
( spl0_161
<=> ! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1895,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3906,plain,
spl0_160,
inference(avatar_split_clause,[],[f1891,f3904]) ).
fof(f3904,plain,
( spl0_160
<=> ! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1891,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3902,plain,
spl0_159,
inference(avatar_split_clause,[],[f1884,f3900]) ).
fof(f3900,plain,
( spl0_159
<=> ! [X92] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1884,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3898,plain,
spl0_158,
inference(avatar_split_clause,[],[f1876,f3896]) ).
fof(f3896,plain,
( spl0_158
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1876,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3894,plain,
spl0_157,
inference(avatar_split_clause,[],[f1875,f3892]) ).
fof(f3892,plain,
( spl0_157
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1875,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3890,plain,
spl0_156,
inference(avatar_split_clause,[],[f1870,f3888]) ).
fof(f3888,plain,
( spl0_156
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1870,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3886,plain,
spl0_155,
inference(avatar_split_clause,[],[f1868,f3884]) ).
fof(f3884,plain,
( spl0_155
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1868,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3882,plain,
spl0_154,
inference(avatar_split_clause,[],[f1866,f3880]) ).
fof(f3880,plain,
( spl0_154
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1866,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3878,plain,
spl0_153,
inference(avatar_split_clause,[],[f1865,f3876]) ).
fof(f3876,plain,
( spl0_153
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1865,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3874,plain,
spl0_152,
inference(avatar_split_clause,[],[f1862,f3872]) ).
fof(f3872,plain,
( spl0_152
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Numeral_Onumber(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1862,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Numeral_Onumber(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3870,plain,
spl0_151,
inference(avatar_split_clause,[],[f1860,f3868]) ).
fof(f3868,plain,
( spl0_151
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1860,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3866,plain,
spl0_150,
inference(avatar_split_clause,[],[f1859,f3864]) ).
fof(f3864,plain,
( spl0_150
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1859,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3862,plain,
spl0_149,
inference(avatar_split_clause,[],[f1858,f3860]) ).
fof(f3860,plain,
( spl0_149
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1858,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3858,plain,
spl0_148,
inference(avatar_split_clause,[],[f1857,f3856]) ).
fof(f3856,plain,
( spl0_148
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1857,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3854,plain,
spl0_147,
inference(avatar_split_clause,[],[f1856,f3852]) ).
fof(f3852,plain,
( spl0_147
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1856,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3850,plain,
spl0_146,
inference(avatar_split_clause,[],[f1855,f3848]) ).
fof(f3848,plain,
( spl0_146
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1855,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3846,plain,
spl0_145,
inference(avatar_split_clause,[],[f1854,f3844]) ).
fof(f3844,plain,
( spl0_145
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1854,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3842,plain,
spl0_144,
inference(avatar_split_clause,[],[f1853,f3840]) ).
fof(f3840,plain,
( spl0_144
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1853,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3838,plain,
spl0_143,
inference(avatar_split_clause,[],[f1852,f3836]) ).
fof(f3836,plain,
( spl0_143
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1852,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3834,plain,
spl0_142,
inference(avatar_split_clause,[],[f1851,f3832]) ).
fof(f3832,plain,
( spl0_142
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1851,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3830,plain,
spl0_141,
inference(avatar_split_clause,[],[f1849,f3828]) ).
fof(f3828,plain,
( spl0_141
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1849,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3826,plain,
spl0_140,
inference(avatar_split_clause,[],[f1848,f3824]) ).
fof(f3824,plain,
( spl0_140
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1848,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3822,plain,
spl0_139,
inference(avatar_split_clause,[],[f1847,f3820]) ).
fof(f3820,plain,
( spl0_139
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1847,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3818,plain,
spl0_138,
inference(avatar_split_clause,[],[f1846,f3816]) ).
fof(f3816,plain,
( spl0_138
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1846,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3814,plain,
spl0_137,
inference(avatar_split_clause,[],[f1845,f3812]) ).
fof(f3812,plain,
( spl0_137
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1845,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3810,plain,
spl0_136,
inference(avatar_split_clause,[],[f1844,f3808]) ).
fof(f3808,plain,
( spl0_136
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1844,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3806,plain,
spl0_135,
inference(avatar_split_clause,[],[f1843,f3804]) ).
fof(f3804,plain,
( spl0_135
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1843,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3802,plain,
spl0_134,
inference(avatar_split_clause,[],[f1841,f3800]) ).
fof(f3800,plain,
( spl0_134
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1841,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3798,plain,
spl0_133,
inference(avatar_split_clause,[],[f1840,f3796]) ).
fof(f3796,plain,
( spl0_133
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1840,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3794,plain,
spl0_132,
inference(avatar_split_clause,[],[f1837,f3792]) ).
fof(f3792,plain,
( spl0_132
<=> ! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1837,axiom,
! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3790,plain,
spl0_131,
inference(avatar_split_clause,[],[f1836,f3788]) ).
fof(f3788,plain,
( spl0_131
<=> ! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1836,axiom,
! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3786,plain,
spl0_130,
inference(avatar_split_clause,[],[f1835,f3784]) ).
fof(f3784,plain,
( spl0_130
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1835,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3782,plain,
spl0_129,
inference(avatar_split_clause,[],[f1834,f3780]) ).
fof(f3780,plain,
( spl0_129
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1834,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3778,plain,
spl0_128,
inference(avatar_split_clause,[],[f1833,f3776]) ).
fof(f3776,plain,
( spl0_128
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1833,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3774,plain,
spl0_127,
inference(avatar_split_clause,[],[f1832,f3772]) ).
fof(f3772,plain,
( spl0_127
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1832,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3770,plain,
spl0_126,
inference(avatar_split_clause,[],[f1831,f3768]) ).
fof(f3768,plain,
( spl0_126
<=> ! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1831,axiom,
! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3766,plain,
spl0_125,
inference(avatar_split_clause,[],[f1830,f3764]) ).
fof(f3764,plain,
( spl0_125
<=> ! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1830,axiom,
! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3762,plain,
spl0_124,
inference(avatar_split_clause,[],[f1675,f3760]) ).
fof(f1675,axiom,
! [X3,X11] : c_in(X11,c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3758,plain,
spl0_123,
inference(avatar_split_clause,[],[f1643,f3756]) ).
fof(f1643,axiom,
! [X10] : ~ c_less(X10,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3754,plain,
spl0_122,
inference(avatar_split_clause,[],[f1641,f3752]) ).
fof(f1641,axiom,
! [X10] : c_lessequals(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3750,plain,
spl0_121,
inference(avatar_split_clause,[],[f1617,f3748]) ).
fof(f3748,plain,
( spl0_121
<=> ! [X25] : c_Divides_Oop_Advd(c_1,X25,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1617,axiom,
! [X25] : c_Divides_Oop_Advd(c_1,X25,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3746,plain,
spl0_120,
inference(avatar_split_clause,[],[f1616,f3744]) ).
fof(f3744,plain,
( spl0_120
<=> ! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1616,axiom,
! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3742,plain,
spl0_119,
inference(avatar_split_clause,[],[f1600,f3740]) ).
fof(f3740,plain,
( spl0_119
<=> ! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1600,axiom,
! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3738,plain,
spl0_118,
inference(avatar_split_clause,[],[f1522,f3736]) ).
fof(f1522,axiom,
! [X3,X26] : ~ c_in(X26,c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3734,plain,
spl0_117,
inference(avatar_split_clause,[],[f1005,f3731]) ).
fof(f3731,plain,
( spl0_117
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1005,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f3729,plain,
spl0_116,
inference(avatar_split_clause,[],[f941,f3727]) ).
fof(f3727,plain,
( spl0_116
<=> ! [X10] : ~ c_less(X10,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f941,axiom,
! [X10] : ~ c_less(X10,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3725,plain,
spl0_115,
inference(avatar_split_clause,[],[f899,f3722]) ).
fof(f899,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3720,plain,
spl0_114,
inference(avatar_split_clause,[],[f559,f3718]) ).
fof(f3718,plain,
( spl0_114
<=> ! [X13,X11] : ~ c_List_Oop_Amem(X11,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f559,axiom,
! [X11,X13] : ~ c_List_Oop_Amem(X11,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3716,plain,
spl0_113,
inference(avatar_split_clause,[],[f332,f3714]) ).
fof(f332,axiom,
! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3712,plain,
spl0_112,
inference(avatar_split_clause,[],[f243,f3710]) ).
fof(f243,axiom,
! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3708,plain,
spl0_111,
inference(avatar_split_clause,[],[f236,f3705]) ).
fof(f3705,plain,
( spl0_111
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f236,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3703,plain,
spl0_110,
inference(avatar_split_clause,[],[f224,f3700]) ).
fof(f3698,plain,
spl0_109,
inference(avatar_split_clause,[],[f221,f3695]) ).
fof(f221,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3693,plain,
spl0_108,
inference(avatar_split_clause,[],[f79,f3691]) ).
fof(f3691,plain,
( spl0_108
<=> ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f79,axiom,
! [X25] : c_Divides_Oop_Advd(X25,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3689,plain,
spl0_107,
inference(avatar_split_clause,[],[f1826,f3687]) ).
fof(f3687,plain,
( spl0_107
<=> ! [X90] : class_Orderings_Oorder(tc_set(X90)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1826,axiom,
! [X90] : class_Orderings_Oorder(tc_set(X90)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3685,plain,
spl0_106,
inference(avatar_split_clause,[],[f1825,f3683]) ).
fof(f3683,plain,
( spl0_106
<=> ! [X90] : class_Orderings_Oord(tc_set(X90)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1825,axiom,
! [X90] : class_Orderings_Oord(tc_set(X90)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3681,plain,
spl0_105,
inference(avatar_split_clause,[],[f1703,f3678]) ).
fof(f3678,plain,
( spl0_105
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1703,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3676,plain,
spl0_104,
inference(avatar_split_clause,[],[f1701,f3673]) ).
fof(f3673,plain,
( spl0_104
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1701,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3671,plain,
spl0_103,
inference(avatar_split_clause,[],[f1700,f3669]) ).
fof(f3669,plain,
( spl0_103
<=> ! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1700,axiom,
! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3667,plain,
~ spl0_102,
inference(avatar_split_clause,[],[f1479,f3664]) ).
fof(f1479,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3662,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f1160,f3659]) ).
fof(f3659,plain,
( spl0_101
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1160,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3657,plain,
spl0_100,
inference(avatar_split_clause,[],[f1153,f3654]) ).
fof(f3654,plain,
( spl0_100
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1153,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3652,plain,
spl0_99,
inference(avatar_split_clause,[],[f1140,f3649]) ).
fof(f3649,plain,
( spl0_99
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1140,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3647,plain,
~ spl0_98,
inference(avatar_split_clause,[],[f1009,f3644]) ).
fof(f3644,plain,
( spl0_98
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1009,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3642,plain,
spl0_97,
inference(avatar_split_clause,[],[f556,f3640]) ).
fof(f3640,plain,
( spl0_97
<=> ! [X13] : c_List_Onull(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f556,axiom,
! [X13] : c_List_Onull(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3638,plain,
spl0_96,
inference(avatar_split_clause,[],[f401,f3636]) ).
fof(f3636,plain,
( spl0_96
<=> ! [X13] : c_List_Odistinct(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f401,axiom,
! [X13] : c_List_Odistinct(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3634,plain,
~ spl0_95,
inference(avatar_split_clause,[],[f220,f3631]) ).
fof(f220,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3629,plain,
~ spl0_94,
inference(avatar_split_clause,[],[f100,f3626]) ).
fof(f3626,plain,
( spl0_94
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f100,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3624,plain,
spl0_93,
inference(avatar_split_clause,[],[f1821,f3621]) ).
fof(f3621,plain,
( spl0_93
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1821,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3619,plain,
spl0_92,
inference(avatar_split_clause,[],[f1820,f3616]) ).
fof(f1820,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3614,plain,
spl0_91,
inference(avatar_split_clause,[],[f1819,f3611]) ).
fof(f3611,plain,
( spl0_91
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1819,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3609,plain,
spl0_90,
inference(avatar_split_clause,[],[f1818,f3606]) ).
fof(f1818,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3604,plain,
spl0_89,
inference(avatar_split_clause,[],[f1816,f3601]) ).
fof(f3601,plain,
( spl0_89
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1816,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3599,plain,
spl0_88,
inference(avatar_split_clause,[],[f1815,f3596]) ).
fof(f1815,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3594,plain,
spl0_87,
inference(avatar_split_clause,[],[f1813,f3591]) ).
fof(f3591,plain,
( spl0_87
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1813,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3589,plain,
spl0_86,
inference(avatar_split_clause,[],[f1812,f3586]) ).
fof(f3586,plain,
( spl0_86
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1812,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3584,plain,
spl0_85,
inference(avatar_split_clause,[],[f1811,f3581]) ).
fof(f3581,plain,
( spl0_85
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1811,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3579,plain,
spl0_84,
inference(avatar_split_clause,[],[f1810,f3576]) ).
fof(f3576,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1810,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3574,plain,
spl0_83,
inference(avatar_split_clause,[],[f1809,f3571]) ).
fof(f1809,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3569,plain,
spl0_82,
inference(avatar_split_clause,[],[f1808,f3566]) ).
fof(f3566,plain,
( spl0_82
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1808,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3564,plain,
spl0_81,
inference(avatar_split_clause,[],[f1807,f3561]) ).
fof(f3561,plain,
( spl0_81
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1807,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3559,plain,
spl0_80,
inference(avatar_split_clause,[],[f1806,f3556]) ).
fof(f3556,plain,
( spl0_80
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1806,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3554,plain,
spl0_79,
inference(avatar_split_clause,[],[f1805,f3551]) ).
fof(f3551,plain,
( spl0_79
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1805,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3549,plain,
spl0_78,
inference(avatar_split_clause,[],[f1804,f3546]) ).
fof(f3546,plain,
( spl0_78
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1804,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3544,plain,
spl0_77,
inference(avatar_split_clause,[],[f1803,f3541]) ).
fof(f3541,plain,
( spl0_77
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1803,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3539,plain,
spl0_76,
inference(avatar_split_clause,[],[f1802,f3536]) ).
fof(f3536,plain,
( spl0_76
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1802,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3534,plain,
spl0_75,
inference(avatar_split_clause,[],[f1801,f3531]) ).
fof(f1801,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3529,plain,
spl0_74,
inference(avatar_split_clause,[],[f1800,f3526]) ).
fof(f3526,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3524,plain,
spl0_73,
inference(avatar_split_clause,[],[f1799,f3521]) ).
fof(f3521,plain,
( spl0_73
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3519,plain,
spl0_72,
inference(avatar_split_clause,[],[f1798,f3516]) ).
fof(f1798,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3514,plain,
spl0_71,
inference(avatar_split_clause,[],[f1797,f3511]) ).
fof(f3511,plain,
( spl0_71
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1797,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3509,plain,
spl0_70,
inference(avatar_split_clause,[],[f1796,f3506]) ).
fof(f3506,plain,
( spl0_70
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1796,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3504,plain,
spl0_69,
inference(avatar_split_clause,[],[f1795,f3501]) ).
fof(f3501,plain,
( spl0_69
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1795,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3499,plain,
spl0_68,
inference(avatar_split_clause,[],[f1794,f3496]) ).
fof(f3496,plain,
( spl0_68
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1794,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3494,plain,
spl0_67,
inference(avatar_split_clause,[],[f1793,f3491]) ).
fof(f3491,plain,
( spl0_67
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1793,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3489,plain,
spl0_66,
inference(avatar_split_clause,[],[f1792,f3486]) ).
fof(f3486,plain,
( spl0_66
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1792,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3484,plain,
spl0_65,
inference(avatar_split_clause,[],[f1791,f3481]) ).
fof(f1791,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3479,plain,
spl0_64,
inference(avatar_split_clause,[],[f1790,f3476]) ).
fof(f3476,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3474,plain,
spl0_63,
inference(avatar_split_clause,[],[f1789,f3471]) ).
fof(f3471,plain,
( spl0_63
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1789,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3469,plain,
spl0_62,
inference(avatar_split_clause,[],[f1788,f3466]) ).
fof(f3466,plain,
( spl0_62
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1788,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3464,plain,
spl0_61,
inference(avatar_split_clause,[],[f1787,f3461]) ).
fof(f3461,plain,
( spl0_61
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1787,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3459,plain,
spl0_60,
inference(avatar_split_clause,[],[f1786,f3456]) ).
fof(f3456,plain,
( spl0_60
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1786,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3454,plain,
spl0_59,
inference(avatar_split_clause,[],[f1785,f3451]) ).
fof(f3451,plain,
( spl0_59
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3449,plain,
spl0_58,
inference(avatar_split_clause,[],[f1780,f3446]) ).
fof(f3446,plain,
( spl0_58
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1780,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3444,plain,
spl0_57,
inference(avatar_split_clause,[],[f1775,f3441]) ).
fof(f3441,plain,
( spl0_57
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1775,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3439,plain,
spl0_56,
inference(avatar_split_clause,[],[f1772,f3436]) ).
fof(f3436,plain,
( spl0_56
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1772,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3434,plain,
spl0_55,
inference(avatar_split_clause,[],[f1771,f3431]) ).
fof(f3431,plain,
( spl0_55
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1771,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3429,plain,
spl0_54,
inference(avatar_split_clause,[],[f1766,f3426]) ).
fof(f1766,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3424,plain,
spl0_53,
inference(avatar_split_clause,[],[f1763,f3421]) ).
fof(f1763,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3419,plain,
spl0_52,
inference(avatar_split_clause,[],[f1761,f3416]) ).
fof(f3416,plain,
( spl0_52
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1761,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3414,plain,
spl0_51,
inference(avatar_split_clause,[],[f1760,f3411]) ).
fof(f1760,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3409,plain,
spl0_50,
inference(avatar_split_clause,[],[f1759,f3406]) ).
fof(f3406,plain,
( spl0_50
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1759,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3404,plain,
spl0_49,
inference(avatar_split_clause,[],[f1758,f3401]) ).
fof(f1758,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3399,plain,
spl0_48,
inference(avatar_split_clause,[],[f1757,f3396]) ).
fof(f3396,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1757,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3394,plain,
spl0_47,
inference(avatar_split_clause,[],[f1755,f3391]) ).
fof(f3391,plain,
( spl0_47
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1755,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3389,plain,
spl0_46,
inference(avatar_split_clause,[],[f1754,f3386]) ).
fof(f3386,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1754,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3384,plain,
spl0_45,
inference(avatar_split_clause,[],[f1753,f3381]) ).
fof(f3381,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1753,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3379,plain,
spl0_44,
inference(avatar_split_clause,[],[f1752,f3376]) ).
fof(f1752,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3374,plain,
spl0_43,
inference(avatar_split_clause,[],[f1751,f3371]) ).
fof(f3371,plain,
( spl0_43
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1751,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3369,plain,
spl0_42,
inference(avatar_split_clause,[],[f1750,f3366]) ).
fof(f3366,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1750,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3364,plain,
spl0_41,
inference(avatar_split_clause,[],[f1749,f3361]) ).
fof(f1749,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3359,plain,
spl0_40,
inference(avatar_split_clause,[],[f1748,f3356]) ).
fof(f1748,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3354,plain,
spl0_39,
inference(avatar_split_clause,[],[f1747,f3351]) ).
fof(f3351,plain,
( spl0_39
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1747,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3349,plain,
spl0_38,
inference(avatar_split_clause,[],[f1746,f3346]) ).
fof(f3346,plain,
( spl0_38
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1746,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3344,plain,
spl0_37,
inference(avatar_split_clause,[],[f1745,f3341]) ).
fof(f3341,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1745,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3339,plain,
spl0_36,
inference(avatar_split_clause,[],[f1744,f3336]) ).
fof(f3336,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1744,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3334,plain,
spl0_35,
inference(avatar_split_clause,[],[f1743,f3331]) ).
fof(f3331,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1743,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3329,plain,
spl0_34,
inference(avatar_split_clause,[],[f1742,f3326]) ).
fof(f3326,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1742,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3324,plain,
spl0_33,
inference(avatar_split_clause,[],[f1741,f3321]) ).
fof(f3321,plain,
( spl0_33
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1741,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3319,plain,
spl0_32,
inference(avatar_split_clause,[],[f1739,f3316]) ).
fof(f3316,plain,
( spl0_32
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1739,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3314,plain,
spl0_31,
inference(avatar_split_clause,[],[f1738,f3311]) ).
fof(f3311,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1738,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3309,plain,
spl0_30,
inference(avatar_split_clause,[],[f1737,f3306]) ).
fof(f3306,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1737,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3304,plain,
spl0_29,
inference(avatar_split_clause,[],[f1736,f3301]) ).
fof(f3301,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1736,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3299,plain,
spl0_28,
inference(avatar_split_clause,[],[f1735,f3296]) ).
fof(f1735,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3294,plain,
spl0_27,
inference(avatar_split_clause,[],[f1734,f3291]) ).
fof(f3291,plain,
( spl0_27
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1734,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3289,plain,
spl0_26,
inference(avatar_split_clause,[],[f1733,f3286]) ).
fof(f1733,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3284,plain,
spl0_25,
inference(avatar_split_clause,[],[f1732,f3281]) ).
fof(f1732,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3279,plain,
spl0_24,
inference(avatar_split_clause,[],[f1731,f3276]) ).
fof(f1731,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3274,plain,
spl0_23,
inference(avatar_split_clause,[],[f1730,f3271]) ).
fof(f1730,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3269,plain,
spl0_22,
inference(avatar_split_clause,[],[f1728,f3266]) ).
fof(f1728,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3264,plain,
spl0_21,
inference(avatar_split_clause,[],[f1727,f3261]) ).
fof(f3261,plain,
( spl0_21
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1727,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3259,plain,
spl0_20,
inference(avatar_split_clause,[],[f1726,f3256]) ).
fof(f3256,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1726,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3254,plain,
spl0_19,
inference(avatar_split_clause,[],[f1725,f3251]) ).
fof(f3251,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1725,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3249,plain,
spl0_18,
inference(avatar_split_clause,[],[f1724,f3246]) ).
fof(f3246,plain,
( spl0_18
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1724,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3244,plain,
spl0_17,
inference(avatar_split_clause,[],[f1723,f3241]) ).
fof(f3241,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1723,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3239,plain,
spl0_16,
inference(avatar_split_clause,[],[f1722,f3236]) ).
fof(f1722,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3234,plain,
spl0_15,
inference(avatar_split_clause,[],[f1721,f3231]) ).
fof(f3231,plain,
( spl0_15
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1721,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3229,plain,
spl0_14,
inference(avatar_split_clause,[],[f1720,f3226]) ).
fof(f3226,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1720,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3224,plain,
spl0_13,
inference(avatar_split_clause,[],[f1719,f3221]) ).
fof(f3221,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1719,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3219,plain,
spl0_12,
inference(avatar_split_clause,[],[f1717,f3216]) ).
fof(f1717,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3214,plain,
spl0_11,
inference(avatar_split_clause,[],[f1716,f3211]) ).
fof(f3211,plain,
( spl0_11
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1716,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3209,plain,
spl0_10,
inference(avatar_split_clause,[],[f1715,f3206]) ).
fof(f1715,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3204,plain,
spl0_9,
inference(avatar_split_clause,[],[f1714,f3201]) ).
fof(f3201,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1714,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3199,plain,
spl0_8,
inference(avatar_split_clause,[],[f1713,f3196]) ).
fof(f3196,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1713,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3194,plain,
spl0_7,
inference(avatar_split_clause,[],[f1712,f3191]) ).
fof(f3191,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1712,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3189,plain,
spl0_6,
inference(avatar_split_clause,[],[f1711,f3186]) ).
fof(f3186,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1711,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3184,plain,
spl0_5,
inference(avatar_split_clause,[],[f1710,f3181]) ).
fof(f1710,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3179,plain,
spl0_4,
inference(avatar_split_clause,[],[f1709,f3176]) ).
fof(f3176,plain,
( spl0_4
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1709,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3174,plain,
spl0_3,
inference(avatar_split_clause,[],[f1708,f3171]) ).
fof(f3171,plain,
( spl0_3
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1708,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3169,plain,
spl0_2,
inference(avatar_split_clause,[],[f1707,f3166]) ).
fof(f3166,plain,
( spl0_2
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1707,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3164,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2744,f3161]) ).
fof(f2744,axiom,
~ c_Relation_Orefl(v_A,v_r,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT278-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri May 3 12:20:04 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % (24626)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.43 % (24629)WARNING: value z3 for option sas not known
% 0.17/0.43 % (24631)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)
% 0.17/0.43 % (24630)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.43 % (24633)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)
% 0.17/0.43 % (24629)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)
% 0.17/0.43 % (24632)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.43 % (24628)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.43 % (24627)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.67/0.69 TRYING [1]
% 5.09/1.12 TRYING [2]
% 5.34/1.22 TRYING [1]
% 7.42/1.52 TRYING [1]
% 9.05/1.70 TRYING [2]
% 9.52/1.80 % (24631)First to succeed.
% 10.23/1.91 % (24631)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24626"
% 10.23/1.92 % (24631)Refutation found. Thanks to Tanya!
% 10.23/1.92 % SZS status Unsatisfiable for theBenchmark
% 10.23/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 10.79/1.99 % (24631)------------------------------
% 10.79/1.99 % (24631)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 10.79/1.99 % (24631)Termination reason: Refutation
% 10.79/1.99
% 10.79/1.99 % (24631)Memory used [KB]: 19745
% 10.79/1.99 % (24631)Time elapsed: 1.487 s
% 10.79/1.99 % (24631)Instructions burned: 2563 (million)
% 10.79/1.99 % (24626)Success in time 1.644 s
%------------------------------------------------------------------------------