TSTP Solution File: ANA012-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA012-1 : 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 : n024.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 04:31:31 EDT 2024
% Result : Unsatisfiable 7.06s 1.44s
% Output : Refutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5083
% Syntax : Number of formulae : 8646 (3158 unt; 0 def)
% Number of atoms : 18776 (2810 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 17351 (7221 ~;7474 |; 0 &)
% (2656 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2737 (2735 usr;2657 prp; 0-3 aty)
% Number of functors : 220 ( 220 usr; 46 con; 0-18 aty)
% Number of variables : 11341 (11341 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30969,plain,
$false,
inference(avatar_sat_refutation,[],[f3206,f3211,f3216,f3221,f3226,f3231,f3236,f3241,f3246,f3251,f3256,f3261,f3266,f3271,f3276,f3281,f3286,f3291,f3296,f3301,f3306,f3311,f3316,f3321,f3326,f3331,f3336,f3341,f3346,f3351,f3356,f3361,f3366,f3371,f3376,f3381,f3386,f3391,f3396,f3401,f3406,f3411,f3416,f3421,f3426,f3431,f3436,f3441,f3446,f3451,f3456,f3461,f3466,f3471,f3476,f3481,f3486,f3491,f3496,f3501,f3506,f3511,f3516,f3521,f3526,f3531,f3536,f3541,f3546,f3551,f3556,f3561,f3566,f3571,f3576,f3581,f3586,f3591,f3596,f3601,f3606,f3611,f3616,f3621,f3626,f3631,f3636,f3641,f3646,f3651,f3656,f3661,f3666,f3671,f3676,f3681,f3686,f3691,f3696,f3701,f3706,f3711,f3716,f3721,f3726,f3731,f3736,f3741,f3746,f3751,f3756,f3760,f3765,f3770,f3774,f3778,f3783,f3788,f3793,f3798,f3803,f3807,f3812,f3817,f3821,f3825,f3829,f3833,f3838,f3843,f3848,f3852,f3856,f3860,f3865,f3869,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,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5902,f5906,f5910,f5914,f5918,f5922,f5926,f5930,f5934,f5938,f5942,f5946,f5950,f5954,f5958,f5962,f5966,f5970,f5974,f5978,f5982,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6014,f6018,f6022,f6026,f6030,f6034,f6038,f6042,f6046,f6050,f6054,f6058,f6062,f6066,f6070,f6074,f6078,f6082,f6086,f6090,f6094,f6098,f6102,f6106,f6110,f6114,f6118,f6122,f6126,f6130,f6134,f6138,f6142,f6146,f6150,f6154,f6158,f6162,f6166,f6170,f6174,f6178,f6182,f6186,f6190,f6194,f6198,f6202,f6206,f6210,f6214,f6218,f6222,f6226,f6230,f6234,f6238,f6242,f6246,f6250,f6254,f6258,f6262,f6266,f6270,f6274,f6278,f6282,f6286,f6290,f6294,f6298,f6302,f6306,f6310,f6314,f6318,f6322,f6326,f6330,f6334,f6338,f6342,f6346,f6350,f6354,f6358,f6362,f6366,f6370,f6374,f6378,f6382,f6386,f6390,f6394,f6398,f6402,f6406,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6446,f6450,f6454,f6458,f6462,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6494,f6498,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6530,f6534,f6538,f6542,f6546,f6550,f6554,f6558,f6562,f6566,f6570,f6574,f6578,f6582,f6586,f6590,f6594,f6598,f6602,f6606,f6610,f6614,f6618,f6622,f6626,f6630,f6634,f6638,f6642,f6646,f6650,f6654,f6658,f6662,f6666,f6670,f6674,f6678,f6682,f6686,f6690,f6694,f6698,f6702,f6706,f6710,f6714,f6718,f6722,f6726,f6730,f6734,f6738,f6742,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f6778,f6782,f6786,f6790,f6794,f6798,f6802,f6806,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f6838,f6842,f6846,f6850,f6854,f6858,f6862,f6866,f6870,f6874,f6878,f6882,f6886,f6890,f6894,f6898,f6902,f6906,f6910,f6914,f6918,f6922,f6926,f6930,f6934,f6938,f6942,f6946,f6950,f6954,f6958,f6962,f6966,f6970,f6974,f6978,f6982,f6986,f6990,f6994,f6998,f7002,f7006,f7010,f7014,f7018,f7022,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,f7174,f7178,f7182,f7186,f7190,f7194,f7198,f7202,f7206,f7210,f7214,f7218,f7222,f7226,f7230,f7234,f7238,f7242,f7246,f7250,f7254,f7258,f7262,f7266,f7270,f7274,f7278,f7282,f7286,f7290,f7294,f7298,f7302,f7306,f7310,f7314,f7318,f7322,f7326,f7330,f7334,f7338,f7342,f7346,f7350,f7354,f7358,f7362,f7366,f7370,f7374,f7378,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7415,f7419,f7424,f7429,f7436,f7457,f8107,f8122,f8137,f8152,f8167,f8182,f8197,f8212,f8227,f8242,f8257,f8314,f8329,f8344,f8365,f8390,f8415,f8440,f8465,f8490,f8515,f8577,f8602,f8627,f8652,f8668,f8683,f8704,f8725,f8740,f8755,f8795,f8820,f8845,f8870,f8895,f8910,f8914,f8918,f8922,f8926,f8930,f8934,f8938,f8942,f8947,f8951,f8955,f8959,f8963,f8967,f8971,f8975,f8980,f8985,f8990,f8995,f8999,f9003,f9007,f9012,f9016,f9020,f9024,f9028,f9032,f9036,f9041,f9045,f9050,f9055,f9060,f9065,f9070,f9075,f9080,f9085,f9090,f9095,f9100,f9105,f9110,f9115,f9120,f9125,f9130,f9134,f9138,f9142,f9162,f9166,f9170,f9175,f9180,f9185,f9189,f9193,f9197,f9201,f9206,f9210,f9214,f9219,f9224,f9228,f9233,f9238,f9242,f9246,f9250,f9255,f9259,f9263,f9267,f9271,f9275,f9279,f9283,f9287,f9291,f9295,f9300,f9304,f9309,f9313,f9318,f9340,f9346,f9357,f9362,f9367,f9373,f9378,f9395,f9399,f9403,f9407,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9547,f9551,f9555,f9559,f9563,f9567,f9572,f9576,f9580,f9584,f9588,f9593,f9597,f9601,f9605,f9609,f9613,f9617,f9621,f9625,f9629,f9633,f9638,f9642,f9646,f9650,f9654,f9658,f9662,f9666,f9670,f9674,f9678,f9683,f9687,f9691,f9695,f9699,f9703,f9707,f9711,f9715,f9719,f9723,f9728,f9732,f9736,f9741,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9774,f9778,f9782,f9786,f9790,f9794,f9798,f9802,f9806,f9810,f9814,f9820,f9824,f9828,f9833,f9837,f9842,f9846,f9851,f9855,f10194,f10198,f10202,f10206,f10210,f10214,f10218,f10222,f10230,f10234,f10238,f10242,f10246,f10250,f10254,f10258,f10262,f10266,f10274,f10278,f10282,f10286,f10290,f10294,f10298,f10302,f10306,f10310,f10316,f10320,f10324,f10328,f10332,f10336,f10340,f10344,f10348,f10352,f10358,f10362,f10366,f10370,f10374,f10378,f10382,f10386,f10390,f10394,f10399,f10403,f10407,f10411,f10415,f10419,f10423,f10427,f10431,f10435,f10468,f10473,f10478,f10482,f10486,f10490,f10676,f10681,f10685,f10689,f10693,f10697,f10701,f10705,f10709,f10713,f10733,f10737,f10741,f10745,f10749,f10753,f10757,f10761,f10765,f10769,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10842,f10846,f10874,f10878,f10882,f10886,f10890,f10894,f10898,f10902,f10906,f10910,f10933,f10937,f10941,f10945,f10949,f10953,f10957,f10961,f10965,f10969,f10987,f10991,f10995,f10999,f11003,f11007,f11011,f11015,f11019,f11023,f11032,f11037,f11041,f11045,f11049,f11053,f11057,f11061,f11065,f11069,f11076,f11080,f11084,f11088,f11092,f11096,f11100,f11104,f11108,f11112,f11147,f11151,f11155,f11440,f11444,f11448,f11452,f11456,f11464,f11468,f11472,f11476,f11480,f11484,f11488,f11492,f11496,f11500,f11507,f11511,f11515,f11519,f11523,f11527,f11531,f11535,f11539,f11543,f11550,f11554,f11558,f11562,f11566,f11570,f11574,f11578,f11582,f11586,f11604,f11608,f11612,f11616,f11620,f11624,f11628,f11632,f11636,f11640,f11653,f11657,f11661,f11665,f11669,f11673,f11677,f11681,f11685,f11689,f11701,f11705,f11709,f11713,f11717,f11721,f11725,f11729,f11733,f11737,f11746,f11750,f11754,f11758,f11762,f11766,f11770,f11774,f11778,f11782,f11787,f11791,f12054,f12081,f12086,f12090,f12094,f12098,f12102,f12106,f12110,f12114,f12118,f12122,f12126,f12131,f12135,f12139,f12143,f12147,f12151,f12155,f12159,f12163,f12167,f12171,f12176,f12180,f12184,f12188,f12192,f12196,f12200,f12204,f12209,f12213,f12217,f12222,f12226,f12230,f12234,f12238,f12242,f12246,f12250,f12254,f12258,f12262,f12267,f12271,f12275,f12279,f12283,f12287,f12291,f12295,f12299,f12303,f12307,f12312,f12316,f12320,f12324,f12328,f12332,f12336,f12340,f12344,f12348,f12352,f12357,f12361,f12365,f12369,f12373,f12378,f12382,f12387,f12394,f12399,f12403,f12407,f12411,f12415,f12518,f12636,f12640,f12644,f12648,f12652,f12656,f12661,f12666,f12670,f12674,f12678,f12682,f12686,f12690,f12694,f12698,f12706,f12710,f12714,f12718,f12722,f12726,f12730,f12734,f12738,f12742,f12746,f12750,f12754,f12758,f12762,f12766,f12770,f12774,f12778,f12782,f12786,f12790,f12794,f12798,f12802,f12806,f12810,f12814,f12818,f12822,f12826,f12830,f12834,f12838,f12842,f12846,f12850,f12854,f12858,f12862,f12866,f12870,f12874,f12878,f12882,f12886,f12890,f12894,f12898,f12902,f12906,f12910,f12914,f12919,f12923,f12931,f12935,f12939,f12943,f12947,f12951,f12967,f12990,f13005,f13067,f13107,f13156,f13266,f13298,f13334,f13338,f13342,f13346,f13350,f13354,f13358,f13362,f13366,f13370,f13374,f13378,f13382,f13386,f13390,f13394,f13398,f13402,f13406,f13410,f13414,f13418,f13422,f13426,f13430,f13434,f13438,f13443,f13448,f13452,f13456,f13460,f13464,f13468,f13472,f13476,f13480,f13484,f13488,f13492,f13496,f13500,f13504,f13508,f13512,f13516,f13520,f13524,f13528,f13532,f13536,f13540,f13544,f13548,f13553,f13557,f13561,f13565,f13569,f13573,f13577,f13581,f13585,f13589,f13593,f13597,f13601,f13605,f13609,f13613,f13617,f13621,f13625,f13629,f13633,f13637,f13641,f13645,f13649,f13653,f13657,f13661,f13665,f13669,f13673,f13677,f13681,f13685,f13689,f13693,f13697,f13701,f13705,f13709,f13713,f13717,f13721,f13725,f13729,f13733,f13737,f13741,f13745,f13749,f13754,f13758,f13762,f13766,f13770,f13774,f13778,f13782,f13786,f13790,f13795,f13799,f13803,f13807,f13811,f13815,f13819,f13823,f13827,f14319,f14451,f14628,f14632,f14636,f14640,f14644,f14649,f14653,f14657,f14661,f14665,f14669,f14673,f14677,f14681,f14685,f14689,f14693,f14697,f14701,f14705,f14709,f14713,f14717,f14721,f14725,f14729,f14734,f14738,f14742,f14746,f14750,f14754,f14758,f14762,f14766,f14770,f14774,f14785,f14789,f14793,f14797,f14801,f14805,f14809,f14813,f14817,f14821,f14826,f14830,f14834,f14838,f14842,f14846,f14850,f14854,f14858,f14862,f14866,f14870,f14874,f14878,f14882,f14886,f14890,f14894,f14898,f14902,f14906,f14910,f14914,f14918,f14922,f14926,f14930,f14934,f14938,f14942,f14946,f14950,f14967,f14971,f14975,f14979,f14983,f14987,f14991,f14995,f14999,f15003,f15008,f15012,f15016,f15021,f15028,f15032,f15036,f15040,f15045,f15054,f15058,f15063,f15095,f15099,f15103,f15107,f15111,f15115,f15120,f15124,f15282,f15475,f15632,f15729,f15832,f15894,f16136,f16140,f16162,f16166,f16170,f16174,f16178,f16182,f16186,f16190,f16194,f16198,f16206,f16210,f16214,f16218,f16222,f16226,f16230,f16234,f16238,f16242,f16255,f16259,f16263,f16267,f16271,f16275,f16279,f16283,f16287,f16291,f16299,f16303,f16307,f16311,f16315,f16319,f16323,f16327,f16331,f16335,f16340,f16344,f16348,f16352,f16356,f16360,f16364,f16368,f16372,f16376,f16380,f16386,f16390,f16394,f16398,f16402,f16406,f16410,f16414,f16418,f16422,f16427,f16431,f16435,f16439,f16443,f16447,f16451,f16455,f16459,f16463,f16468,f16477,f16481,f16485,f16489,f16532,f16901,f17080,f17167,f17301,f17413,f17436,f17440,f17444,f17448,f17452,f17456,f17460,f17464,f17468,f17472,f17486,f17490,f17494,f17498,f17502,f17506,f17510,f17514,f17518,f17522,f17535,f17539,f17543,f17547,f17551,f17555,f17559,f17563,f17567,f17571,f17592,f17596,f17600,f17604,f17608,f17612,f17616,f17620,f17624,f17628,f17632,f17636,f17640,f17644,f17648,f17652,f17656,f17660,f17664,f17668,f17672,f17677,f17681,f17685,f17689,f17693,f17697,f17701,f17706,f17730,f17735,f17739,f17757,f17762,f17782,f17786,f17790,f17794,f17798,f17805,f17809,f17813,f17817,f17821,f17825,f17902,f18260,f18432,f18737,f18785,f18789,f18793,f18797,f18801,f18805,f18809,f18813,f18817,f18821,f18825,f18829,f18833,f18837,f18841,f18845,f18849,f18853,f18857,f18861,f18865,f18869,f18873,f18878,f18882,f18886,f18890,f18894,f18899,f18903,f18907,f18911,f18915,f18919,f18923,f18927,f18931,f18935,f18940,f18944,f18948,f18952,f18956,f18960,f18964,f18968,f18972,f18976,f18981,f18985,f18989,f18993,f18997,f19001,f19005,f19009,f19013,f19017,f19022,f19026,f19030,f19034,f19039,f19058,f19063,f19114,f19119,f19212,f19217,f19313,f19318,f19348,f19353,f19371,f19375,f19380,f19388,f19393,f19403,f19409,f19415,f19419,f19425,f19431,f19437,f19441,f19445,f19449,f19453,f19459,f19494,f19498,f19502,f19517,f19801,f20055,f20580,f20724,f20728,f20741,f20745,f20749,f20753,f20757,f20761,f20765,f20769,f20773,f20777,f20781,f20785,f20789,f20793,f20797,f20801,f20805,f20809,f20813,f20817,f20821,f20835,f20839,f20843,f20847,f20851,f20855,f20859,f20863,f20867,f20871,f20875,f20879,f20883,f20887,f20891,f20895,f20899,f20903,f20907,f20911,f20915,f20926,f20930,f20934,f20938,f20942,f20946,f20950,f20954,f20958,f20962,f20966,f20970,f20974,f20978,f20984,f21010,f21016,f21102,f21107,f21140,f21144,f21148,f21153,f21158,f21163,f21168,f21173,f21177,f21182,f21186,f21190,f21194,f21199,f21216,f21220,f21231,f21236,f21241,f21246,f21250,f21255,f21259,f21264,f21268,f21276,f21280,f21285,f21293,f21297,f21301,f21305,f21318,f21423,f21709,f21802,f21920,f22076,f22248,f22252,f22295,f22299,f22303,f22307,f22311,f22315,f22319,f22323,f22327,f22331,f22374,f22380,f22386,f22390,f22394,f22398,f22402,f22406,f22410,f22414,f22457,f22461,f22465,f22469,f22473,f22477,f22481,f22485,f22489,f22493,f22536,f22540,f22544,f22548,f22552,f22556,f22560,f22566,f22728,f22935,f22939,f23165,f23568,f23573,f23577,f23581,f23586,f23590,f23594,f23599,f23603,f23607,f23611,f23615,f23619,f23623,f23627,f23631,f23635,f23639,f23643,f23703,f23707,f23739,f24135,f24139,f24143,f24147,f24151,f24155,f24159,f24163,f24167,f24171,f24175,f24179,f24183,f24187,f24192,f24196,f24200,f24204,f24208,f24213,f24218,f24224,f24245,f24250,f24254,f24266,f24270,f24274,f24279,f24299,f24304,f24331,f24335,f24339,f24344,f24464,f24661,f24665,f24758,f24762,f24766,f24770,f24774,f24778,f24782,f24786,f24790,f24794,f24798,f24808,f24812,f24816,f24820,f24824,f24828,f24832,f24836,f24840,f24844,f24848,f24852,f24856,f24860,f24864,f24868,f24872,f24876,f24880,f24884,f24888,f24900,f24904,f24908,f24912,f24916,f24920,f24924,f24928,f24932,f24936,f24940,f24944,f24948,f24952,f24956,f24960,f24964,f24968,f24972,f24976,f24980,f24987,f24991,f24995,f24999,f25003,f25007,f25011,f25015,f25019,f25023,f25030,f25034,f25052,f25059,f25080,f25084,f25088,f25092,f25098,f25173,f25177,f25181,f25185,f25189,f25193,f25197,f25201,f25206,f25210,f25237,f25243,f25514,f25522,f25725,f26125,f26129,f26133,f26137,f26141,f26145,f26149,f26153,f26157,f26161,f26165,f26169,f26173,f26177,f26181,f26185,f26189,f26193,f26197,f26201,f26205,f26209,f26213,f26217,f26221,f26225,f26229,f26233,f26237,f26244,f26248,f26252,f26256,f26260,f26264,f26268,f26272,f26276,f26280,f26284,f26530,f26804,f27051,f27055,f27059,f27063,f27067,f27071,f27075,f27079,f27083,f27087,f27091,f27095,f27099,f27103,f27110,f27114,f27118,f27122,f27126,f27130,f27134,f27139,f27164,f27169,f27173,f27223,f27227,f27231,f27236,f28030,f28034,f28044,f28048,f28052,f28056,f28061,f28066,f28070,f28074,f28078,f28082,f28092,f28096,f28100,f28106,f28112,f28196,f28200,f28204,f28208,f28213,f28217,f28227,f28231,f28304,f28308,f28312,f28568,f28635,f28670,f28674,f28678,f28682,f28686,f28690,f28694,f28698,f28843,f28847,f28851,f28855,f28859,f28863,f28867,f28871,f28875,f28879,f28883,f28929,f28933,f28937,f28941,f28945,f29038,f29279,f29283,f29287,f29291,f29295,f29300,f29402,f29456,f29460,f29464,f29468,f29472,f29476,f29480,f29484,f29488,f29492,f29496,f29500,f29504,f29508,f29512,f29516,f29520,f29524,f29528,f29532,f29536,f29540,f29544,f29548,f29552,f29558,f29566,f29572,f29596,f29602,f29618,f29624,f29673,f29679,f29734,f29739,f30300,f30389,f30393,f30418,f30422,f30426,f30430,f30434,f30439,f30494,f30528,f30532,f30536,f30540,f30544,f30548,f30552,f30637,f30827,f30831,f30903,f30919,f30923,f30927,f30931,f30935,f30939,f30945,f30965,f30968]) ).
fof(f30968,plain,
( ~ spl0_1127
| spl0_2
| ~ spl0_1546
| ~ spl0_2637 ),
inference(avatar_split_clause,[],[f30914,f30487,f12277,f3208,f9203]) ).
fof(f9203,plain,
( spl0_1127
<=> class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f3208,plain,
( spl0_2
<=> c_0 = v_c ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f12277,plain,
( spl0_1546
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_0 != c_HOL_Oabs(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f30487,plain,
( spl0_2637
<=> c_0 = c_HOL_Oabs(v_c,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2637])]) ).
fof(f30914,plain,
( c_0 = v_c
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1546
| ~ spl0_2637 ),
inference(trivial_inequality_removal,[],[f30909]) ).
fof(f30909,plain,
( c_0 != c_0
| c_0 = v_c
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1546
| ~ spl0_2637 ),
inference(superposition,[],[f12278,f30489]) ).
fof(f30489,plain,
( c_0 = c_HOL_Oabs(v_c,t_a)
| ~ spl0_2637 ),
inference(avatar_component_clause,[],[f30487]) ).
fof(f12278,plain,
( ! [X3,X0] :
( c_0 != c_HOL_Oabs(X3,X0)
| c_0 = X3
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1546 ),
inference(avatar_component_clause,[],[f12277]) ).
fof(f30965,plain,
spl0_2656,
inference(avatar_split_clause,[],[f3073,f30963]) ).
fof(f30963,plain,
( spl0_2656
<=> ! [X34,X24] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2656])]) ).
fof(f3073,plain,
! [X34,X24] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3072,f1050]) ).
fof(f1050,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(f3072,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3071,f2838]) ).
fof(f2838,plain,
! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),
inference(definition_unfolding,[],[f995,f1438,f1438]) ).
fof(f1438,axiom,
! [X36] : c_Suc(X36) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f995,axiom,
! [X11,X24] : c_Suc(c_plus(X24,X11,tc_nat)) = c_plus(c_Suc(X24),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3071,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2888,f3038]) ).
fof(f3038,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3037,f1050]) ).
fof(f3037,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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,[],[f3036,f1048]) ).
fof(f1048,axiom,
! [X33] : c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3036,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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,[],[f2857,f1050]) ).
fof(f2857,plain,
! [X11] : c_plus(X11,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(X11,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f776,f1438,f1438]) ).
fof(f776,axiom,
! [X11] : c_Suc(c_Suc(X11)) = c_plus(X11,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(f2888,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,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(X24,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(definition_unfolding,[],[f774,f1438,f1438,f1438]) ).
fof(f774,axiom,
! [X34,X24] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X24))),c_Numeral_Onumber__of(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f30945,plain,
( spl0_2655
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2654 ),
inference(avatar_split_clause,[],[f30941,f30937,f22564,f13801,f13502,f9018,f3835,f30943]) ).
fof(f30943,plain,
( spl0_2655
<=> ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X24,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2655])]) ).
fof(f3835,plain,
( spl0_129
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f9018,plain,
( spl0_1090
<=> ! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f13502,plain,
( spl0_1707
<=> ! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f13801,plain,
( spl0_1781
<=> ! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f22564,plain,
( spl0_2306
<=> ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).
fof(f30937,plain,
( spl0_2654
<=> ! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2654])]) ).
fof(f30941,plain,
( ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X24,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2654 ),
inference(forward_demodulation,[],[f30940,f22565]) ).
fof(f22565,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat)
| ~ spl0_2306 ),
inference(avatar_component_clause,[],[f22564]) ).
fof(f30940,plain,
( ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X24,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(X34,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2654 ),
inference(forward_demodulation,[],[f30938,f14546]) ).
fof(f14546,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f14545,f9019]) ).
fof(f9019,plain,
( ! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f9018]) ).
fof(f14545,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_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781 ),
inference(forward_demodulation,[],[f14507,f14035]) ).
fof(f14035,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_129
| ~ spl0_1707 ),
inference(superposition,[],[f13503,f3837]) ).
fof(f3837,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f3835]) ).
fof(f13503,plain,
( ! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_1707 ),
inference(avatar_component_clause,[],[f13502]) ).
fof(f14507,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_1090
| ~ spl0_1781 ),
inference(superposition,[],[f9019,f13802]) ).
fof(f13802,plain,
( ! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat))
| ~ spl0_1781 ),
inference(avatar_component_clause,[],[f13801]) ).
fof(f30938,plain,
( ! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ spl0_2654 ),
inference(avatar_component_clause,[],[f30937]) ).
fof(f30939,plain,
spl0_2654,
inference(avatar_split_clause,[],[f3070,f30937]) ).
fof(f3070,plain,
! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3069,f1050]) ).
fof(f3069,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3068,f2838]) ).
fof(f3068,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2887,f3038]) ).
fof(f2887,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,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(X24,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(definition_unfolding,[],[f773,f1438,f1438,f1438]) ).
fof(f773,axiom,
! [X34,X24] : c_div(c_Suc(c_Suc(c_Suc(X24))),c_Numeral_Onumber__of(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f30935,plain,
spl0_2653,
inference(avatar_split_clause,[],[f2965,f30933]) ).
fof(f30933,plain,
( spl0_2653
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2653])]) ).
fof(f2965,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1618,f1610]) ).
fof(f1610,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1618,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f30931,plain,
spl0_2652,
inference(avatar_split_clause,[],[f2964,f30929]) ).
fof(f30929,plain,
( spl0_2652
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2652])]) ).
fof(f2964,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1615,f1610]) ).
fof(f1615,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f30927,plain,
spl0_2651,
inference(avatar_split_clause,[],[f1640,f30925]) ).
fof(f30925,plain,
( spl0_2651
<=> ! [X26,X0,X36,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2651])]) ).
fof(f1640,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f30923,plain,
spl0_2650,
inference(avatar_split_clause,[],[f1639,f30921]) ).
fof(f30921,plain,
( spl0_2650
<=> ! [X30,X0,X36,X16,X26] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2650])]) ).
fof(f1639,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f30919,plain,
spl0_2649,
inference(avatar_split_clause,[],[f515,f30917]) ).
fof(f30917,plain,
( spl0_2649
<=> ! [X10,X19,X0,X12,X3,X1] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2649])]) ).
fof(f515,axiom,
! [X3,X10,X0,X1,X19,X12] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f30903,plain,
spl0_2648,
inference(avatar_split_clause,[],[f354,f30901]) ).
fof(f30901,plain,
( spl0_2648
<=> ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2648])]) ).
fof(f354,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f30831,plain,
spl0_2647,
inference(avatar_split_clause,[],[f2936,f30829]) ).
fof(f30829,plain,
( spl0_2647
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2647])]) ).
fof(f2936,plain,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),tc_nat),X0),X0) ),
inference(definition_unfolding,[],[f662,f660,f660]) ).
fof(f660,axiom,
! [X72,X0,X11] : c_List_Osublist(X72,c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Otake(X11,X72,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f662,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olist_OCons(X12,c_List_Otake(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f30827,plain,
spl0_2646,
inference(avatar_split_clause,[],[f1638,f30825]) ).
fof(f30825,plain,
( spl0_2646
<=> ! [X26,X0,X36,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2646])]) ).
fof(f1638,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f30637,plain,
( ~ spl0_2065
| spl0_2638 ),
inference(avatar_contradiction_clause,[],[f30635]) ).
fof(f30635,plain,
( $false
| ~ spl0_2065
| spl0_2638 ),
inference(resolution,[],[f30493,f17901]) ).
fof(f17901,plain,
( ! [X0] : c_lessequals(X0,X0,t_a)
| ~ spl0_2065 ),
inference(avatar_component_clause,[],[f17900]) ).
fof(f17900,plain,
( spl0_2065
<=> ! [X0] : c_lessequals(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f30493,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| spl0_2638 ),
inference(avatar_component_clause,[],[f30491]) ).
fof(f30491,plain,
( spl0_2638
<=> c_lessequals(c_1,c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2638])]) ).
fof(f30552,plain,
spl0_2645,
inference(avatar_split_clause,[],[f2884,f30550]) ).
fof(f30550,plain,
( spl0_2645
<=> ! [X11,X40,X0,X39] : c_List_Osublist(c_append(X39,X40,X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_append(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Osublist(X40,c_SetInterval_OlessThan(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),tc_nat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2645])]) ).
fof(f2884,plain,
! [X40,X39,X0,X11] : c_List_Osublist(c_append(X39,X40,X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_append(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Osublist(X40,c_SetInterval_OlessThan(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),tc_nat),X0),X0),
inference(definition_unfolding,[],[f665,f660,f660,f660]) ).
fof(f665,axiom,
! [X40,X39,X0,X11] : c_List_Otake(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Otake(X11,X39,X0),c_List_Otake(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f30548,plain,
spl0_2644,
inference(avatar_split_clause,[],[f1736,f30546]) ).
fof(f30546,plain,
( spl0_2644
<=> ! [X36,X0,X16,X26,X30] :
( ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2644])]) ).
fof(f1736,axiom,
! [X0,X36,X26,X16,X30] :
( ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f30544,plain,
spl0_2643,
inference(avatar_split_clause,[],[f1705,f30542]) ).
fof(f30542,plain,
( spl0_2643
<=> ! [X81,X82,X20,X0,X16,X19] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X0,X16) = X81 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f1705,axiom,
! [X82,X0,X81,X19,X16,X20] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X0,X16) = X81 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f30540,plain,
spl0_2642,
inference(avatar_split_clause,[],[f892,f30538]) ).
fof(f30538,plain,
( spl0_2642
<=> ! [X34,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f892,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f30536,plain,
spl0_2641,
inference(avatar_split_clause,[],[f886,f30534]) ).
fof(f30534,plain,
( spl0_2641
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f886,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f30532,plain,
spl0_2640,
inference(avatar_split_clause,[],[f880,f30530]) ).
fof(f30530,plain,
( spl0_2640
<=> ! [X34,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f880,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f30528,plain,
spl0_2639,
inference(avatar_split_clause,[],[f874,f30526]) ).
fof(f30526,plain,
( spl0_2639
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2639])]) ).
fof(f874,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f30494,plain,
( spl0_2637
| ~ spl0_2638
| ~ spl0_112
| ~ spl0_2563 ),
inference(avatar_split_clause,[],[f29999,f28684,f3758,f30491,f30487]) ).
fof(f3758,plain,
( spl0_112
<=> ! [X29] : ~ c_lessequals(c_1,c_times(X29,c_HOL_Oabs(v_c,t_a),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f28684,plain,
( spl0_2563
<=> ! [X0] :
( c_0 = X0
| c_1 = c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).
fof(f29999,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_0 = c_HOL_Oabs(v_c,t_a)
| ~ spl0_112
| ~ spl0_2563 ),
inference(superposition,[],[f3759,f28685]) ).
fof(f28685,plain,
( ! [X0] :
( c_1 = c_times(c_HOL_Oinverse(X0,t_a),X0,t_a)
| c_0 = X0 )
| ~ spl0_2563 ),
inference(avatar_component_clause,[],[f28684]) ).
fof(f3759,plain,
( ! [X29] : ~ c_lessequals(c_1,c_times(X29,c_HOL_Oabs(v_c,t_a),t_a),t_a)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3758]) ).
fof(f30439,plain,
( spl0_2636
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2635 ),
inference(avatar_split_clause,[],[f30435,f30432,f22564,f9730,f9689,f30437]) ).
fof(f30437,plain,
( spl0_2636
<=> ! [X0,X11,X3] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2636])]) ).
fof(f9689,plain,
( spl0_1233
<=> ! [X10] : c_plus(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f9730,plain,
( spl0_1243
<=> ! [X10] : c_plus(c_0,X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f30432,plain,
( spl0_2635
<=> ! [X0,X11,X3] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2635])]) ).
fof(f30435,plain,
( ! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2635 ),
inference(forward_demodulation,[],[f30433,f22648]) ).
fof(f22648,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_1233
| ~ spl0_1243
| ~ spl0_2306 ),
inference(forward_demodulation,[],[f22569,f9690]) ).
fof(f9690,plain,
( ! [X10] : c_plus(X10,c_0,tc_nat) = X10
| ~ spl0_1233 ),
inference(avatar_component_clause,[],[f9689]) ).
fof(f22569,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_1243
| ~ spl0_2306 ),
inference(superposition,[],[f22565,f9731]) ).
fof(f9731,plain,
( ! [X10] : c_plus(c_0,X10,tc_nat) = X10
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f9730]) ).
fof(f30433,plain,
( ! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_2635 ),
inference(avatar_component_clause,[],[f30432]) ).
fof(f30434,plain,
spl0_2635,
inference(avatar_split_clause,[],[f3161,f30432]) ).
fof(f3161,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f3160,f1050]) ).
fof(f3160,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f3159,f1048]) ).
fof(f3159,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f769,f1050]) ).
fof(f769,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Nat_Opower(c_uminus(X3,X0),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),X11,tc_nat),X0) = c_Nat_Opower(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),X11,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f30430,plain,
spl0_2634,
inference(avatar_split_clause,[],[f2952,f30428]) ).
fof(f30428,plain,
( spl0_2634
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2634])]) ).
fof(f2952,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1617,f1610]) ).
fof(f1617,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f30426,plain,
spl0_2633,
inference(avatar_split_clause,[],[f2951,f30424]) ).
fof(f30424,plain,
( spl0_2633
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2633])]) ).
fof(f2951,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1614,f1610]) ).
fof(f1614,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f30422,plain,
spl0_2632,
inference(avatar_split_clause,[],[f2858,f30420]) ).
fof(f30420,plain,
( spl0_2632
<=> ! [X77,X0] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2632])]) ).
fof(f2858,plain,
! [X0,X77] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0,X0),
inference(definition_unfolding,[],[f1605,f1610,f1610,f1610]) ).
fof(f1605,axiom,
! [X0,X77] : c_Transitive__Closure_Ortrancl(X77,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X77,X0),c_Transitive__Closure_Ortrancl(X77,X0),X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f30418,plain,
spl0_2631,
inference(avatar_split_clause,[],[f1637,f30416]) ).
fof(f30416,plain,
( spl0_2631
<=> ! [X18,X0,X16,X17,X26,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2631])]) ).
fof(f1637,axiom,
! [X0,X18,X26,X16,X17,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f30393,plain,
( spl0_2630
| ~ spl0_1558
| ~ spl0_1851
| ~ spl0_2627 ),
inference(avatar_split_clause,[],[f29740,f29737,f14880,f12326,f30391]) ).
fof(f30391,plain,
( spl0_2630
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2630])]) ).
fof(f12326,plain,
( spl0_1558
<=> ! [X0,X16,X3,X10] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f14880,plain,
( spl0_1851
<=> ! [X16,X0,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f29737,plain,
( spl0_2627
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2627])]) ).
fof(f29740,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1558
| ~ spl0_1851
| ~ spl0_2627 ),
inference(forward_demodulation,[],[f29738,f15823]) ).
fof(f15823,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1558
| ~ spl0_1851 ),
inference(superposition,[],[f12327,f14881]) ).
fof(f14881,plain,
( ! [X0,X16,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f14880]) ).
fof(f12327,plain,
( ! [X3,X10,X0,X16] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10
| ~ spl0_1558 ),
inference(avatar_component_clause,[],[f12326]) ).
fof(f29738,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2627 ),
inference(avatar_component_clause,[],[f29737]) ).
fof(f30389,plain,
( spl0_2629
| ~ spl0_1557
| ~ spl0_1851
| ~ spl0_2626 ),
inference(avatar_split_clause,[],[f29735,f29732,f14880,f12322,f30387]) ).
fof(f30387,plain,
( spl0_2629
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2629])]) ).
fof(f12322,plain,
( spl0_1557
<=> ! [X10,X0,X16,X1] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f29732,plain,
( spl0_2626
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2626])]) ).
fof(f29735,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1557
| ~ spl0_1851
| ~ spl0_2626 ),
inference(forward_demodulation,[],[f29733,f15824]) ).
fof(f15824,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1557
| ~ spl0_1851 ),
inference(superposition,[],[f12323,f14881]) ).
fof(f12323,plain,
( ! [X10,X0,X1,X16] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f12322]) ).
fof(f29733,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2626 ),
inference(avatar_component_clause,[],[f29732]) ).
fof(f30300,plain,
( spl0_114
| spl0_2628
| ~ spl0_1639
| ~ spl0_2563 ),
inference(avatar_split_clause,[],[f29978,f28684,f12876,f30297,f3767]) ).
fof(f3767,plain,
( spl0_114
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f30297,plain,
( spl0_2628
<=> c_1 = c_HOL_Oinverse(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2628])]) ).
fof(f12876,plain,
( spl0_1639
<=> ! [X0] : c_times(X0,c_1,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f29978,plain,
( c_1 = c_HOL_Oinverse(c_1,t_a)
| c_0 = c_1
| ~ spl0_1639
| ~ spl0_2563 ),
inference(superposition,[],[f28685,f12877]) ).
fof(f12877,plain,
( ! [X0] : c_times(X0,c_1,t_a) = X0
| ~ spl0_1639 ),
inference(avatar_component_clause,[],[f12876]) ).
fof(f29739,plain,
spl0_2627,
inference(avatar_split_clause,[],[f3118,f29737]) ).
fof(f3118,plain,
! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f339,f350]) ).
fof(f350,axiom,
! [X37,X19] : c_IntDiv_OnegateSnd(c_Pair(X37,X19,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X37,c_uminus(X19,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f339,axiom,
! [X33] :
( ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,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(f29734,plain,
spl0_2626,
inference(avatar_split_clause,[],[f3117,f29732]) ).
fof(f3117,plain,
! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f329,f350]) ).
fof(f329,axiom,
! [X33] :
( ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,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(f29679,plain,
( spl0_2625
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2624 ),
inference(avatar_split_clause,[],[f29675,f29671,f22564,f13801,f13502,f9730,f9689,f9018,f3835,f29677]) ).
fof(f29677,plain,
( spl0_2625
<=> ! [X24] : c_div(c_plus(X24,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(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2625])]) ).
fof(f29671,plain,
( spl0_2624
<=> ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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_2624])]) ).
fof(f29675,plain,
( ! [X24] : c_div(c_plus(X24,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(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2624 ),
inference(forward_demodulation,[],[f29674,f14546]) ).
fof(f29674,plain,
( ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X24,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2624 ),
inference(forward_demodulation,[],[f29672,f22648]) ).
fof(f29672,plain,
( ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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_2624 ),
inference(avatar_component_clause,[],[f29671]) ).
fof(f29673,plain,
spl0_2624,
inference(avatar_split_clause,[],[f3067,f29671]) ).
fof(f3067,plain,
! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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,[],[f3066,f3038]) ).
fof(f3066,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f3065,f1050]) ).
fof(f3065,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f3064,f1048]) ).
fof(f3064,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f2886,f1050]) ).
fof(f2886,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f778,f1438,f1438,f1438]) ).
fof(f778,axiom,
! [X24] : c_div(c_Suc(c_Suc(X24)),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(X24,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(f29624,plain,
( spl0_2623
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2622 ),
inference(avatar_split_clause,[],[f29620,f29616,f22564,f13801,f13502,f9018,f3835,f29622]) ).
fof(f29622,plain,
( spl0_2623
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2623])]) ).
fof(f29616,plain,
( spl0_2622
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2622])]) ).
fof(f29620,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2622 ),
inference(forward_demodulation,[],[f29619,f22565]) ).
fof(f29619,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2622 ),
inference(forward_demodulation,[],[f29617,f14546]) ).
fof(f29617,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat)
| ~ spl0_2622 ),
inference(avatar_component_clause,[],[f29616]) ).
fof(f29618,plain,
spl0_2622,
inference(avatar_split_clause,[],[f3059,f29616]) ).
fof(f3059,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3058,f1050]) ).
fof(f3058,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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,[],[f3057,f2838]) ).
fof(f3057,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,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,[],[f2881,f3038]) ).
fof(f2881,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f871,f1438,f1438,f1438]) ).
fof(f871,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,c_Suc(c_Suc(c_Suc(X11))),tc_nat) = c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f29602,plain,
( spl0_2621
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2620 ),
inference(avatar_split_clause,[],[f29598,f29594,f22564,f13801,f13502,f9018,f3835,f29600]) ).
fof(f29600,plain,
( spl0_2621
<=> ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f29594,plain,
( spl0_2620
<=> ! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2620])]) ).
fof(f29598,plain,
( ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2620 ),
inference(forward_demodulation,[],[f29597,f22565]) ).
fof(f29597,plain,
( ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2620 ),
inference(forward_demodulation,[],[f29595,f14546]) ).
fof(f29595,plain,
( ! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat)
| ~ spl0_2620 ),
inference(avatar_component_clause,[],[f29594]) ).
fof(f29596,plain,
spl0_2620,
inference(avatar_split_clause,[],[f3056,f29594]) ).
fof(f3056,plain,
! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3055,f1050]) ).
fof(f3055,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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,[],[f3054,f2838]) ).
fof(f3054,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,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,[],[f2880,f3038]) ).
fof(f2880,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f779,f1438,f1438,f1438]) ).
fof(f779,axiom,
! [X11,X24] : c_div(X24,c_Suc(c_Suc(c_Suc(X11))),tc_nat) = c_div(X24,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),X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f29572,plain,
( spl0_2619
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2618 ),
inference(avatar_split_clause,[],[f29568,f29564,f22564,f13801,f13502,f9018,f3835,f29570]) ).
fof(f29570,plain,
( spl0_2619
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2619])]) ).
fof(f29564,plain,
( spl0_2618
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2618])]) ).
fof(f29568,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2618 ),
inference(forward_demodulation,[],[f29567,f14546]) ).
fof(f29567,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16)
| ~ spl0_2306
| ~ spl0_2618 ),
inference(forward_demodulation,[],[f29565,f22565]) ).
fof(f29565,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16)
| ~ spl0_2618 ),
inference(avatar_component_clause,[],[f29564]) ).
fof(f29566,plain,
spl0_2618,
inference(avatar_split_clause,[],[f3053,f29564]) ).
fof(f3053,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2879,f3038]) ).
fof(f2879,plain,
! [X0,X9,X16,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(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f99,f1438,f1438,f1438]) ).
fof(f99,axiom,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X9),X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f29558,plain,
( spl0_2617
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2616 ),
inference(avatar_split_clause,[],[f29554,f29550,f22564,f13801,f13502,f9018,f3835,f29556]) ).
fof(f29556,plain,
( spl0_2617
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2617])]) ).
fof(f29550,plain,
( spl0_2616
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2616])]) ).
fof(f29554,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2306
| ~ spl0_2616 ),
inference(forward_demodulation,[],[f29553,f14546]) ).
fof(f29553,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16)
| ~ spl0_2306
| ~ spl0_2616 ),
inference(forward_demodulation,[],[f29551,f22565]) ).
fof(f29551,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16)
| ~ spl0_2616 ),
inference(avatar_component_clause,[],[f29550]) ).
fof(f29552,plain,
spl0_2616,
inference(avatar_split_clause,[],[f3052,f29550]) ).
fof(f3052,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = 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(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2878,f3038]) ).
fof(f2878,plain,
! [X0,X9,X16,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(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f98,f1438,f1438,f1438]) ).
fof(f98,axiom,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X9),X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f29548,plain,
spl0_2615,
inference(avatar_split_clause,[],[f1738,f29546]) ).
fof(f29546,plain,
( spl0_2615
<=> ! [X30,X0,X36,X16,X26] :
( c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2615])]) ).
fof(f1738,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f29544,plain,
spl0_2614,
inference(avatar_split_clause,[],[f1737,f29542]) ).
fof(f29542,plain,
( spl0_2614
<=> ! [X26,X0,X36,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2614])]) ).
fof(f1737,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f29540,plain,
spl0_2613,
inference(avatar_split_clause,[],[f1634,f29538]) ).
fof(f29538,plain,
( spl0_2613
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X26,X30,X25,X0,X16),c_Main_OuprodE__2(X26,X30,X25,X0,X16),X0,X16) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2613])]) ).
fof(f1634,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X26,X30,X25,X0,X16),c_Main_OuprodE__2(X26,X30,X25,X0,X16),X0,X16) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f29536,plain,
spl0_2612,
inference(avatar_split_clause,[],[f897,f29534]) ).
fof(f29534,plain,
( spl0_2612
<=> ! [X34,X16,X25,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_plus(X1,X25,X16),X16) = c_plus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2612])]) ).
fof(f897,axiom,
! [X1,X16,X34,X25] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_plus(X1,X25,X16),X16) = c_plus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f29532,plain,
spl0_2611,
inference(avatar_split_clause,[],[f896,f29530]) ).
fof(f29530,plain,
( spl0_2611
<=> ! [X34,X16,X25,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_minus(X1,X25,X16),X16) = c_minus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2611])]) ).
fof(f896,axiom,
! [X1,X16,X34,X25] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_minus(X1,X25,X16),X16) = c_minus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f29528,plain,
spl0_2610,
inference(avatar_split_clause,[],[f894,f29526]) ).
fof(f29526,plain,
( spl0_2610
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f894,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f29524,plain,
spl0_2609,
inference(avatar_split_clause,[],[f893,f29522]) ).
fof(f29522,plain,
( spl0_2609
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f893,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f29520,plain,
spl0_2608,
inference(avatar_split_clause,[],[f891,f29518]) ).
fof(f29518,plain,
( spl0_2608
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f891,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f29516,plain,
spl0_2607,
inference(avatar_split_clause,[],[f890,f29514]) ).
fof(f29514,plain,
( spl0_2607
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2607])]) ).
fof(f890,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f29512,plain,
spl0_2606,
inference(avatar_split_clause,[],[f888,f29510]) ).
fof(f29510,plain,
( spl0_2606
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2606])]) ).
fof(f888,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f29508,plain,
spl0_2605,
inference(avatar_split_clause,[],[f887,f29506]) ).
fof(f29506,plain,
( spl0_2605
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2605])]) ).
fof(f887,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f29504,plain,
spl0_2604,
inference(avatar_split_clause,[],[f885,f29502]) ).
fof(f29502,plain,
( spl0_2604
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2604])]) ).
fof(f885,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f29500,plain,
spl0_2603,
inference(avatar_split_clause,[],[f884,f29498]) ).
fof(f29498,plain,
( spl0_2603
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2603])]) ).
fof(f884,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f29496,plain,
spl0_2602,
inference(avatar_split_clause,[],[f882,f29494]) ).
fof(f29494,plain,
( spl0_2602
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f882,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f29492,plain,
spl0_2601,
inference(avatar_split_clause,[],[f881,f29490]) ).
fof(f29490,plain,
( spl0_2601
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2601])]) ).
fof(f881,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f29488,plain,
spl0_2600,
inference(avatar_split_clause,[],[f879,f29486]) ).
fof(f29486,plain,
( spl0_2600
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2600])]) ).
fof(f879,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f29484,plain,
spl0_2599,
inference(avatar_split_clause,[],[f878,f29482]) ).
fof(f29482,plain,
( spl0_2599
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).
fof(f878,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f29480,plain,
spl0_2598,
inference(avatar_split_clause,[],[f876,f29478]) ).
fof(f29478,plain,
( spl0_2598
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).
fof(f876,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f29476,plain,
spl0_2597,
inference(avatar_split_clause,[],[f875,f29474]) ).
fof(f29474,plain,
( spl0_2597
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).
fof(f875,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f29472,plain,
spl0_2596,
inference(avatar_split_clause,[],[f873,f29470]) ).
fof(f29470,plain,
( spl0_2596
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).
fof(f873,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f29468,plain,
spl0_2595,
inference(avatar_split_clause,[],[f872,f29466]) ).
fof(f29466,plain,
( spl0_2595
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).
fof(f872,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f29464,plain,
spl0_2594,
inference(avatar_split_clause,[],[f842,f29462]) ).
fof(f29462,plain,
( spl0_2594
<=> ! [X3,X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_plus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_plus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).
fof(f842,axiom,
! [X3,X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_plus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_plus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f29460,plain,
spl0_2593,
inference(avatar_split_clause,[],[f841,f29458]) ).
fof(f29458,plain,
( spl0_2593
<=> ! [X3,X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_minus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_minus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f841,axiom,
! [X3,X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_minus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_minus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f29456,plain,
spl0_2592,
inference(avatar_split_clause,[],[f756,f29454]) ).
fof(f29454,plain,
( spl0_2592
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).
fof(f756,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f29402,plain,
( spl0_2590
| ~ spl0_2591
| ~ spl0_2307
| ~ spl0_2583 ),
inference(avatar_split_clause,[],[f29254,f29035,f22726,f29399,f29395]) ).
fof(f29395,plain,
( spl0_2590
<=> c_1 = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).
fof(f29399,plain,
( spl0_2591
<=> c_1 = c_uminus(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f22726,plain,
( spl0_2307
<=> ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_a)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).
fof(f29035,plain,
( spl0_2583
<=> c_uminus(c_1,t_a) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f29254,plain,
( c_1 != c_uminus(c_1,t_a)
| c_1 = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_2307
| ~ spl0_2583 ),
inference(superposition,[],[f22727,f29037]) ).
fof(f29037,plain,
( c_uminus(c_1,t_a) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),t_a)
| ~ spl0_2583 ),
inference(avatar_component_clause,[],[f29035]) ).
fof(f22727,plain,
( ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_a)
| c_1 = X0 )
| ~ spl0_2307 ),
inference(avatar_component_clause,[],[f22726]) ).
fof(f29300,plain,
( spl0_2589
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2588 ),
inference(avatar_split_clause,[],[f29296,f29293,f13801,f13502,f9018,f3835,f29298]) ).
fof(f29298,plain,
( spl0_2589
<=> ! [X18,X9,X0,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).
fof(f29293,plain,
( spl0_2588
<=> ! [X18,X9,X0,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).
fof(f29296,plain,
( ! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2588 ),
inference(forward_demodulation,[],[f29294,f14546]) ).
fof(f29294,plain,
( ! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16)
| ~ spl0_2588 ),
inference(avatar_component_clause,[],[f29293]) ).
fof(f29295,plain,
spl0_2588,
inference(avatar_split_clause,[],[f2885,f29293]) ).
fof(f2885,plain,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16),
inference(definition_unfolding,[],[f102,f1438]) ).
fof(f102,axiom,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f29291,plain,
spl0_2587,
inference(avatar_split_clause,[],[f1698,f29289]) ).
fof(f29289,plain,
( spl0_2587
<=> ! [X0,X16,X80,X19] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_OconverseE__1(X19,X80,X16,X0),c_Main_OconverseE__2(X19,X80,X16,X0),X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2587])]) ).
fof(f1698,axiom,
! [X0,X80,X19,X16] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_OconverseE__1(X19,X80,X16,X0),c_Main_OconverseE__2(X19,X80,X16,X0),X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f29287,plain,
spl0_2586,
inference(avatar_split_clause,[],[f1225,f29285]) ).
fof(f29285,plain,
( spl0_2586
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X12,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2586])]) ).
fof(f1225,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X12,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f29283,plain,
spl0_2585,
inference(avatar_split_clause,[],[f1215,f29281]) ).
fof(f29281,plain,
( spl0_2585
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).
fof(f1215,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f29279,plain,
spl0_2584,
inference(avatar_split_clause,[],[f363,f29277]) ).
fof(f29277,plain,
( spl0_2584
<=> ! [X34,X1,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).
fof(f363,axiom,
! [X1,X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,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(f29038,plain,
( spl0_2583
| ~ spl0_1497
| ~ spl0_2550 ),
inference(avatar_split_clause,[],[f28885,f28211,f12051,f29035]) ).
fof(f12051,plain,
( spl0_1497
<=> c_1 = c_IntDef_Oof__int(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f28211,plain,
( spl0_2550
<=> ! [X0] : c_IntDef_Oof__int(c_uminus(X0,tc_IntDef_Oint),t_a) = c_uminus(c_IntDef_Oof__int(X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f28885,plain,
( c_uminus(c_1,t_a) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),t_a)
| ~ spl0_1497
| ~ spl0_2550 ),
inference(superposition,[],[f28212,f12053]) ).
fof(f12053,plain,
( c_1 = c_IntDef_Oof__int(c_1,t_a)
| ~ spl0_1497 ),
inference(avatar_component_clause,[],[f12051]) ).
fof(f28212,plain,
( ! [X0] : c_IntDef_Oof__int(c_uminus(X0,tc_IntDef_Oint),t_a) = c_uminus(c_IntDef_Oof__int(X0,t_a),t_a)
| ~ spl0_2550 ),
inference(avatar_component_clause,[],[f28211]) ).
fof(f28945,plain,
spl0_2582,
inference(avatar_split_clause,[],[f3006,f28943]) ).
fof(f28943,plain,
( spl0_2582
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f3006,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f734,f1023]) ).
fof(f1023,axiom,
! [X33] : c_Numeral_Obin__minus(X33) = c_Numeral_Obin__mult(c_Numeral_OMin,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f734,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f28941,plain,
spl0_2581,
inference(avatar_split_clause,[],[f3005,f28939]) ).
fof(f28939,plain,
( spl0_2581
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).
fof(f3005,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f733,f1023]) ).
fof(f733,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f28937,plain,
spl0_2580,
inference(avatar_split_clause,[],[f3004,f28935]) ).
fof(f28935,plain,
( spl0_2580
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2580])]) ).
fof(f3004,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f736,f1023]) ).
fof(f736,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f28933,plain,
spl0_2579,
inference(avatar_split_clause,[],[f3003,f28931]) ).
fof(f28931,plain,
( spl0_2579
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2579])]) ).
fof(f3003,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f738,f1023]) ).
fof(f738,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f28929,plain,
spl0_2578,
inference(avatar_split_clause,[],[f3001,f28927]) ).
fof(f28927,plain,
( spl0_2578
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).
fof(f3001,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f740,f1023]) ).
fof(f740,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f28883,plain,
spl0_2577,
inference(avatar_split_clause,[],[f1739,f28881]) ).
fof(f28881,plain,
( spl0_2577
<=> ! [X26,X0,X36,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).
fof(f1739,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f28879,plain,
spl0_2576,
inference(avatar_split_clause,[],[f895,f28877]) ).
fof(f28877,plain,
( spl0_2576
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2576])]) ).
fof(f895,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f28875,plain,
spl0_2575,
inference(avatar_split_clause,[],[f889,f28873]) ).
fof(f28873,plain,
( spl0_2575
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2575])]) ).
fof(f889,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f28871,plain,
spl0_2574,
inference(avatar_split_clause,[],[f883,f28869]) ).
fof(f28869,plain,
( spl0_2574
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).
fof(f883,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f28867,plain,
spl0_2573,
inference(avatar_split_clause,[],[f877,f28865]) ).
fof(f28865,plain,
( spl0_2573
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).
fof(f877,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f28863,plain,
spl0_2572,
inference(avatar_split_clause,[],[f688,f28861]) ).
fof(f28861,plain,
( spl0_2572
<=> ! [X16,X40,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2572])]) ).
fof(f688,axiom,
! [X40,X39,X0,X16,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f28859,plain,
spl0_2571,
inference(avatar_split_clause,[],[f687,f28857]) ).
fof(f28857,plain,
( spl0_2571
<=> ! [X16,X40,X0,X12,X39] :
( ~ c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2571])]) ).
fof(f687,axiom,
! [X40,X39,X0,X16,X12] :
( ~ c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f28855,plain,
spl0_2570,
inference(avatar_split_clause,[],[f683,f28853]) ).
fof(f28853,plain,
( spl0_2570
<=> ! [X10,X40,X0,X12,X16,X39] : c_List_Ozip(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X16),X0,X16) = c_List_Olist_OCons(c_Pair(X12,X10,X0,X16),c_List_Ozip(X39,X40,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2570])]) ).
fof(f683,axiom,
! [X40,X39,X0,X10,X16,X12] : c_List_Ozip(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X16),X0,X16) = c_List_Olist_OCons(c_Pair(X12,X10,X0,X16),c_List_Ozip(X39,X40,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f28851,plain,
spl0_2569,
inference(avatar_split_clause,[],[f510,f28849]) ).
fof(f28849,plain,
( spl0_2569
<=> ! [X0,X19,X10] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X10,X0),c_Main_Olexord__Nil__left__2(X10,X0),X0) = X10
| ~ c_in(c_Pair(c_List_Olist_ONil,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2569])]) ).
fof(f510,axiom,
! [X10,X0,X19] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X10,X0),c_Main_Olexord__Nil__left__2(X10,X0),X0) = X10
| ~ c_in(c_Pair(c_List_Olist_ONil,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f28847,plain,
spl0_2568,
inference(avatar_split_clause,[],[f352,f28845]) ).
fof(f28845,plain,
( spl0_2568
<=> ! [X33] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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_2568])]) ).
fof(f352,axiom,
! [X33] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28843,plain,
( spl0_2567
| ~ spl0_1028
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f15839,f14892,f8104,f28841]) ).
fof(f28841,plain,
( spl0_2567
<=> ! [X0] :
( c_0 = X0
| c_1 = c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2567])]) ).
fof(f8104,plain,
( spl0_1028
<=> class_Ring__and__Field_Ofield(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f14892,plain,
( spl0_1854
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(X3,c_HOL_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f15839,plain,
( ! [X0] :
( c_0 = X0
| c_1 = c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) )
| ~ spl0_1028
| ~ spl0_1854 ),
inference(resolution,[],[f14893,f8106]) ).
fof(f8106,plain,
( class_Ring__and__Field_Ofield(t_a)
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8104]) ).
fof(f14893,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(X3,c_HOL_Oinverse(X3,X0),X0) )
| ~ spl0_1854 ),
inference(avatar_component_clause,[],[f14892]) ).
fof(f28698,plain,
spl0_2566,
inference(avatar_split_clause,[],[f3000,f28696]) ).
fof(f28696,plain,
( spl0_2566
<=> ! [X40,X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2566])]) ).
fof(f3000,plain,
! [X40,X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ),
inference(definition_unfolding,[],[f452,f1267]) ).
fof(f1267,axiom,
! [X0,X26,X30] : c_inter(X26,X30,X0) = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f452,axiom,
! [X40,X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_inter(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f28694,plain,
spl0_2565,
inference(avatar_split_clause,[],[f2972,f28692]) ).
fof(f28692,plain,
( spl0_2565
<=> ! [X0,X3,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2565])]) ).
fof(f2972,plain,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1573,f1267,f1267]) ).
fof(f1573,axiom,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_inter(X26,X30,X0)
| c_emptyset = c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
fof(f28690,plain,
spl0_2564,
inference(avatar_split_clause,[],[f2970,f28688]) ).
fof(f28688,plain,
( spl0_2564
<=> ! [X0,X3,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2564])]) ).
fof(f2970,plain,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ),
inference(definition_unfolding,[],[f1557,f1267,f1267]) ).
fof(f1557,axiom,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_inter(X30,X26,X0)
| c_emptyset = c_inter(X30,c_insert(X3,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
fof(f28686,plain,
( spl0_2563
| ~ spl0_1028
| ~ spl0_1853 ),
inference(avatar_split_clause,[],[f15838,f14888,f8104,f28684]) ).
fof(f14888,plain,
( spl0_1853
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(c_HOL_Oinverse(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f15838,plain,
( ! [X0] :
( c_0 = X0
| c_1 = c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) )
| ~ spl0_1028
| ~ spl0_1853 ),
inference(resolution,[],[f14889,f8106]) ).
fof(f14889,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(c_HOL_Oinverse(X3,X0),X3,X0) )
| ~ spl0_1853 ),
inference(avatar_component_clause,[],[f14888]) ).
fof(f28682,plain,
spl0_2562,
inference(avatar_split_clause,[],[f686,f28680]) ).
fof(f28680,plain,
( spl0_2562
<=> ! [X10,X0,X50,X12,X16,X23] : c_List_Ozip(c_List_Oreplicate(X23,X12,X0),c_List_Oreplicate(X50,X10,X16),X0,X16) = c_List_Oreplicate(c_Orderings_Omin(X23,X50,tc_nat),c_Pair(X12,X10,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).
fof(f686,axiom,
! [X50,X10,X0,X16,X12,X23] : c_List_Ozip(c_List_Oreplicate(X23,X12,X0),c_List_Oreplicate(X50,X10,X16),X0,X16) = c_List_Oreplicate(c_Orderings_Omin(X23,X50,tc_nat),c_Pair(X12,X10,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f28678,plain,
spl0_2561,
inference(avatar_split_clause,[],[f592,f28676]) ).
fof(f28676,plain,
( spl0_2561
<=> ! [X11,X0,X23,X39] :
( ~ c_lessequals(c_plus(X11,X23,tc_nat),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Odrop(X11,X39,X0),X23,X0) = c_List_Onth(X39,c_plus(X11,X23,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).
fof(f592,axiom,
! [X39,X0,X11,X23] :
( ~ c_lessequals(c_plus(X11,X23,tc_nat),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Odrop(X11,X39,X0),X23,X0) = c_List_Onth(X39,c_plus(X11,X23,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f28674,plain,
spl0_2560,
inference(avatar_split_clause,[],[f9,f28672]) ).
fof(f28672,plain,
( spl0_2560
<=> ! [X5,X4,X0,X6,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_times(X2,X5,tc_set(X0)),c_times(X4,X6,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2560])]) ).
fof(f9,axiom,
! [X2,X0,X6,X4,X5] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_times(X2,X5,tc_set(X0)),c_times(X4,X6,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono2_0) ).
fof(f28670,plain,
spl0_2559,
inference(avatar_split_clause,[],[f3,f28668]) ).
fof(f28668,plain,
( spl0_2559
<=> ! [X5,X4,X0,X6,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_plus(X2,X5,tc_set(X0)),c_plus(X4,X6,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2559])]) ).
fof(f3,axiom,
! [X2,X0,X6,X4,X5] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_plus(X2,X5,tc_set(X0)),c_plus(X4,X6,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono2_0) ).
fof(f28635,plain,
( spl0_2558
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2553 ),
inference(avatar_split_clause,[],[f28232,f28229,f15052,f3498,f28633]) ).
fof(f28633,plain,
( spl0_2558
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2558])]) ).
fof(f3498,plain,
( spl0_60
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f15052,plain,
( spl0_1888
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f28229,plain,
( spl0_2553
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).
fof(f28232,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2553 ),
inference(forward_demodulation,[],[f28230,f16073]) ).
fof(f16073,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_60
| ~ spl0_1888 ),
inference(resolution,[],[f15053,f3500]) ).
fof(f3500,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f15053,plain,
( ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) )
| ~ spl0_1888 ),
inference(avatar_component_clause,[],[f15052]) ).
fof(f28230,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2553 ),
inference(avatar_component_clause,[],[f28229]) ).
fof(f28568,plain,
( spl0_2557
| ~ spl0_1231
| ~ spl0_1832 ),
inference(avatar_split_clause,[],[f15641,f14803,f9680,f28566]) ).
fof(f28566,plain,
( spl0_2557
<=> ! [X0,X1] : c_uminus(c_minus(X0,X1,t_a),t_a) = c_minus(X1,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).
fof(f9680,plain,
( spl0_1231
<=> class_OrderedGroup_Oab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f14803,plain,
( spl0_1832
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X3,X1,X0),X0) = c_minus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f15641,plain,
( ! [X0,X1] : c_uminus(c_minus(X0,X1,t_a),t_a) = c_minus(X1,X0,t_a)
| ~ spl0_1231
| ~ spl0_1832 ),
inference(resolution,[],[f14804,f9682]) ).
fof(f9682,plain,
( class_OrderedGroup_Oab__group__add(t_a)
| ~ spl0_1231 ),
inference(avatar_component_clause,[],[f9680]) ).
fof(f14804,plain,
( ! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X3,X1,X0),X0) = c_minus(X1,X3,X0) )
| ~ spl0_1832 ),
inference(avatar_component_clause,[],[f14803]) ).
fof(f28312,plain,
( spl0_2556
| ~ spl0_1558
| ~ spl0_1851
| ~ spl0_2535 ),
inference(avatar_split_clause,[],[f28062,f28059,f14880,f12326,f28310]) ).
fof(f28310,plain,
( spl0_2556
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).
fof(f28059,plain,
( spl0_2535
<=> ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).
fof(f28062,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1558
| ~ spl0_1851
| ~ spl0_2535 ),
inference(forward_demodulation,[],[f28060,f15823]) ).
fof(f28060,plain,
( ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2535 ),
inference(avatar_component_clause,[],[f28059]) ).
fof(f28308,plain,
( spl0_2555
| ~ spl0_1231
| ~ spl0_1827 ),
inference(avatar_split_clause,[],[f15585,f14783,f9680,f28306]) ).
fof(f28306,plain,
( spl0_2555
<=> ! [X0,X1] : c_plus(X0,X1,t_a) = c_minus(X0,c_uminus(X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f14783,plain,
( spl0_1827
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,X1,X0) = c_minus(X3,c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f15585,plain,
( ! [X0,X1] : c_plus(X0,X1,t_a) = c_minus(X0,c_uminus(X1,t_a),t_a)
| ~ spl0_1231
| ~ spl0_1827 ),
inference(resolution,[],[f14784,f9682]) ).
fof(f14784,plain,
( ! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,X1,X0) = c_minus(X3,c_uminus(X1,X0),X0) )
| ~ spl0_1827 ),
inference(avatar_component_clause,[],[f14783]) ).
fof(f28304,plain,
( spl0_2554
| ~ spl0_1557
| ~ spl0_1851
| ~ spl0_2534 ),
inference(avatar_split_clause,[],[f28057,f28054,f14880,f12322,f28302]) ).
fof(f28302,plain,
( spl0_2554
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).
fof(f28054,plain,
( spl0_2534
<=> ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).
fof(f28057,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1557
| ~ spl0_1851
| ~ spl0_2534 ),
inference(forward_demodulation,[],[f28055,f15824]) ).
fof(f28055,plain,
( ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2534 ),
inference(avatar_component_clause,[],[f28054]) ).
fof(f28231,plain,
spl0_2553,
inference(avatar_split_clause,[],[f2979,f28229]) ).
fof(f2979,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f753,f1023,f1023]) ).
fof(f753,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f28227,plain,
spl0_2552,
inference(avatar_split_clause,[],[f2894,f28225]) ).
fof(f28225,plain,
( spl0_2552
<=> ! [X34,X0,X33,X25] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f2894,plain,
! [X0,X34,X25,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0),X25,X0) ),
inference(definition_unfolding,[],[f1001,f1023]) ).
fof(f1001,axiom,
! [X0,X34,X25,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X33)),X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f28217,plain,
( spl0_2551
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2549 ),
inference(avatar_split_clause,[],[f28209,f28206,f13801,f13502,f9018,f3835,f28215]) ).
fof(f28215,plain,
( spl0_2551
<=> ! [X77,X11,X14] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_plus(c_1,X11,tc_nat),tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f28206,plain,
( spl0_2549
<=> ! [X77,X11,X14] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f28209,plain,
( ! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_plus(c_1,X11,tc_nat),tc_set(tc_prod(X14,X14)))
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2549 ),
inference(forward_demodulation,[],[f28207,f14546]) ).
fof(f28207,plain,
( ! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14)))
| ~ spl0_2549 ),
inference(avatar_component_clause,[],[f28206]) ).
fof(f28213,plain,
( spl0_2550
| ~ spl0_1050
| ~ spl0_1801 ),
inference(avatar_split_clause,[],[f15218,f14671,f8599,f28211]) ).
fof(f8599,plain,
( spl0_1050
<=> class_Ring__and__Field_Ocomm__ring__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f14671,plain,
( spl0_1801
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_uminus(X35,tc_IntDef_Oint),X0) = c_uminus(c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f15218,plain,
( ! [X0] : c_IntDef_Oof__int(c_uminus(X0,tc_IntDef_Oint),t_a) = c_uminus(c_IntDef_Oof__int(X0,t_a),t_a)
| ~ spl0_1050
| ~ spl0_1801 ),
inference(resolution,[],[f14672,f8601]) ).
fof(f8601,plain,
( class_Ring__and__Field_Ocomm__ring__1(t_a)
| ~ spl0_1050 ),
inference(avatar_component_clause,[],[f8599]) ).
fof(f14672,plain,
( ! [X0,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_uminus(X35,tc_IntDef_Oint),X0) = c_uminus(c_IntDef_Oof__int(X35,X0),X0) )
| ~ spl0_1801 ),
inference(avatar_component_clause,[],[f14671]) ).
fof(f28208,plain,
spl0_2549,
inference(avatar_split_clause,[],[f2882,f28206]) ).
fof(f2882,plain,
! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14))),
inference(definition_unfolding,[],[f1285,f1438]) ).
fof(f1285,axiom,
! [X11,X14,X77] : c_Nat_Opower(X77,c_Suc(X11),tc_set(tc_prod(X14,X14))) = c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f28204,plain,
spl0_2548,
inference(avatar_split_clause,[],[f2877,f28202]) ).
fof(f28202,plain,
( spl0_2548
<=> ! [X0,X3,X26,X30] : c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),c_insert(X3,X30,X0),X0,X0) = c_insert(X3,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).
fof(f2877,plain,
! [X3,X0,X26,X30] : c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),c_insert(X3,X30,X0),X0,X0) = c_insert(X3,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0),
inference(definition_unfolding,[],[f1580,f1267,f1267]) ).
fof(f1580,axiom,
! [X3,X0,X26,X30] : c_inter(c_insert(X3,X26,X0),c_insert(X3,X30,X0),X0) = c_insert(X3,c_inter(X26,X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f28200,plain,
spl0_2547,
inference(avatar_split_clause,[],[f2871,f28198]) ).
fof(f28198,plain,
( spl0_2547
<=> ! [X0,X30,X26] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X26,X0),tc_List_Olist(X0)),c_List_Olists(X30,X0),tc_List_Olist(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2547])]) ).
fof(f2871,plain,
! [X0,X26,X30] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X26,X0),tc_List_Olist(X0)),c_List_Olists(X30,X0),tc_List_Olist(X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f531,f1267,f1267]) ).
fof(f531,axiom,
! [X0,X26,X30] : c_List_Olists(c_inter(X26,X30,X0),X0) = c_inter(c_List_Olists(X26,X0),c_List_Olists(X30,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f28196,plain,
spl0_2546,
inference(avatar_split_clause,[],[f2870,f28194]) ).
fof(f28194,plain,
( spl0_2546
<=> ! [X0,X30,X26] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X26,X0),tc_set(X0)),c_Pow(X30,X0),tc_set(X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).
fof(f2870,plain,
! [X0,X26,X30] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X26,X0),tc_set(X0)),c_Pow(X30,X0),tc_set(X0),tc_set(X0)),
inference(definition_unfolding,[],[f1518,f1267,f1267]) ).
fof(f1518,axiom,
! [X0,X26,X30] : c_Pow(c_inter(X26,X30,X0),X0) = c_inter(c_Pow(X26,X0),c_Pow(X30,X0),tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f28112,plain,
( spl0_2545
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2544 ),
inference(avatar_split_clause,[],[f28108,f28104,f13801,f13502,f9018,f3835,f28110]) ).
fof(f28110,plain,
( spl0_2545
<=> ! [X9,X11] : c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),c_plus(c_1,X9,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).
fof(f28104,plain,
( spl0_2544
<=> ! [X9,X11] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f28108,plain,
( ! [X11,X9] : c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),c_plus(c_1,X9,tc_nat))
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2544 ),
inference(forward_demodulation,[],[f28107,f14546]) ).
fof(f28107,plain,
( ! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2544 ),
inference(forward_demodulation,[],[f28105,f14546]) ).
fof(f28105,plain,
( ! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2544 ),
inference(avatar_component_clause,[],[f28104]) ).
fof(f28106,plain,
spl0_2544,
inference(avatar_split_clause,[],[f2864,f28104]) ).
fof(f2864,plain,
! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f56,f1438,f1438,f1438]) ).
fof(f56,axiom,
! [X11,X9] : c_Binomial_Obinomial(c_Suc(X11),c_Suc(X9)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Suc(X9)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f28100,plain,
spl0_2543,
inference(avatar_split_clause,[],[f2828,f28098]) ).
fof(f28098,plain,
( spl0_2543
<=> ! [X0,X19] : c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).
fof(f2828,plain,
! [X0,X19] : c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1604,f1610,f1610,f1610]) ).
fof(f1604,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X19,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f28096,plain,
spl0_2542,
inference(avatar_split_clause,[],[f1699,f28094]) ).
fof(f28094,plain,
( spl0_2542
<=> ! [X0,X16,X80,X19] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_OconverseE__2(X19,X80,X16,X0),c_Main_OconverseE__1(X19,X80,X16,X0),X0,X16) = X80 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f1699,axiom,
! [X0,X80,X19,X16] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_OconverseE__2(X19,X80,X16,X0),c_Main_OconverseE__1(X19,X80,X16,X0),X0,X16) = X80 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f28092,plain,
spl0_2541,
inference(avatar_split_clause,[],[f1210,f28090]) ).
fof(f28090,plain,
( spl0_2541
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X12,X0),c_Numeral_Onumber__of(X33,tc_nat),X0) = c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f1210,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X12,X0),c_Numeral_Onumber__of(X33,tc_nat),X0) = c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f28082,plain,
spl0_2540,
inference(avatar_split_clause,[],[f720,f28080]) ).
fof(f28080,plain,
( spl0_2540
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X75),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f720,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X75),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f28078,plain,
spl0_2539,
inference(avatar_split_clause,[],[f589,f28076]) ).
fof(f28076,plain,
( spl0_2539
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Numeral_Onumber__of(X34,tc_nat),X0) = c_List_Onth(X39,c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f589,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Numeral_Onumber__of(X34,tc_nat),X0) = c_List_Onth(X39,c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f28074,plain,
spl0_2538,
inference(avatar_split_clause,[],[f467,f28072]) ).
fof(f28072,plain,
( spl0_2538
<=> ! [X11,X40,X0,X39] : c_List_Odrop(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Odrop(X11,X39,X0),c_List_Odrop(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f467,axiom,
! [X40,X39,X0,X11] : c_List_Odrop(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Odrop(X11,X39,X0),c_List_Odrop(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f28070,plain,
spl0_2537,
inference(avatar_split_clause,[],[f465,f28068]) ).
fof(f28068,plain,
( spl0_2537
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).
fof(f465,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f28066,plain,
spl0_2536,
inference(avatar_split_clause,[],[f420,f28064]) ).
fof(f28064,plain,
( spl0_2536
<=> ! [X40,X0,X39,X26] :
( ~ c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).
fof(f420,axiom,
! [X40,X39,X0,X26] :
( ~ c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f28061,plain,
spl0_2535,
inference(avatar_split_clause,[],[f341,f28059]) ).
fof(f341,axiom,
! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28056,plain,
spl0_2534,
inference(avatar_split_clause,[],[f331,f28054]) ).
fof(f331,axiom,
! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28052,plain,
spl0_2533,
inference(avatar_split_clause,[],[f275,f28050]) ).
fof(f28050,plain,
( spl0_2533
<=> ! [X12,X10] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X12,X10,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_2533])]) ).
fof(f275,axiom,
! [X10,X12] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X12,X10,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(f28048,plain,
spl0_2532,
inference(avatar_split_clause,[],[f163,f28046]) ).
fof(f28046,plain,
( spl0_2532
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(X12,c_Finite__Set_OMin(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f163,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(X12,c_Finite__Set_OMin(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f28044,plain,
spl0_2531,
inference(avatar_split_clause,[],[f160,f28042]) ).
fof(f28042,plain,
( spl0_2531
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f160,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f28034,plain,
spl0_2530,
inference(avatar_split_clause,[],[f156,f28032]) ).
fof(f28032,plain,
( spl0_2530
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(c_Finite__Set_OMax(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f156,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(c_Finite__Set_OMax(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f28030,plain,
spl0_2529,
inference(avatar_split_clause,[],[f153,f28028]) ).
fof(f28028,plain,
( spl0_2529
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f153,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f27236,plain,
( spl0_2528
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2527 ),
inference(avatar_split_clause,[],[f27232,f27229,f22564,f9730,f9689,f27234]) ).
fof(f27234,plain,
( spl0_2528
<=> ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_plus(c_1,c_1,tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).
fof(f27229,plain,
( spl0_2527
<=> ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).
fof(f27232,plain,
( ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_plus(c_1,c_1,tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) )
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2527 ),
inference(forward_demodulation,[],[f27230,f22648]) ).
fof(f27230,plain,
( ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) )
| ~ spl0_2527 ),
inference(avatar_component_clause,[],[f27229]) ).
fof(f27231,plain,
spl0_2527,
inference(avatar_split_clause,[],[f3158,f27229]) ).
fof(f3158,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f3157,f1050]) ).
fof(f3157,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f3156,f1048]) ).
fof(f3156,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f768,f1050]) ).
fof(f768,axiom,
! [X16,X33] :
( ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16)
| c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X16) = c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f27227,plain,
spl0_2526,
inference(avatar_split_clause,[],[f3097,f27225]) ).
fof(f27225,plain,
( spl0_2526
<=> ! [X9,X50,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X24,c_minus(X50,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f3097,plain,
! [X50,X9,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X24,c_minus(X50,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f3096,f2843]) ).
fof(f2843,plain,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat),
inference(definition_unfolding,[],[f1434,f1438]) ).
fof(f1434,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Suc(X36),X72,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3096,plain,
! [X50,X9,X24] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),X24,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f2917,f2843]) ).
fof(f2917,plain,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),X24,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat),c_plus(X9,X24,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f692,f1438,f1438]) ).
fof(f692,axiom,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(c_Suc(c_minus(X50,X9,tc_nat)),X24,tc_nat) = c_minus(c_Suc(X50),c_plus(X9,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f27223,plain,
spl0_2525,
inference(avatar_split_clause,[],[f3095,f27221]) ).
fof(f27221,plain,
( spl0_2525
<=> ! [X9,X50,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X50,X9,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f3095,plain,
! [X50,X9,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X50,X9,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f3094,f2842]) ).
fof(f2842,plain,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1441,f1438]) ).
fof(f1441,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Suc(X72),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3094,plain,
! [X50,X9,X24] :
( c_minus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f2916,f2842]) ).
fof(f2916,plain,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f691,f1438,f1438]) ).
fof(f691,axiom,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X24,c_Suc(c_minus(X50,X9,tc_nat)),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),c_Suc(X50),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f27173,plain,
( spl0_2524
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2522 ),
inference(avatar_split_clause,[],[f27165,f27162,f13801,f13502,f9018,f3835,f27171]) ).
fof(f27171,plain,
( spl0_2524
<=> ! [X0,X12,X26] :
( c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_plus(c_1,c_Finite__Set_Ocard(X26,X0),tc_nat)
| c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f27162,plain,
( spl0_2522
<=> ! [X0,X12,X26] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f27165,plain,
( ! [X0,X26,X12] :
( c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_plus(c_1,c_Finite__Set_Ocard(X26,X0),tc_nat)
| c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2522 ),
inference(forward_demodulation,[],[f27163,f14546]) ).
fof(f27163,plain,
( ! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) )
| ~ spl0_2522 ),
inference(avatar_component_clause,[],[f27162]) ).
fof(f27169,plain,
( spl0_2523
| ~ spl0_46
| ~ spl0_1627
| ~ spl0_2262 ),
inference(avatar_split_clause,[],[f21552,f21421,f12828,f3428,f27167]) ).
fof(f27167,plain,
( spl0_2523
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f3428,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f12828,plain,
( spl0_1627
<=> ! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f21421,plain,
( spl0_2262
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f21552,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1627
| ~ spl0_2262 ),
inference(resolution,[],[f21422,f12829]) ).
fof(f12829,plain,
( ! [X0,X12] :
( ~ c_lessequals(c_0,X12,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) )
| ~ spl0_1627 ),
inference(avatar_component_clause,[],[f12828]) ).
fof(f21422,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2262 ),
inference(avatar_component_clause,[],[f21421]) ).
fof(f27164,plain,
spl0_2522,
inference(avatar_split_clause,[],[f2969,f27162]) ).
fof(f2969,plain,
! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f174,f1438]) ).
fof(f174,axiom,
! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Suc(c_Finite__Set_Ocard(X26,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f27139,plain,
( spl0_2521
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2520 ),
inference(avatar_split_clause,[],[f27135,f27132,f13801,f13502,f9018,f3835,f27137]) ).
fof(f27137,plain,
( spl0_2521
<=> ! [X11,X0,X12,X39] : c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) = c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_plus(c_1,X11,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f27132,plain,
( spl0_2520
<=> ! [X11,X0,X12,X39] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).
fof(f27135,plain,
( ! [X39,X0,X11,X12] : c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) = c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_plus(c_1,X11,tc_nat),tc_nat),X0)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2520 ),
inference(forward_demodulation,[],[f27133,f14546]) ).
fof(f27133,plain,
( ! [X39,X0,X11,X12] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0)
| ~ spl0_2520 ),
inference(avatar_component_clause,[],[f27132]) ).
fof(f27134,plain,
spl0_2520,
inference(avatar_split_clause,[],[f2873,f27132]) ).
fof(f2873,plain,
! [X39,X0,X11,X12] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0),
inference(definition_unfolding,[],[f663,f660,f1438,f660]) ).
fof(f663,axiom,
! [X39,X0,X11,X12] : c_List_Otake(c_Suc(X11),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olist_OCons(X12,c_List_Otake(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f27130,plain,
spl0_2519,
inference(avatar_split_clause,[],[f1694,f27128]) ).
fof(f27128,plain,
( spl0_2519
<=> ! [X1,X0,X16,X19,X26] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Pair(c_Main_OImageE__1(X26,X1,X19,X16,X0),X1,X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f1694,axiom,
! [X0,X1,X19,X26,X16] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Pair(c_Main_OImageE__1(X26,X1,X19,X16,X0),X1,X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f27126,plain,
spl0_2518,
inference(avatar_split_clause,[],[f1636,f27124]) ).
fof(f27124,plain,
( spl0_2518
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__1(X26,X30,X25,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f1636,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__1(X26,X30,X25,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f27122,plain,
spl0_2517,
inference(avatar_split_clause,[],[f1635,f27120]) ).
fof(f27120,plain,
( spl0_2517
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__2(X26,X30,X25,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f1635,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__2(X26,X30,X25,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f27118,plain,
spl0_2516,
inference(avatar_split_clause,[],[f1279,f27116]) ).
fof(f27116,plain,
( spl0_2516
<=> ! [X19,X0,X3,X16,X1] :
( ~ c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f1279,axiom,
! [X3,X0,X1,X19,X16] :
( ~ c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f27114,plain,
spl0_2515,
inference(avatar_split_clause,[],[f1278,f27112]) ).
fof(f27112,plain,
( spl0_2515
<=> ! [X19,X0,X3,X16,X1] :
( c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f1278,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f27110,plain,
spl0_2514,
inference(avatar_split_clause,[],[f1226,f27108]) ).
fof(f27108,plain,
( spl0_2514
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f1226,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f27103,plain,
spl0_2513,
inference(avatar_split_clause,[],[f1216,f27101]) ).
fof(f27101,plain,
( spl0_2513
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f1216,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f27099,plain,
spl0_2512,
inference(avatar_split_clause,[],[f771,f27097]) ).
fof(f27097,plain,
( spl0_2512
<=> ! [X34,X33] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f771,axiom,
! [X34,X33] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f27095,plain,
spl0_2511,
inference(avatar_split_clause,[],[f722,f27093]) ).
fof(f27093,plain,
( spl0_2511
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f722,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f27091,plain,
spl0_2510,
inference(avatar_split_clause,[],[f167,f27089]) ).
fof(f27089,plain,
( spl0_2510
<=> ! [X16,X12,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMin(c_insert(X12,X26,X16),X16) = c_Orderings_Omin(X12,c_Finite__Set_OMin(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f167,axiom,
! [X26,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMin(c_insert(X12,X26,X16),X16) = c_Orderings_Omin(X12,c_Finite__Set_OMin(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f27087,plain,
spl0_2509,
inference(avatar_split_clause,[],[f165,f27085]) ).
fof(f27085,plain,
( spl0_2509
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_less(X12,c_Main_OMin__gr__iff__1(X26,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f165,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_less(X12,c_Main_OMin__gr__iff__1(X26,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f27083,plain,
spl0_2508,
inference(avatar_split_clause,[],[f164,f27081]) ).
fof(f27081,plain,
( spl0_2508
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__gr__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f164,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__gr__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f27079,plain,
spl0_2507,
inference(avatar_split_clause,[],[f162,f27077]) ).
fof(f27077,plain,
( spl0_2507
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_lessequals(X12,c_Main_OMin__ge__iff__1(X26,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f162,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_lessequals(X12,c_Main_OMin__ge__iff__1(X26,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f27075,plain,
spl0_2506,
inference(avatar_split_clause,[],[f161,f27073]) ).
fof(f27073,plain,
( spl0_2506
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__ge__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f161,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__ge__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f27071,plain,
spl0_2505,
inference(avatar_split_clause,[],[f158,f27069]) ).
fof(f27069,plain,
( spl0_2505
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_less(c_Main_OMax__less__iff__1(X26,X12,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f158,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_less(c_Main_OMax__less__iff__1(X26,X12,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f27067,plain,
spl0_2504,
inference(avatar_split_clause,[],[f157,f27065]) ).
fof(f27065,plain,
( spl0_2504
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__less__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).
fof(f157,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__less__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f27063,plain,
( spl0_2503
| ~ spl0_46
| ~ spl0_1627
| ~ spl0_2252 ),
inference(avatar_split_clause,[],[f21310,f21262,f12828,f3428,f27061]) ).
fof(f27061,plain,
( spl0_2503
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).
fof(f21262,plain,
( spl0_2252
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f21310,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1627
| ~ spl0_2252 ),
inference(resolution,[],[f21263,f12829]) ).
fof(f21263,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2252 ),
inference(avatar_component_clause,[],[f21262]) ).
fof(f27059,plain,
spl0_2502,
inference(avatar_split_clause,[],[f155,f27057]) ).
fof(f27057,plain,
( spl0_2502
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X26,X12,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).
fof(f155,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X26,X12,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f27055,plain,
spl0_2501,
inference(avatar_split_clause,[],[f154,f27053]) ).
fof(f27053,plain,
( spl0_2501
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__le__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).
fof(f154,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__le__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f27051,plain,
spl0_2500,
inference(avatar_split_clause,[],[f152,f27049]) ).
fof(f27049,plain,
( spl0_2500
<=> ! [X16,X12,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMax(c_insert(X12,X26,X16),X16) = c_Orderings_Omax(X12,c_Finite__Set_OMax(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f152,axiom,
! [X26,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMax(c_insert(X12,X26,X16),X16) = c_Orderings_Omax(X12,c_Finite__Set_OMax(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f26804,plain,
( spl0_2499
| ~ spl0_1590
| ~ spl0_2220 ),
inference(avatar_split_clause,[],[f21116,f20964,f12676,f26802]) ).
fof(f26802,plain,
( spl0_2499
<=> ! [X0,X1] : c_less(c_Orderings_Omin(c_minus(X0,c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f12676,plain,
( spl0_1590
<=> ! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f20964,plain,
( spl0_2220
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f21116,plain,
( ! [X0,X1] : c_less(c_Orderings_Omin(c_minus(X0,c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1590
| ~ spl0_2220 ),
inference(resolution,[],[f20965,f12677]) ).
fof(f12677,plain,
( ! [X35,X33] :
( ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1590 ),
inference(avatar_component_clause,[],[f12676]) ).
fof(f20965,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2220 ),
inference(avatar_component_clause,[],[f20964]) ).
fof(f26530,plain,
( spl0_2498
| ~ spl0_46
| ~ spl0_1630
| ~ spl0_2220 ),
inference(avatar_split_clause,[],[f21112,f20964,f12840,f3428,f26528]) ).
fof(f26528,plain,
( spl0_2498
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f12840,plain,
( spl0_1630
<=> ! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f21112,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1630
| ~ spl0_2220 ),
inference(resolution,[],[f20965,f12841]) ).
fof(f12841,plain,
( ! [X0,X12] :
( ~ c_lessequals(X12,c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) )
| ~ spl0_1630 ),
inference(avatar_component_clause,[],[f12840]) ).
fof(f26284,plain,
( spl0_2497
| ~ spl0_1590
| ~ spl0_2178 ),
inference(avatar_split_clause,[],[f20830,f20779,f12676,f26282]) ).
fof(f26282,plain,
( spl0_2497
<=> ! [X0,X1] : c_less(c_Orderings_Omin(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f20779,plain,
( spl0_2178
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f20830,plain,
( ! [X0,X1] : c_less(c_Orderings_Omin(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ spl0_1590
| ~ spl0_2178 ),
inference(resolution,[],[f20780,f12677]) ).
fof(f20780,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ spl0_2178 ),
inference(avatar_component_clause,[],[f20779]) ).
fof(f26280,plain,
spl0_2496,
inference(avatar_split_clause,[],[f2978,f26278]) ).
fof(f26278,plain,
( spl0_2496
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f2978,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f750,f1023]) ).
fof(f750,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f26276,plain,
spl0_2495,
inference(avatar_split_clause,[],[f2977,f26274]) ).
fof(f26274,plain,
( spl0_2495
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f2977,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f751,f1023]) ).
fof(f751,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f26272,plain,
spl0_2494,
inference(avatar_split_clause,[],[f2950,f26270]) ).
fof(f26270,plain,
( spl0_2494
<=> ! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) = c_List_Osublist(c_List_Oupt(X23,X11),c_SetInterval_OlessThan(X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f2950,plain,
! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) = c_List_Osublist(c_List_Oupt(X23,X11),c_SetInterval_OlessThan(X24,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f671,f660]) ).
fof(f671,axiom,
! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Otake(X24,c_List_Oupt(X23,X11),tc_nat) = c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f26268,plain,
spl0_2493,
inference(avatar_split_clause,[],[f2840,f26266]) ).
fof(f26266,plain,
( spl0_2493
<=> ! [X77,X0] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).
fof(f2840,plain,
! [X0,X77] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1606,f1610,f1610]) ).
fof(f1606,axiom,
! [X0,X77] : c_Transitive__Closure_Ortrancl(X77,X0) = c_Transitive__Closure_Ortrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f26264,plain,
spl0_2492,
inference(avatar_split_clause,[],[f1742,f26262]) ).
fof(f26262,plain,
( spl0_2492
<=> ! [X19,X0,X3,X1] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X3,X1,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f1742,axiom,
! [X3,X0,X1,X19] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X3,X1,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f26260,plain,
spl0_2491,
inference(avatar_split_clause,[],[f1695,f26258]) ).
fof(f26258,plain,
( spl0_2491
<=> ! [X1,X19,X0,X16,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X1,c_Relation_OImage(X19,X26,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f1695,axiom,
! [X3,X0,X1,X19,X26,X16] :
( ~ c_in(X3,X26,X0)
| c_in(X1,c_Relation_OImage(X19,X26,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f26256,plain,
spl0_2490,
inference(avatar_split_clause,[],[f1456,f26254]) ).
fof(f26254,plain,
( spl0_2490
<=> ! [X24,X11,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X23,X11,X0)
| c_minus(c_SetInterval_OatLeastLessThan(X23,X24,X0),c_SetInterval_OatLeastLessThan(X23,X11,X0),tc_set(X0)) = c_SetInterval_OatLeastLessThan(X11,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f1456,axiom,
! [X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X23,X11,X0)
| c_minus(c_SetInterval_OatLeastLessThan(X23,X24,X0),c_SetInterval_OatLeastLessThan(X23,X11,X0),tc_set(X0)) = c_SetInterval_OatLeastLessThan(X11,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f26252,plain,
spl0_2489,
inference(avatar_split_clause,[],[f1339,f26250]) ).
fof(f26250,plain,
( spl0_2489
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,X3,X0)
| ~ c_less(X3,c_0,X0)
| ~ c_less(X1,c_0,X0)
| c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f1339,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,X3,X0)
| ~ c_less(X3,c_0,X0)
| ~ c_less(X1,c_0,X0)
| c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).
fof(f26248,plain,
spl0_2488,
inference(avatar_split_clause,[],[f1338,f26246]) ).
fof(f26246,plain,
( spl0_2488
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| c_less(X1,X3,X0)
| ~ c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f1338,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| c_less(X1,X3,X0)
| ~ c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).
fof(f26244,plain,
spl0_2487,
inference(avatar_split_clause,[],[f1337,f26242]) ).
fof(f26242,plain,
( spl0_2487
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,X3,X0)
| ~ c_less(c_0,X3,X0)
| ~ c_less(c_0,X1,X0)
| c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f1337,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,X3,X0)
| ~ c_less(c_0,X3,X0)
| ~ c_less(c_0,X1,X0)
| c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).
fof(f26237,plain,
spl0_2486,
inference(avatar_split_clause,[],[f1336,f26235]) ).
fof(f26235,plain,
( spl0_2486
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| c_less(X1,X3,X0)
| ~ c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f1336,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| c_less(X1,X3,X0)
| ~ c_less(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).
fof(f26233,plain,
spl0_2485,
inference(avatar_split_clause,[],[f1335,f26231]) ).
fof(f26231,plain,
( spl0_2485
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f1335,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).
fof(f26229,plain,
spl0_2484,
inference(avatar_split_clause,[],[f1334,f26227]) ).
fof(f26227,plain,
( spl0_2484
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f1334,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(X1,c_0,X0)
| ~ c_less(X3,c_0,X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).
fof(f26225,plain,
spl0_2483,
inference(avatar_split_clause,[],[f1333,f26223]) ).
fof(f26223,plain,
( spl0_2483
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f1333,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).
fof(f26221,plain,
spl0_2482,
inference(avatar_split_clause,[],[f1332,f26219]) ).
fof(f26219,plain,
( spl0_2482
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).
fof(f1332,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_less(c_0,X1,X0)
| ~ c_less(c_0,X3,X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Oinverse(X3,X0),c_HOL_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).
fof(f26217,plain,
spl0_2481,
inference(avatar_split_clause,[],[f1250,f26215]) ).
fof(f26215,plain,
( spl0_2481
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f1250,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f26213,plain,
spl0_2480,
inference(avatar_split_clause,[],[f1249,f26211]) ).
fof(f26211,plain,
( spl0_2480
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_less(X12,X10,tc_nat)
| ~ c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f1249,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_less(X12,X10,tc_nat)
| ~ c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f26209,plain,
spl0_2479,
inference(avatar_split_clause,[],[f1245,f26207]) ).
fof(f26207,plain,
( spl0_2479
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f1245,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f26205,plain,
spl0_2478,
inference(avatar_split_clause,[],[f1244,f26203]) ).
fof(f26203,plain,
( spl0_2478
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_lessequals(X12,X10,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f1244,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_lessequals(X12,X10,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f26201,plain,
spl0_2477,
inference(avatar_split_clause,[],[f1230,f26199]) ).
fof(f26199,plain,
( spl0_2477
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f1230,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f26197,plain,
( spl0_2476
| ~ spl0_46
| ~ spl0_1630
| ~ spl0_2178 ),
inference(avatar_split_clause,[],[f20826,f20779,f12840,f3428,f26195]) ).
fof(f26195,plain,
( spl0_2476
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).
fof(f20826,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1630
| ~ spl0_2178 ),
inference(resolution,[],[f20780,f12841]) ).
fof(f26193,plain,
spl0_2475,
inference(avatar_split_clause,[],[f1227,f26191]) ).
fof(f26191,plain,
( spl0_2475
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f1227,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f26189,plain,
spl0_2474,
inference(avatar_split_clause,[],[f1224,f26187]) ).
fof(f26187,plain,
( spl0_2474
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f1224,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f26185,plain,
spl0_2473,
inference(avatar_split_clause,[],[f1222,f26183]) ).
fof(f26183,plain,
( spl0_2473
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f1222,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f26181,plain,
spl0_2472,
inference(avatar_split_clause,[],[f1219,f26179]) ).
fof(f26179,plain,
( spl0_2472
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f1219,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f26177,plain,
spl0_2471,
inference(avatar_split_clause,[],[f1213,f26175]) ).
fof(f26175,plain,
( spl0_2471
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2471])]) ).
fof(f1213,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f26173,plain,
spl0_2470,
inference(avatar_split_clause,[],[f1062,f26171]) ).
fof(f26171,plain,
( spl0_2470
<=> ! [X35,X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_times(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).
fof(f1062,axiom,
! [X0,X34,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_times(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f26169,plain,
spl0_2469,
inference(avatar_split_clause,[],[f1002,f26167]) ).
fof(f26167,plain,
( spl0_2469
<=> ! [X35,X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_plus(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).
fof(f1002,axiom,
! [X0,X34,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_plus(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f26165,plain,
spl0_2468,
inference(avatar_split_clause,[],[f755,f26163]) ).
fof(f26163,plain,
( spl0_2468
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).
fof(f755,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f26161,plain,
spl0_2467,
inference(avatar_split_clause,[],[f729,f26159]) ).
fof(f26159,plain,
( spl0_2467
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f729,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f26157,plain,
spl0_2466,
inference(avatar_split_clause,[],[f719,f26155]) ).
fof(f26155,plain,
( spl0_2466
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).
fof(f719,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f26153,plain,
( spl0_2465
| ~ spl0_1588
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f18600,f18430,f12668,f26151]) ).
fof(f26151,plain,
( spl0_2465
<=> ! [X0] : c_lessequals(c_minus(c_plus(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).
fof(f12668,plain,
( spl0_1588
<=> ! [X35,X33] :
( c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f18430,plain,
( spl0_2067
<=> ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f18600,plain,
( ! [X0] : c_lessequals(c_minus(c_plus(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1588
| ~ spl0_2067 ),
inference(resolution,[],[f18431,f12669]) ).
fof(f12669,plain,
( ! [X35,X33] :
( ~ c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1588 ),
inference(avatar_component_clause,[],[f12668]) ).
fof(f18431,plain,
( ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2067 ),
inference(avatar_component_clause,[],[f18430]) ).
fof(f26149,plain,
spl0_2464,
inference(avatar_split_clause,[],[f529,f26147]) ).
fof(f26147,plain,
( spl0_2464
<=> ! [X23,X0,X12,X10,X39] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X39,X23,X12,X0),X23,X10,X0) = c_List_Olist__update(X39,X23,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).
fof(f529,axiom,
! [X39,X0,X10,X12,X23] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X39,X23,X12,X0),X23,X10,X0) = c_List_Olist__update(X39,X23,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f26145,plain,
spl0_2463,
inference(avatar_split_clause,[],[f528,f26143]) ).
fof(f26143,plain,
( spl0_2463
<=> ! [X40,X0,X12,X10,X39] : c_List_Olist__update(c_append(X39,c_List_Olist_OCons(X12,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X10,X0) = c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).
fof(f528,axiom,
! [X40,X39,X0,X10,X12] : c_List_Olist__update(c_append(X39,c_List_Olist_OCons(X12,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X10,X0) = c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f26141,plain,
spl0_2462,
inference(avatar_split_clause,[],[f249,f26139]) ).
fof(f26139,plain,
( spl0_2462
<=> ! [X12,X10] :
( X10 = X12
| c_IntDef_OAbs__Integ(X12) != c_IntDef_OAbs__Integ(X10)
| ~ c_in(X12,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X10,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).
fof(f249,axiom,
! [X10,X12] :
( X10 = X12
| c_IntDef_OAbs__Integ(X12) != c_IntDef_OAbs__Integ(X10)
| ~ c_in(X12,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X10,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(f26137,plain,
spl0_2461,
inference(avatar_split_clause,[],[f188,f26135]) ).
fof(f26135,plain,
( spl0_2461
<=> ! [X16,X10,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omax(X10,c_Finite__Set_OMin(X26,X16),X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f188,axiom,
! [X10,X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omax(X10,c_Finite__Set_OMin(X26,X16),X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f26133,plain,
spl0_2460,
inference(avatar_split_clause,[],[f187,f26131]) ).
fof(f26131,plain,
( spl0_2460
<=> ! [X16,X10,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omin(X10,c_Finite__Set_OMax(X26,X16),X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(f187,axiom,
! [X10,X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omin(X10,c_Finite__Set_OMax(X26,X16),X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f26129,plain,
spl0_2459,
inference(avatar_split_clause,[],[f116,f26127]) ).
fof(f26127,plain,
( spl0_2459
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) = c_div(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(f116,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) = c_div(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f26125,plain,
spl0_2458,
inference(avatar_split_clause,[],[f114,f26123]) ).
fof(f26123,plain,
( spl0_2458
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) = c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(f114,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) = c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f25725,plain,
( spl0_2457
| ~ spl0_1591
| ~ spl0_2371 ),
inference(avatar_split_clause,[],[f24800,f24756,f12680,f25723]) ).
fof(f25723,plain,
( spl0_2457
<=> ! [X0] : ~ c_less(c_plus(c_minus(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).
fof(f12680,plain,
( spl0_1591
<=> ! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f24756,plain,
( spl0_2371
<=> ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2371])]) ).
fof(f24800,plain,
( ! [X0] : ~ c_less(c_plus(c_minus(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1591
| ~ spl0_2371 ),
inference(resolution,[],[f24757,f12681]) ).
fof(f12681,plain,
( ! [X35,X33] :
( c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1591 ),
inference(avatar_component_clause,[],[f12680]) ).
fof(f24757,plain,
( ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2371 ),
inference(avatar_component_clause,[],[f24756]) ).
fof(f25522,plain,
( spl0_2456
| ~ spl0_1155
| ~ spl0_1627
| ~ spl0_2165 ),
inference(avatar_split_clause,[],[f20732,f20578,f12828,f9343,f25520]) ).
fof(f25520,plain,
( spl0_2456
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(c_0,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).
fof(f9343,plain,
( spl0_1155
<=> class_OrderedGroup_Olordered__ab__group(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f20578,plain,
( spl0_2165
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f20732,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(c_0,X0,t_a),t_a) )
| ~ spl0_1627
| ~ spl0_2165 ),
inference(resolution,[],[f20579,f12829]) ).
fof(f20579,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,t_a),t_a)
| ~ spl0_2165 ),
inference(avatar_component_clause,[],[f20578]) ).
fof(f25514,plain,
( spl0_2455
| ~ spl0_1155
| ~ spl0_1627
| ~ spl0_2164 ),
inference(avatar_split_clause,[],[f20346,f20053,f12828,f9343,f25512]) ).
fof(f25512,plain,
( spl0_2455
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).
fof(f20053,plain,
( spl0_2164
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f20346,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,t_a),t_a) )
| ~ spl0_1627
| ~ spl0_2164 ),
inference(resolution,[],[f20054,f12829]) ).
fof(f20054,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,t_a),t_a)
| ~ spl0_2164 ),
inference(avatar_component_clause,[],[f20053]) ).
fof(f25243,plain,
( spl0_2454
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2453 ),
inference(avatar_split_clause,[],[f25239,f25235,f22564,f9730,f9689,f25241]) ).
fof(f25241,plain,
( spl0_2454
<=> ! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).
fof(f25235,plain,
( spl0_2453
<=> ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,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_2453])]) ).
fof(f25239,plain,
( ! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2453 ),
inference(forward_demodulation,[],[f25238,f22648]) ).
fof(f25238,plain,
( ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1233
| ~ spl0_1243
| ~ spl0_2306
| ~ spl0_2453 ),
inference(forward_demodulation,[],[f25236,f22648]) ).
fof(f25236,plain,
( ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_2453 ),
inference(avatar_component_clause,[],[f25235]) ).
fof(f25237,plain,
spl0_2453,
inference(avatar_split_clause,[],[f3144,f25235]) ).
fof(f3144,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3143,f1050]) ).
fof(f3143,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3142,f1048]) ).
fof(f3142,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3141,f1050]) ).
fof(f3141,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f3140,f1050]) ).
fof(f3140,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f3139,f1048]) ).
fof(f3139,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f869,f1050]) ).
fof(f869,axiom,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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(f25210,plain,
( spl0_2452
| ~ spl0_1155
| ~ spl0_1630
| ~ spl0_2163 ),
inference(avatar_split_clause,[],[f19955,f19799,f12840,f9343,f25208]) ).
fof(f25208,plain,
( spl0_2452
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).
fof(f19799,plain,
( spl0_2163
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f19955,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,t_a),t_a) )
| ~ spl0_1630
| ~ spl0_2163 ),
inference(resolution,[],[f19800,f12841]) ).
fof(f19800,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_a),X0,t_a)
| ~ spl0_2163 ),
inference(avatar_component_clause,[],[f19799]) ).
fof(f25206,plain,
( spl0_2451
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2450 ),
inference(avatar_split_clause,[],[f25202,f25199,f13801,f13502,f9018,f3835,f25204]) ).
fof(f25204,plain,
( spl0_2451
<=> ! [X9,X11,X24] : c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2451])]) ).
fof(f25199,plain,
( spl0_2450
<=> ! [X9,X11,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).
fof(f25202,plain,
( ! [X11,X9,X24] : c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2450 ),
inference(forward_demodulation,[],[f25200,f14546]) ).
fof(f25200,plain,
( ! [X11,X9,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat)
| ~ spl0_2450 ),
inference(avatar_component_clause,[],[f25199]) ).
fof(f25201,plain,
spl0_2450,
inference(avatar_split_clause,[],[f3050,f25199]) ).
fof(f3050,plain,
! [X11,X9,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3049,f931]) ).
fof(f931,axiom,
! [X50,X9,X23] : c_minus(c_minus(X23,X50,tc_nat),X9,tc_nat) = c_minus(X23,c_plus(X50,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3049,plain,
! [X11,X9,X24] : c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2874,f2843]) ).
fof(f2874,plain,
! [X11,X9,X24] : c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f912,f1438,f1438]) ).
fof(f912,axiom,
! [X11,X9,X24] : c_minus(c_minus(c_Suc(X24),X11,tc_nat),c_Suc(X9),tc_nat) = c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f25197,plain,
spl0_2449,
inference(avatar_split_clause,[],[f2999,f25195]) ).
fof(f25195,plain,
( spl0_2449
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).
fof(f2999,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1034,f1023]) ).
fof(f1034,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f25193,plain,
spl0_2448,
inference(avatar_split_clause,[],[f2998,f25191]) ).
fof(f25191,plain,
( spl0_2448
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f2998,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1042,f1023]) ).
fof(f1042,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f25189,plain,
spl0_2447,
inference(avatar_split_clause,[],[f2997,f25187]) ).
fof(f25187,plain,
( spl0_2447
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).
fof(f2997,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1043,f1023]) ).
fof(f1043,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f25185,plain,
spl0_2446,
inference(avatar_split_clause,[],[f2996,f25183]) ).
fof(f25183,plain,
( spl0_2446
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).
fof(f2996,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1033,f1023]) ).
fof(f1033,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f25181,plain,
spl0_2445,
inference(avatar_split_clause,[],[f2976,f25179]) ).
fof(f25179,plain,
( spl0_2445
<=> ! [X0,X30,X2,X26] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f2976,plain,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1505,f1267]) ).
fof(f1505,axiom,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f25177,plain,
spl0_2444,
inference(avatar_split_clause,[],[f2947,f25175]) ).
fof(f25175,plain,
( spl0_2444
<=> ! [X3,X0,X30,X26] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).
fof(f2947,plain,
! [X3,X0,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1572,f1267,f1267]) ).
fof(f1572,axiom,
! [X3,X0,X26,X30] :
( c_emptyset = c_inter(X26,X30,X0)
| c_emptyset != c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
fof(f25173,plain,
spl0_2443,
inference(avatar_split_clause,[],[f2945,f25171]) ).
fof(f25171,plain,
( spl0_2443
<=> ! [X0,X3,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f2945,plain,
! [X3,X0,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ),
inference(definition_unfolding,[],[f1556,f1267,f1267]) ).
fof(f1556,axiom,
! [X3,X0,X26,X30] :
( c_emptyset = c_inter(X30,X26,X0)
| c_emptyset != c_inter(X30,c_insert(X3,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
fof(f25098,plain,
( spl0_2442
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2139
| ~ spl0_2441 ),
inference(avatar_split_clause,[],[f25094,f25090,f19316,f13801,f13502,f9689,f9668,f9018,f3835,f25096]) ).
fof(f25096,plain,
( spl0_2442
<=> ! [X50,X23] :
( c_List_Oupt(X23,c_plus(c_1,X50,tc_nat)) = c_append(c_List_Oupt(X23,X50),c_List_Oreplicate(c_1,X50,tc_nat),tc_nat)
| ~ c_lessequals(X23,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2442])]) ).
fof(f9668,plain,
( spl0_1228
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f19316,plain,
( spl0_2139
<=> ! [X11,X12,X14] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f25090,plain,
( spl0_2441
<=> ! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).
fof(f25094,plain,
( ! [X50,X23] :
( c_List_Oupt(X23,c_plus(c_1,X50,tc_nat)) = c_append(c_List_Oupt(X23,X50),c_List_Oreplicate(c_1,X50,tc_nat),tc_nat)
| ~ c_lessequals(X23,X50,tc_nat) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2139
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f25093,f19342]) ).
fof(f19342,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139 ),
inference(forward_demodulation,[],[f19319,f9690]) ).
fof(f19319,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_1228
| ~ spl0_2139 ),
inference(superposition,[],[f19317,f9669]) ).
fof(f9669,plain,
( ! [X14,X12] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14)
| ~ spl0_1228 ),
inference(avatar_component_clause,[],[f9668]) ).
fof(f19317,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14)
| ~ spl0_2139 ),
inference(avatar_component_clause,[],[f19316]) ).
fof(f25093,plain,
( ! [X50,X23] :
( c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| ~ c_lessequals(X23,X50,tc_nat) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f25091,f14546]) ).
fof(f25091,plain,
( ! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) )
| ~ spl0_2441 ),
inference(avatar_component_clause,[],[f25090]) ).
fof(f25092,plain,
spl0_2441,
inference(avatar_split_clause,[],[f2915,f25090]) ).
fof(f2915,plain,
! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f676,f1438]) ).
fof(f676,axiom,
! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_List_Oupt(X23,c_Suc(X50)) = c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f25088,plain,
spl0_2440,
inference(avatar_split_clause,[],[f2876,f25086]) ).
fof(f25086,plain,
( spl0_2440
<=> ! [X0,X30,X26] : c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2440])]) ).
fof(f2876,plain,
! [X0,X26,X30] : c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)),
inference(definition_unfolding,[],[f1469,f1267]) ).
fof(f1469,axiom,
! [X0,X26,X30] : c_uminus(c_inter(X26,X30,X0),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f25084,plain,
spl0_2439,
inference(avatar_split_clause,[],[f2875,f25082]) ).
fof(f25082,plain,
( spl0_2439
<=> ! [X0,X30,X26] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),c_uminus(X30,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2439])]) ).
fof(f2875,plain,
! [X0,X26,X30] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),c_uminus(X30,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1471,f1267]) ).
fof(f1471,axiom,
! [X0,X26,X30] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_inter(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f25080,plain,
spl0_2438,
inference(avatar_split_clause,[],[f2869,f25078]) ).
fof(f25078,plain,
( spl0_2438
<=> ! [X24,X11,X0,X39] : c_List_Osublist(c_List_Osublist(X39,c_SetInterval_OlessThan(X24,tc_nat),X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Osublist(X39,c_SetInterval_OlessThan(c_Orderings_Omin(X11,X24,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2438])]) ).
fof(f2869,plain,
! [X39,X0,X11,X24] : c_List_Osublist(c_List_Osublist(X39,c_SetInterval_OlessThan(X24,tc_nat),X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Osublist(X39,c_SetInterval_OlessThan(c_Orderings_Omin(X11,X24,tc_nat),tc_nat),X0),
inference(definition_unfolding,[],[f670,f660,f660,f660]) ).
fof(f670,axiom,
! [X39,X0,X11,X24] : c_List_Otake(X11,c_List_Otake(X24,X39,X0),X0) = c_List_Otake(c_Orderings_Omin(X11,X24,tc_nat),X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f25059,plain,
( spl0_2437
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2436 ),
inference(avatar_split_clause,[],[f25055,f25050,f13801,f13502,f9018,f3835,f25057]) ).
fof(f25057,plain,
( spl0_2437
<=> ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2437])]) ).
fof(f25050,plain,
( spl0_2436
<=> ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f25055,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2436 ),
inference(forward_demodulation,[],[f25054,f14546]) ).
fof(f25054,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2436 ),
inference(forward_demodulation,[],[f25053,f14546]) ).
fof(f25053,plain,
( ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2436 ),
inference(forward_demodulation,[],[f25051,f14546]) ).
fof(f25051,plain,
( ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2436 ),
inference(avatar_component_clause,[],[f25050]) ).
fof(f25052,plain,
spl0_2436,
inference(avatar_split_clause,[],[f2845,f25050]) ).
fof(f2845,plain,
! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f949,f1438,f1438,f1438]) ).
fof(f949,axiom,
! [X11,X24] : c_Orderings_Omin(c_Suc(X24),c_Suc(X11),tc_nat) = c_Suc(c_Orderings_Omin(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f25034,plain,
( spl0_2435
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2433 ),
inference(avatar_split_clause,[],[f25026,f25021,f13801,f13502,f9018,f3835,f25032]) ).
fof(f25032,plain,
( spl0_2435
<=> ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2435])]) ).
fof(f25021,plain,
( spl0_2433
<=> ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2433])]) ).
fof(f25026,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2433 ),
inference(forward_demodulation,[],[f25025,f14546]) ).
fof(f25025,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2433 ),
inference(forward_demodulation,[],[f25024,f14546]) ).
fof(f25024,plain,
( ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2433 ),
inference(forward_demodulation,[],[f25022,f14546]) ).
fof(f25022,plain,
( ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2433 ),
inference(avatar_component_clause,[],[f25021]) ).
fof(f25030,plain,
( spl0_2434
| ~ spl0_1155
| ~ spl0_1630
| ~ spl0_2161 ),
inference(avatar_split_clause,[],[f19660,f19496,f12840,f9343,f25028]) ).
fof(f25028,plain,
( spl0_2434
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2434])]) ).
fof(f19496,plain,
( spl0_2161
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_a),X1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f19660,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,t_a),t_a) )
| ~ spl0_1630
| ~ spl0_2161 ),
inference(resolution,[],[f19497,f12841]) ).
fof(f19497,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_a),X1,t_a)
| ~ spl0_2161 ),
inference(avatar_component_clause,[],[f19496]) ).
fof(f25023,plain,
spl0_2433,
inference(avatar_split_clause,[],[f2844,f25021]) ).
fof(f2844,plain,
! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f946,f1438,f1438,f1438]) ).
fof(f946,axiom,
! [X11,X24] : c_Orderings_Omax(c_Suc(X24),c_Suc(X11),tc_nat) = c_Suc(c_Orderings_Omax(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f25019,plain,
spl0_2432,
inference(avatar_split_clause,[],[f1700,f25017]) ).
fof(f25017,plain,
( spl0_2432
<=> ! [X25,X0,X26] :
( ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0))
| c_Pair(c_Main_OdiagE__1(X26,X25,X0),c_Main_OdiagE__1(X26,X25,X0),X0,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2432])]) ).
fof(f1700,axiom,
! [X0,X26,X25] :
( ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0))
| c_Pair(c_Main_OdiagE__1(X26,X25,X0),c_Main_OdiagE__1(X26,X25,X0),X0,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f25015,plain,
spl0_2431,
inference(avatar_split_clause,[],[f1696,f25013]) ).
fof(f25013,plain,
( spl0_2431
<=> ! [X19,X0,X16,X1] :
( ~ c_in(X1,c_Relation_ORange(X19,X16,X0),X0)
| c_in(c_Pair(c_Main_ORangeE__1(X1,X19,X0,X16),X1,X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f1696,axiom,
! [X0,X1,X19,X16] :
( ~ c_in(X1,c_Relation_ORange(X19,X16,X0),X0)
| c_in(c_Pair(c_Main_ORangeE__1(X1,X19,X0,X16),X1,X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f25011,plain,
spl0_2430,
inference(avatar_split_clause,[],[f1690,f25009]) ).
fof(f25009,plain,
( spl0_2430
<=> ! [X19,X0,X3,X16] :
( ~ c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| c_in(c_Pair(X3,c_Main_ODomainE__1(X3,X19,X0,X16),X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2430])]) ).
fof(f1690,axiom,
! [X3,X0,X19,X16] :
( ~ c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| c_in(c_Pair(X3,c_Main_ODomainE__1(X3,X19,X0,X16),X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f25007,plain,
spl0_2429,
inference(avatar_split_clause,[],[f1681,f25005]) ).
fof(f25005,plain,
( spl0_2429
<=> ! [X0,X3,X26,X72] :
( ~ c_in(X3,X26,X0)
| ~ c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_List_Olist_OCons(X3,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).
fof(f1681,axiom,
! [X3,X72,X0,X26] :
( ~ c_in(X3,X26,X0)
| ~ c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_List_Olist_OCons(X3,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f25003,plain,
spl0_2428,
inference(avatar_split_clause,[],[f1643,f25001]) ).
fof(f25001,plain,
( spl0_2428
<=> ! [X18,X0,X16,X26,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).
fof(f1643,axiom,
! [X0,X18,X26,X16,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f24999,plain,
spl0_2427,
inference(avatar_split_clause,[],[f1642,f24997]) ).
fof(f24997,plain,
( spl0_2427
<=> ! [X17,X0,X16,X26,X30] :
( ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2427])]) ).
fof(f1642,axiom,
! [X0,X26,X16,X17,X30] :
( ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f24995,plain,
spl0_2426,
inference(avatar_split_clause,[],[f1460,f24993]) ).
fof(f24993,plain,
( spl0_2426
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X24,X23,X0)
| ~ c_lessequals(X50,X11,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2426])]) ).
fof(f1460,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X24,X23,X0)
| ~ c_lessequals(X50,X11,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f24991,plain,
spl0_2425,
inference(avatar_split_clause,[],[f1458,f24989]) ).
fof(f24989,plain,
( spl0_2425
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X50,X11,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2425])]) ).
fof(f1458,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X50,X11,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f24987,plain,
spl0_2424,
inference(avatar_split_clause,[],[f1457,f24985]) ).
fof(f24985,plain,
( spl0_2424
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X24,X23,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f1457,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X24,X23,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f24980,plain,
spl0_2423,
inference(avatar_split_clause,[],[f1270,f24978]) ).
fof(f24978,plain,
( spl0_2423
<=> ! [X3,X19,X0,X16,X1] :
( ~ c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).
fof(f1270,axiom,
! [X3,X0,X1,X19,X16] :
( ~ c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f24976,plain,
spl0_2422,
inference(avatar_split_clause,[],[f1269,f24974]) ).
fof(f24974,plain,
( spl0_2422
<=> ! [X3,X19,X0,X16,X1] :
( c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).
fof(f1269,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f24972,plain,
spl0_2421,
inference(avatar_split_clause,[],[f1229,f24970]) ).
fof(f24970,plain,
( spl0_2421
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).
fof(f1229,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f24968,plain,
spl0_2420,
inference(avatar_split_clause,[],[f1212,f24966]) ).
fof(f24966,plain,
( spl0_2420
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).
fof(f1212,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f24964,plain,
spl0_2419,
inference(avatar_split_clause,[],[f1068,f24962]) ).
fof(f24962,plain,
( spl0_2419
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f1068,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f24960,plain,
spl0_2418,
inference(avatar_split_clause,[],[f1015,f24958]) ).
fof(f24958,plain,
( spl0_2418
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) = c_uminus(c_Numeral_Onumber__of(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f1015,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) = c_uminus(c_Numeral_Onumber__of(X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f24956,plain,
spl0_2417,
inference(avatar_split_clause,[],[f704,f24954]) ).
fof(f24954,plain,
( spl0_2417
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_lessequals(X11,X24,tc_nat)
| c_NatArith_Oof__nat(c_minus(X24,X11,tc_nat),X0) = c_minus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).
fof(f704,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_lessequals(X11,X24,tc_nat)
| c_NatArith_Oof__nat(c_minus(X24,X11,tc_nat),X0) = c_minus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f24952,plain,
spl0_2416,
inference(avatar_split_clause,[],[f566,f24950]) ).
fof(f24950,plain,
( spl0_2416
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f566,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f24948,plain,
spl0_2415,
inference(avatar_split_clause,[],[f565,f24946]) ).
fof(f24946,plain,
( spl0_2415
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).
fof(f565,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f24944,plain,
spl0_2414,
inference(avatar_split_clause,[],[f564,f24942]) ).
fof(f24942,plain,
( spl0_2414
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f564,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f24940,plain,
( spl0_2413
| ~ spl0_1985
| ~ spl0_2307 ),
inference(avatar_split_clause,[],[f22925,f22726,f16899,f24938]) ).
fof(f24938,plain,
( spl0_2413
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = c_NatArith_Oof__nat(X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).
fof(f16899,plain,
( spl0_1985
<=> ! [X0] : c_NatArith_Oof__nat(X0,t_a) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f22925,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = c_NatArith_Oof__nat(X0,tc_IntDef_Oint) )
| ~ spl0_1985
| ~ spl0_2307 ),
inference(superposition,[],[f22727,f16900]) ).
fof(f16900,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,t_a) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_a)
| ~ spl0_1985 ),
inference(avatar_component_clause,[],[f16899]) ).
fof(f24936,plain,
spl0_2412,
inference(avatar_split_clause,[],[f563,f24934]) ).
fof(f24934,plain,
( spl0_2412
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).
fof(f563,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f24932,plain,
spl0_2411,
inference(avatar_split_clause,[],[f562,f24930]) ).
fof(f24930,plain,
( spl0_2411
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2411])]) ).
fof(f562,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f24928,plain,
spl0_2410,
inference(avatar_split_clause,[],[f561,f24926]) ).
fof(f24926,plain,
( spl0_2410
<=> ! [X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2410])]) ).
fof(f561,axiom,
! [X65,X28,X58,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f24924,plain,
spl0_2409,
inference(avatar_split_clause,[],[f560,f24922]) ).
fof(f24922,plain,
( spl0_2409
<=> ! [X59,X65,X28,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2409])]) ).
fof(f560,axiom,
! [X65,X28,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f24920,plain,
spl0_2408,
inference(avatar_split_clause,[],[f559,f24918]) ).
fof(f24918,plain,
( spl0_2408
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).
fof(f559,axiom,
! [X65,X28,X10,X58,X59,X71,X70,X0,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f24916,plain,
spl0_2407,
inference(avatar_split_clause,[],[f558,f24914]) ).
fof(f24914,plain,
( spl0_2407
<=> ! [X59,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).
fof(f558,axiom,
! [X65,X58,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f24912,plain,
spl0_2406,
inference(avatar_split_clause,[],[f557,f24910]) ).
fof(f24910,plain,
( spl0_2406
<=> ! [X59,X28,X65,X58,X10,X0,X71,X68,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).
fof(f557,axiom,
! [X65,X28,X58,X59,X71,X10,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f24908,plain,
spl0_2405,
inference(avatar_split_clause,[],[f556,f24906]) ).
fof(f24906,plain,
( spl0_2405
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2405])]) ).
fof(f556,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f24904,plain,
spl0_2404,
inference(avatar_split_clause,[],[f555,f24902]) ).
fof(f24902,plain,
( spl0_2404
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).
fof(f555,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f24900,plain,
spl0_2403,
inference(avatar_split_clause,[],[f554,f24898]) ).
fof(f24898,plain,
( spl0_2403
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2403])]) ).
fof(f554,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f24888,plain,
spl0_2402,
inference(avatar_split_clause,[],[f553,f24886]) ).
fof(f24886,plain,
( spl0_2402
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2402])]) ).
fof(f553,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f24884,plain,
spl0_2401,
inference(avatar_split_clause,[],[f552,f24882]) ).
fof(f24882,plain,
( spl0_2401
<=> ! [X28,X59,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).
fof(f552,axiom,
! [X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f24880,plain,
spl0_2400,
inference(avatar_split_clause,[],[f551,f24878]) ).
fof(f24878,plain,
( spl0_2400
<=> ! [X59,X28,X65,X58,X10,X0,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).
fof(f551,axiom,
! [X65,X28,X58,X59,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f24876,plain,
spl0_2399,
inference(avatar_split_clause,[],[f550,f24874]) ).
fof(f24874,plain,
( spl0_2399
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).
fof(f550,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f24872,plain,
spl0_2398,
inference(avatar_split_clause,[],[f549,f24870]) ).
fof(f24870,plain,
( spl0_2398
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).
fof(f549,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f24868,plain,
spl0_2397,
inference(avatar_split_clause,[],[f548,f24866]) ).
fof(f24866,plain,
( spl0_2397
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).
fof(f548,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f24864,plain,
spl0_2396,
inference(avatar_split_clause,[],[f547,f24862]) ).
fof(f24862,plain,
( spl0_2396
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2396])]) ).
fof(f547,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f24860,plain,
spl0_2395,
inference(avatar_split_clause,[],[f546,f24858]) ).
fof(f24858,plain,
( spl0_2395
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2395])]) ).
fof(f546,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f24856,plain,
spl0_2394,
inference(avatar_split_clause,[],[f545,f24854]) ).
fof(f24854,plain,
( spl0_2394
<=> ! [X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f545,axiom,
! [X65,X28,X58,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f24852,plain,
spl0_2393,
inference(avatar_split_clause,[],[f544,f24850]) ).
fof(f24850,plain,
( spl0_2393
<=> ! [X59,X65,X28,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).
fof(f544,axiom,
! [X65,X28,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f24848,plain,
( spl0_2392
| ~ spl0_1568
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17575,f17299,f12367,f24846]) ).
fof(f24846,plain,
( spl0_2392
<=> ! [X0,X1] :
( ~ c_in(X1,c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).
fof(f12367,plain,
( spl0_1568
<=> ! [X0,X1,X3] :
( X1 = X3
| ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f17299,plain,
( spl0_1988
<=> ! [X0] : c_insert(X0,c_emptyset,t_a) = c_SetInterval_OatLeastAtMost(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f17575,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a)
| X0 = X1 )
| ~ spl0_1568
| ~ spl0_1988 ),
inference(superposition,[],[f12368,f17300]) ).
fof(f17300,plain,
( ! [X0] : c_insert(X0,c_emptyset,t_a) = c_SetInterval_OatLeastAtMost(X0,X0,t_a)
| ~ spl0_1988 ),
inference(avatar_component_clause,[],[f17299]) ).
fof(f12368,plain,
( ! [X3,X0,X1] :
( ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0)
| X1 = X3 )
| ~ spl0_1568 ),
inference(avatar_component_clause,[],[f12367]) ).
fof(f24844,plain,
spl0_2391,
inference(avatar_split_clause,[],[f543,f24842]) ).
fof(f24842,plain,
( spl0_2391
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).
fof(f543,axiom,
! [X65,X28,X10,X58,X59,X71,X70,X0,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f24840,plain,
spl0_2390,
inference(avatar_split_clause,[],[f542,f24838]) ).
fof(f24838,plain,
( spl0_2390
<=> ! [X59,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2390])]) ).
fof(f542,axiom,
! [X65,X58,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f24836,plain,
spl0_2389,
inference(avatar_split_clause,[],[f541,f24834]) ).
fof(f24834,plain,
( spl0_2389
<=> ! [X59,X28,X65,X58,X10,X0,X71,X68,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).
fof(f541,axiom,
! [X65,X28,X58,X59,X71,X10,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f24832,plain,
spl0_2388,
inference(avatar_split_clause,[],[f540,f24830]) ).
fof(f24830,plain,
( spl0_2388
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).
fof(f540,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f24828,plain,
spl0_2387,
inference(avatar_split_clause,[],[f539,f24826]) ).
fof(f24826,plain,
( spl0_2387
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).
fof(f539,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f24824,plain,
spl0_2386,
inference(avatar_split_clause,[],[f538,f24822]) ).
fof(f24822,plain,
( spl0_2386
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).
fof(f538,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f24820,plain,
spl0_2385,
inference(avatar_split_clause,[],[f537,f24818]) ).
fof(f24818,plain,
( spl0_2385
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f537,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f24816,plain,
spl0_2384,
inference(avatar_split_clause,[],[f536,f24814]) ).
fof(f24814,plain,
( spl0_2384
<=> ! [X28,X59,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).
fof(f536,axiom,
! [X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f24812,plain,
spl0_2383,
inference(avatar_split_clause,[],[f535,f24810]) ).
fof(f24810,plain,
( spl0_2383
<=> ! [X59,X28,X65,X58,X10,X0,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).
fof(f535,axiom,
! [X65,X28,X58,X59,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f24808,plain,
spl0_2382,
inference(avatar_split_clause,[],[f523,f24806]) ).
fof(f24806,plain,
( spl0_2382
<=> ! [X51,X14,X56,X3] :
( ~ c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist_OCons(X3,c_List_Olist__inter(X51,X56,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f523,axiom,
! [X51,X3,X56,X14] :
( ~ c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist_OCons(X3,c_List_Olist__inter(X51,X56,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f24798,plain,
spl0_2381,
inference(avatar_split_clause,[],[f508,f24796]) ).
fof(f24796,plain,
( spl0_2381
<=> ! [X40,X0,X16,X39] : c_Nat_Osize(c_List_Ozip(X39,X40,X0,X16),tc_List_Olist(tc_prod(X0,X16))) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).
fof(f508,axiom,
! [X40,X39,X0,X16] : c_Nat_Osize(c_List_Ozip(X39,X40,X0,X16),tc_List_Olist(tc_prod(X0,X16))) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f24794,plain,
spl0_2380,
inference(avatar_split_clause,[],[f417,f24792]) ).
fof(f24792,plain,
( spl0_2380
<=> ! [X44,X40,X0,X43,X39] :
( X43 = X44
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).
fof(f417,axiom,
! [X40,X39,X0,X44,X43] :
( X43 = X44
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f24790,plain,
spl0_2379,
inference(avatar_split_clause,[],[f416,f24788]) ).
fof(f24788,plain,
( spl0_2379
<=> ! [X44,X43,X40,X0,X39] :
( X39 = X40
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).
fof(f416,axiom,
! [X40,X39,X0,X44,X43] :
( X39 = X40
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f24786,plain,
spl0_2378,
inference(avatar_split_clause,[],[f415,f24784]) ).
fof(f24784,plain,
( spl0_2378
<=> ! [X44,X40,X0,X43,X39] :
( X43 = X44
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).
fof(f415,axiom,
! [X40,X39,X0,X44,X43] :
( X43 = X44
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f24782,plain,
spl0_2377,
inference(avatar_split_clause,[],[f414,f24780]) ).
fof(f24780,plain,
( spl0_2377
<=> ! [X44,X43,X40,X0,X39] :
( X39 = X40
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2377])]) ).
fof(f414,axiom,
! [X40,X39,X0,X44,X43] :
( X39 = X40
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f24778,plain,
spl0_2376,
inference(avatar_split_clause,[],[f362,f24776]) ).
fof(f24776,plain,
( spl0_2376
<=> ! [X34,X33] : c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f362,axiom,
! [X34,X33] : c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,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(f24774,plain,
spl0_2375,
inference(avatar_split_clause,[],[f177,f24772]) ).
fof(f24772,plain,
( spl0_2375
<=> ! [X0,X3,X26,X30] :
( ~ c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f177,axiom,
! [X3,X0,X26,X30] :
( ~ c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f24770,plain,
spl0_2374,
inference(avatar_split_clause,[],[f176,f24768]) ).
fof(f24768,plain,
( spl0_2374
<=> ! [X0,X3,X26,X30] :
( c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).
fof(f176,axiom,
! [X3,X0,X26,X30] :
( c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f24766,plain,
spl0_2373,
inference(avatar_split_clause,[],[f8,f24764]) ).
fof(f24764,plain,
( spl0_2373
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_times(X3,X1,X0),c_times(X2,X4,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_times(X3,X1,X0),c_times(X2,X4,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro_0) ).
fof(f24762,plain,
spl0_2372,
inference(avatar_split_clause,[],[f2,f24760]) ).
fof(f24760,plain,
( spl0_2372
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_plus(X3,X1,X0),c_plus(X2,X4,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2372])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_plus(X3,X1,X0),c_plus(X2,X4,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro_0) ).
fof(f24758,plain,
( spl0_2371
| ~ spl0_1589
| ~ spl0_2368 ),
inference(avatar_split_clause,[],[f24607,f24462,f12672,f24756]) ).
fof(f12672,plain,
( spl0_1589
<=> ! [X35,X33] :
( ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f24462,plain,
( spl0_2368
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).
fof(f24607,plain,
( ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1589
| ~ spl0_2368 ),
inference(resolution,[],[f24463,f12673]) ).
fof(f12673,plain,
( ! [X35,X33] :
( c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f12672]) ).
fof(f24463,plain,
( ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ spl0_2368 ),
inference(avatar_component_clause,[],[f24462]) ).
fof(f24665,plain,
( spl0_2370
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2352 ),
inference(avatar_split_clause,[],[f24214,f24211,f15052,f3498,f24663]) ).
fof(f24663,plain,
( spl0_2370
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2370])]) ).
fof(f24211,plain,
( spl0_2352
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2352])]) ).
fof(f24214,plain,
( ! [X34,X75] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2352 ),
inference(forward_demodulation,[],[f24212,f16073]) ).
fof(f24212,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2352 ),
inference(avatar_component_clause,[],[f24211]) ).
fof(f24661,plain,
( spl0_2369
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2351 ),
inference(avatar_split_clause,[],[f24209,f24206,f15052,f3498,f24659]) ).
fof(f24659,plain,
( spl0_2369
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f24206,plain,
( spl0_2351
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f24209,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_60
| ~ spl0_1888
| ~ spl0_2351 ),
inference(forward_demodulation,[],[f24207,f16073]) ).
fof(f24207,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2351 ),
inference(avatar_component_clause,[],[f24206]) ).
fof(f24464,plain,
( ~ spl0_1055
| spl0_2368
| ~ spl0_1911
| ~ spl0_2356 ),
inference(avatar_split_clause,[],[f24326,f24248,f16176,f24462,f8701]) ).
fof(f8701,plain,
( spl0_1055
<=> class_Ring__and__Field_Oordered__idom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f16176,plain,
( spl0_1911
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f24248,plain,
( spl0_2356
<=> ! [X0] : ~ c_less(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).
fof(f24326,plain,
( ! [X0] :
( ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
| ~ spl0_1911
| ~ spl0_2356 ),
inference(resolution,[],[f24249,f16177]) ).
fof(f16177,plain,
( ! [X0,X35,X33] :
( c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0)
| ~ c_less(X33,X35,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1911 ),
inference(avatar_component_clause,[],[f16176]) ).
fof(f24249,plain,
( ! [X0] : ~ c_less(X0,X0,t_a)
| ~ spl0_2356 ),
inference(avatar_component_clause,[],[f24248]) ).
fof(f24344,plain,
( spl0_2367
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2366 ),
inference(avatar_split_clause,[],[f24340,f24337,f15101,f10480,f9738,f9306,f9187,f9177,f24342]) ).
fof(f24342,plain,
( spl0_2367
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2367])]) ).
fof(f9177,plain,
( spl0_1121
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f9187,plain,
( spl0_1123
<=> ! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f9306,plain,
( spl0_1151
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f9738,plain,
( spl0_1245
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f10480,plain,
( spl0_1334
<=> ! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f15101,plain,
( spl0_1893
<=> ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f24337,plain,
( spl0_2366
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).
fof(f24340,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2366 ),
inference(forward_demodulation,[],[f24338,f16097]) ).
fof(f16097,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893 ),
inference(forward_demodulation,[],[f16096,f9179]) ).
fof(f9179,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_1121 ),
inference(avatar_component_clause,[],[f9177]) ).
fof(f16096,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_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893 ),
inference(forward_demodulation,[],[f16095,f9740]) ).
fof(f9740,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_1245 ),
inference(avatar_component_clause,[],[f9738]) ).
fof(f16095,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_1123
| ~ spl0_1151
| ~ spl0_1334
| ~ spl0_1893 ),
inference(forward_demodulation,[],[f16094,f9188]) ).
fof(f9188,plain,
( ! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10
| ~ spl0_1123 ),
inference(avatar_component_clause,[],[f9187]) ).
fof(f16094,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_1151
| ~ spl0_1334
| ~ spl0_1893 ),
inference(forward_demodulation,[],[f16088,f10481]) ).
fof(f10481,plain,
( ! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin)
| ~ spl0_1334 ),
inference(avatar_component_clause,[],[f10480]) ).
fof(f16088,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_1151
| ~ spl0_1893 ),
inference(superposition,[],[f15102,f9308]) ).
fof(f9308,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f9306]) ).
fof(f15102,plain,
( ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1)
| ~ spl0_1893 ),
inference(avatar_component_clause,[],[f15101]) ).
fof(f24338,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_2366 ),
inference(avatar_component_clause,[],[f24337]) ).
fof(f24339,plain,
spl0_2366,
inference(avatar_split_clause,[],[f3197,f24337]) ).
fof(f3197,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f2994,f1050]) ).
fof(f2994,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f213,f1023]) ).
fof(f213,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f24335,plain,
spl0_2365,
inference(avatar_split_clause,[],[f3195,f24333]) ).
fof(f24333,plain,
( spl0_2365
<=> ! [X0,X10] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2365])]) ).
fof(f3195,plain,
! [X10,X0] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2992,f1050]) ).
fof(f2992,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f209,f1023]) ).
fof(f209,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f24331,plain,
spl0_2364,
inference(avatar_split_clause,[],[f3193,f24329]) ).
fof(f24329,plain,
( spl0_2364
<=> ! [X0,X12] :
( 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f3193,plain,
! [X0,X12] :
( 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f2990,f1050]) ).
fof(f2990,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| 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,X12)),X0),X0) ),
inference(definition_unfolding,[],[f221,f1023]) ).
fof(f221,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| 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(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f24304,plain,
( spl0_2363
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2362 ),
inference(avatar_split_clause,[],[f24300,f24297,f15101,f10480,f9738,f9306,f9187,f9177,f24302]) ).
fof(f24302,plain,
( spl0_2363
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f24297,plain,
( spl0_2362
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).
fof(f24300,plain,
( ! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2362 ),
inference(forward_demodulation,[],[f24298,f16097]) ).
fof(f24298,plain,
( ! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_2362 ),
inference(avatar_component_clause,[],[f24297]) ).
fof(f24299,plain,
spl0_2362,
inference(avatar_split_clause,[],[f3190,f24297]) ).
fof(f3190,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2988,f1050]) ).
fof(f2988,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f217,f1023]) ).
fof(f217,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f24279,plain,
( spl0_2361
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2360 ),
inference(avatar_split_clause,[],[f24275,f24272,f15101,f10480,f9738,f9306,f9187,f9177,f24277]) ).
fof(f24277,plain,
( spl0_2361
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f24272,plain,
( spl0_2360
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2360])]) ).
fof(f24275,plain,
( ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2360 ),
inference(forward_demodulation,[],[f24273,f16097]) ).
fof(f24273,plain,
( ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_2360 ),
inference(avatar_component_clause,[],[f24272]) ).
fof(f24274,plain,
spl0_2360,
inference(avatar_split_clause,[],[f3187,f24272]) ).
fof(f3187,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f2986,f1050]) ).
fof(f2986,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f212,f1023]) ).
fof(f212,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f24270,plain,
spl0_2359,
inference(avatar_split_clause,[],[f3185,f24268]) ).
fof(f24268,plain,
( spl0_2359
<=> ! [X0,X10] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).
fof(f3185,plain,
! [X10,X0] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2984,f1050]) ).
fof(f2984,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f208,f1023]) ).
fof(f208,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f24266,plain,
spl0_2358,
inference(avatar_split_clause,[],[f3183,f24264]) ).
fof(f24264,plain,
( spl0_2358
<=> ! [X0,X12] :
( ~ 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).
fof(f3183,plain,
! [X0,X12] :
( ~ 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f2982,f1050]) ).
fof(f2982,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ 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,X12)),X0),X0) ),
inference(definition_unfolding,[],[f220,f1023]) ).
fof(f220,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ 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(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f24254,plain,
( spl0_2357
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2355 ),
inference(avatar_split_clause,[],[f24246,f24243,f15101,f10480,f9738,f9306,f9187,f9177,f24252]) ).
fof(f24252,plain,
( spl0_2357
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2357])]) ).
fof(f24243,plain,
( spl0_2355
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).
fof(f24246,plain,
( ! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2355 ),
inference(forward_demodulation,[],[f24244,f16097]) ).
fof(f24244,plain,
( ! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_2355 ),
inference(avatar_component_clause,[],[f24243]) ).
fof(f24250,plain,
( ~ spl0_1159
| spl0_2356
| spl0_1795
| ~ spl0_1689
| ~ spl0_1826 ),
inference(avatar_split_clause,[],[f15581,f14772,f13428,f14646,f24248,f9370]) ).
fof(f9370,plain,
( spl0_1159
<=> class_OrderedGroup_Opordered__ab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f14646,plain,
( spl0_1795
<=> c_less(c_0,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f13428,plain,
( spl0_1689
<=> ! [X0] : c_0 = c_minus(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f14772,plain,
( spl0_1826
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f15581,plain,
( ! [X0] :
( c_less(c_0,c_0,t_a)
| ~ c_less(X0,X0,t_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_a) )
| ~ spl0_1689
| ~ spl0_1826 ),
inference(superposition,[],[f14773,f13429]) ).
fof(f13429,plain,
( ! [X0] : c_0 = c_minus(X0,X0,t_a)
| ~ spl0_1689 ),
inference(avatar_component_clause,[],[f13428]) ).
fof(f14773,plain,
( ! [X3,X0,X1] :
( c_less(c_minus(X3,X1,X0),c_0,X0)
| ~ c_less(X3,X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_1826 ),
inference(avatar_component_clause,[],[f14772]) ).
fof(f24245,plain,
spl0_2355,
inference(avatar_split_clause,[],[f3180,f24243]) ).
fof(f3180,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2980,f1050]) ).
fof(f2980,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f216,f1023]) ).
fof(f216,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f24224,plain,
( spl0_2354
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2353 ),
inference(avatar_split_clause,[],[f24220,f24216,f13817,f3498,f24222]) ).
fof(f24222,plain,
( spl0_2354
<=> ! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).
fof(f13817,plain,
( spl0_1785
<=> ! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f24216,plain,
( spl0_2353
<=> ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,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_2353])]) ).
fof(f24220,plain,
( ! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2353 ),
inference(forward_demodulation,[],[f24219,f14618]) ).
fof(f14618,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_60
| ~ spl0_1785 ),
inference(resolution,[],[f13818,f3500]) ).
fof(f13818,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0) )
| ~ spl0_1785 ),
inference(avatar_component_clause,[],[f13817]) ).
fof(f24219,plain,
( ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2353 ),
inference(forward_demodulation,[],[f24217,f14618]) ).
fof(f24217,plain,
( ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2353 ),
inference(avatar_component_clause,[],[f24216]) ).
fof(f24218,plain,
spl0_2353,
inference(avatar_split_clause,[],[f3138,f24216]) ).
fof(f3138,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3137,f1050]) ).
fof(f3137,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3136,f1048]) ).
fof(f3136,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3135,f1050]) ).
fof(f3135,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f3134,f1050]) ).
fof(f3134,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f3133,f1048]) ).
fof(f3133,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f1202,f1050]) ).
fof(f1202,axiom,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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(f24213,plain,
spl0_2352,
inference(avatar_split_clause,[],[f2975,f24211]) ).
fof(f2975,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f749,f1023]) ).
fof(f749,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f24208,plain,
spl0_2351,
inference(avatar_split_clause,[],[f2974,f24206]) ).
fof(f2974,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f752,f1023]) ).
fof(f752,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f24204,plain,
spl0_2350,
inference(avatar_split_clause,[],[f1654,f24202]) ).
fof(f24202,plain,
( spl0_2350
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| ~ c_in(c_Main_Ofinite__Union__1(X26,X0),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f1654,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| ~ c_in(c_Main_Ofinite__Union__1(X26,X0),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f24200,plain,
spl0_2349,
inference(avatar_split_clause,[],[f1653,f24198]) ).
fof(f24198,plain,
( spl0_2349
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| c_in(c_Main_Ofinite__Union__1(X26,X0),X26,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f1653,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| c_in(c_Main_Ofinite__Union__1(X26,X0),X26,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f24196,plain,
spl0_2348,
inference(avatar_split_clause,[],[f1246,f24194]) ).
fof(f24194,plain,
( spl0_2348
<=> ! [X24,X11,X0,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| ~ c_less(c_1,X3,X0)
| c_Nat_Opower(X3,X11,X0) != c_Nat_Opower(X3,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).
fof(f1246,axiom,
! [X3,X0,X11,X24] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| ~ c_less(c_1,X3,X0)
| c_Nat_Opower(X3,X11,X0) != c_Nat_Opower(X3,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f24192,plain,
spl0_2347,
inference(avatar_split_clause,[],[f1221,f24190]) ).
fof(f24190,plain,
( spl0_2347
<=> ! [X12,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_uminus(c_Nat_Opower(X12,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2347])]) ).
fof(f1221,axiom,
! [X0,X11,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_uminus(c_Nat_Opower(X12,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f24187,plain,
spl0_2346,
inference(avatar_split_clause,[],[f1214,f24185]) ).
fof(f24185,plain,
( spl0_2346
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| c_lessequals(X12,c_0,X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).
fof(f1214,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| c_lessequals(X12,c_0,X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f24183,plain,
spl0_2345,
inference(avatar_split_clause,[],[f867,f24181]) ).
fof(f24181,plain,
( spl0_2345
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).
fof(f867,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f24179,plain,
spl0_2344,
inference(avatar_split_clause,[],[f866,f24177]) ).
fof(f24177,plain,
( spl0_2344
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).
fof(f866,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f24175,plain,
spl0_2343,
inference(avatar_split_clause,[],[f863,f24173]) ).
fof(f24173,plain,
( spl0_2343
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2343])]) ).
fof(f863,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f24171,plain,
spl0_2342,
inference(avatar_split_clause,[],[f862,f24169]) ).
fof(f24169,plain,
( spl0_2342
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).
fof(f862,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f24167,plain,
spl0_2341,
inference(avatar_split_clause,[],[f856,f24165]) ).
fof(f24165,plain,
( spl0_2341
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2341])]) ).
fof(f856,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f24163,plain,
spl0_2340,
inference(avatar_split_clause,[],[f855,f24161]) ).
fof(f24161,plain,
( spl0_2340
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).
fof(f855,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f24159,plain,
spl0_2339,
inference(avatar_split_clause,[],[f840,f24157]) ).
fof(f24157,plain,
( spl0_2339
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).
fof(f840,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f24155,plain,
spl0_2338,
inference(avatar_split_clause,[],[f839,f24153]) ).
fof(f24153,plain,
( spl0_2338
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f839,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f24151,plain,
spl0_2337,
inference(avatar_split_clause,[],[f770,f24149]) ).
fof(f24149,plain,
( spl0_2337
<=> ! [X34,X33] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).
fof(f770,axiom,
! [X34,X33] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f24147,plain,
( ~ spl0_1231
| spl0_2336
| ~ spl0_1550
| ~ spl0_1858 ),
inference(avatar_split_clause,[],[f14952,f14908,f12293,f24145,f9680]) ).
fof(f24145,plain,
( spl0_2336
<=> ! [X0] :
( c_0 != X0
| c_0 = c_uminus(X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).
fof(f12293,plain,
( spl0_1550
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = X3
| c_0 != c_uminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f14908,plain,
( spl0_1858
<=> ! [X0] : c_uminus(c_uminus(X0,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f14952,plain,
( ! [X0] :
( c_0 != X0
| c_0 = c_uminus(X0,t_a)
| ~ class_OrderedGroup_Oab__group__add(t_a) )
| ~ spl0_1550
| ~ spl0_1858 ),
inference(superposition,[],[f12294,f14909]) ).
fof(f14909,plain,
( ! [X0] : c_uminus(c_uminus(X0,t_a),t_a) = X0
| ~ spl0_1858 ),
inference(avatar_component_clause,[],[f14908]) ).
fof(f12294,plain,
( ! [X3,X0] :
( c_0 != c_uminus(X3,X0)
| c_0 = X3
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_1550 ),
inference(avatar_component_clause,[],[f12293]) ).
fof(f24143,plain,
spl0_2335,
inference(avatar_split_clause,[],[f649,f24141]) ).
fof(f24141,plain,
( spl0_2335
<=> ! [X0,X12,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Oset(c_List_Oremove1(X12,X39,X0),X0) = c_minus(c_List_Oset(X39,X0),c_insert(X12,c_emptyset,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2335])]) ).
fof(f649,axiom,
! [X39,X0,X12] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Oset(c_List_Oremove1(X12,X39,X0),X0) = c_minus(c_List_Oset(X39,X0),c_insert(X12,c_emptyset,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f24139,plain,
spl0_2334,
inference(avatar_split_clause,[],[f168,f24137]) ).
fof(f24137,plain,
( spl0_2334
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMin(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2334])]) ).
fof(f168,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMin(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f24135,plain,
spl0_2333,
inference(avatar_split_clause,[],[f150,f24133]) ).
fof(f24133,plain,
( spl0_2333
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMax(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).
fof(f150,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMax(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f23739,plain,
( spl0_2332
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2317 ),
inference(avatar_split_clause,[],[f23595,f23592,f19316,f9689,f9668,f23737]) ).
fof(f23737,plain,
( spl0_2332
<=> ! [X40,X0,X10,X39] :
( c_append(c_List_Orev(X40,X0),c_List_Oreplicate(c_1,X10,X0),X0) = X39
| c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f23592,plain,
( spl0_2317
<=> ! [X40,X0,X10,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).
fof(f23595,plain,
( ! [X40,X10,X0,X39] :
( c_append(c_List_Orev(X40,X0),c_List_Oreplicate(c_1,X10,X0),X0) = X39
| c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0) )
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2317 ),
inference(forward_demodulation,[],[f23593,f19342]) ).
fof(f23593,plain,
( ! [X40,X10,X0,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 )
| ~ spl0_2317 ),
inference(avatar_component_clause,[],[f23592]) ).
fof(f23707,plain,
( ~ spl0_1220
| spl0_2331
| ~ spl0_1574
| ~ spl0_1706 ),
inference(avatar_split_clause,[],[f14028,f13498,f12396,f23705,f9635]) ).
fof(f9635,plain,
( spl0_1220
<=> class_Ring__and__Field_Oordered__semidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f23705,plain,
( spl0_2331
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).
fof(f12396,plain,
( spl0_1574
<=> c_1 = c_NatArith_Oof__nat(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f13498,plain,
( spl0_1706
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f14028,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = X0
| ~ class_Ring__and__Field_Oordered__semidom(t_a) )
| ~ spl0_1574
| ~ spl0_1706 ),
inference(superposition,[],[f13499,f12398]) ).
fof(f12398,plain,
( c_1 = c_NatArith_Oof__nat(c_1,t_a)
| ~ spl0_1574 ),
inference(avatar_component_clause,[],[f12396]) ).
fof(f13499,plain,
( ! [X0,X11,X24] :
( c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0)
| X11 = X24
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_1706 ),
inference(avatar_component_clause,[],[f13498]) ).
fof(f23703,plain,
( spl0_2330
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_2314 ),
inference(avatar_split_clause,[],[f23582,f23579,f11630,f3498,f23701]) ).
fof(f23701,plain,
( spl0_2330
<=> ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2330])]) ).
fof(f11630,plain,
( spl0_1462
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f23579,plain,
( spl0_2314
<=> ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).
fof(f23582,plain,
( ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_2314 ),
inference(forward_demodulation,[],[f23580,f11976]) ).
fof(f11976,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1462 ),
inference(resolution,[],[f11631,f3500]) ).
fof(f11631,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) )
| ~ spl0_1462 ),
inference(avatar_component_clause,[],[f11630]) ).
fof(f23580,plain,
( ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_2314 ),
inference(avatar_component_clause,[],[f23579]) ).
fof(f23643,plain,
spl0_2329,
inference(avatar_split_clause,[],[f3113,f23641]) ).
fof(f23641,plain,
( spl0_2329
<=> ! [X75] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2329])]) ).
fof(f3113,plain,
! [X75] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2938,f2791]) ).
fof(f2791,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f910,f1438]) ).
fof(f910,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2938,plain,
! [X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f766,f1438]) ).
fof(f766,axiom,
! [X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f23639,plain,
spl0_2328,
inference(avatar_split_clause,[],[f2944,f23637]) ).
fof(f23637,plain,
( spl0_2328
<=> ! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2328])]) ).
fof(f2944,plain,
! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1740,f1610]) ).
fof(f1740,axiom,
! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f23635,plain,
spl0_2327,
inference(avatar_split_clause,[],[f2942,f23633]) ).
fof(f23633,plain,
( spl0_2327
<=> ! [X39,X0,X40] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).
fof(f2942,plain,
! [X40,X39,X0] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ),
inference(definition_unfolding,[],[f451,f1267]) ).
fof(f451,axiom,
! [X40,X39,X0] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_inter(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f23631,plain,
spl0_2326,
inference(avatar_split_clause,[],[f2893,f23629]) ).
fof(f23629,plain,
( spl0_2326
<=> ! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2326])]) ).
fof(f2893,plain,
! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0),X35,X0) ),
inference(definition_unfolding,[],[f1059,f1023]) ).
fof(f1059,axiom,
! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f23627,plain,
spl0_2325,
inference(avatar_split_clause,[],[f2867,f23625]) ).
fof(f23625,plain,
( spl0_2325
<=> ! [X40,X14,X12,X39] : c_append(c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14),X40,X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,X40,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).
fof(f2867,plain,
! [X40,X39,X14,X12] : c_append(c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14),X40,X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,X40,X14),X14),
inference(definition_unfolding,[],[f481,f479,f479]) ).
fof(f479,axiom,
! [X39,X0,X12] : c_List_Oitrev(X39,X12,X0) = c_append(c_List_Orev(X39,X0),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f481,axiom,
! [X40,X39,X14,X12] : c_List_Oitrev(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Oitrev(X39,c_List_Olist_OCons(X12,X40,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f23623,plain,
spl0_2324,
inference(avatar_split_clause,[],[f1678,f23621]) ).
fof(f23621,plain,
( spl0_2324
<=> ! [X0,X39,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).
fof(f1678,axiom,
! [X39,X0,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f23619,plain,
spl0_2323,
inference(avatar_split_clause,[],[f1677,f23617]) ).
fof(f23617,plain,
( spl0_2323
<=> ! [X0,X39,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(c_List_Olist_ONil,X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).
fof(f1677,axiom,
! [X39,X0,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(c_List_Olist_ONil,X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f23615,plain,
spl0_2322,
inference(avatar_split_clause,[],[f1016,f23613]) ).
fof(f23613,plain,
( spl0_2322
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_Numeral_Onumber__of(X12,X0) = c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2322])]) ).
fof(f1016,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_Numeral_Onumber__of(X12,X0) = c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f23611,plain,
spl0_2321,
inference(avatar_split_clause,[],[f758,f23609]) ).
fof(f23609,plain,
( spl0_2321
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X75),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).
fof(f758,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X75),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f23607,plain,
spl0_2320,
inference(avatar_split_clause,[],[f694,f23605]) ).
fof(f23605,plain,
( spl0_2320
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X9,tc_nat),X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).
fof(f694,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X9,tc_nat),X50,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f23603,plain,
spl0_2319,
inference(avatar_split_clause,[],[f690,f23601]) ).
fof(f23601,plain,
( spl0_2319
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X50,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2319])]) ).
fof(f690,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X50,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f23599,plain,
spl0_2318,
inference(avatar_split_clause,[],[f689,f23597]) ).
fof(f23597,plain,
( spl0_2318
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(c_minus(X50,X9,tc_nat),X23,tc_nat) = c_minus(c_plus(X50,X23,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).
fof(f689,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(c_minus(X50,X9,tc_nat),X23,tc_nat) = c_minus(c_plus(X50,X23,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f23594,plain,
spl0_2317,
inference(avatar_split_clause,[],[f620,f23592]) ).
fof(f620,axiom,
! [X40,X10,X0,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f23590,plain,
spl0_2316,
inference(avatar_split_clause,[],[f608,f23588]) ).
fof(f23588,plain,
( spl0_2316
<=> ! [X12,X39,X14] :
( c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Oremdups(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f608,axiom,
! [X39,X14,X12] :
( c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Oremdups(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f23586,plain,
spl0_2315,
inference(avatar_split_clause,[],[f511,f23584]) ).
fof(f23584,plain,
( spl0_2315
<=> ! [X29,X52,X0,X19] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X29,X52,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2315])]) ).
fof(f511,axiom,
! [X29,X0,X19,X52] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X29,X52,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f23581,plain,
spl0_2314,
inference(avatar_split_clause,[],[f347,f23579]) ).
fof(f347,axiom,
! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f23577,plain,
spl0_2313,
inference(avatar_split_clause,[],[f113,f23575]) ).
fof(f23575,plain,
( spl0_2313
<=> ! [X25,X1,X3] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(X3,X1,tc_nat) = c_div(c_times(X3,X25,tc_nat),c_times(X1,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2313])]) ).
fof(f113,axiom,
! [X3,X1,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(X3,X1,tc_nat) = c_div(c_times(X3,X25,tc_nat),c_times(X1,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f23573,plain,
( ~ spl0_1055
| ~ spl0_2312
| spl0_1779
| ~ spl0_1497
| ~ spl0_1683 ),
inference(avatar_split_clause,[],[f13914,f13404,f12051,f13792,f23570,f8701]) ).
fof(f23570,plain,
( spl0_2312
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2312])]) ).
fof(f13792,plain,
( spl0_1779
<=> c_lessequals(c_1,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f13404,plain,
( spl0_1683
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f13914,plain,
( c_lessequals(c_1,c_0,t_a)
| ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ spl0_1497
| ~ spl0_1683 ),
inference(superposition,[],[f13405,f12053]) ).
fof(f13405,plain,
( ! [X0,X33] :
( c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1683 ),
inference(avatar_component_clause,[],[f13404]) ).
fof(f23568,plain,
spl0_2311,
inference(avatar_split_clause,[],[f112,f23566]) ).
fof(f23566,plain,
( spl0_2311
<=> ! [X25,X1,X3] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(c_times(X25,X3,tc_nat),c_times(X25,X1,tc_nat),tc_nat) = c_div(X3,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).
fof(f112,axiom,
! [X3,X1,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(c_times(X25,X3,tc_nat),c_times(X25,X1,tc_nat),tc_nat) = c_div(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f23165,plain,
( spl0_2310
| ~ spl0_1901
| ~ spl0_2307 ),
inference(avatar_split_clause,[],[f22926,f22726,f15630,f23163]) ).
fof(f23163,plain,
( spl0_2310
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = c_IntDef_Oint(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f15630,plain,
( spl0_1901
<=> ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_a) = c_NatArith_Oof__nat(X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f22926,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_a)
| c_1 = c_IntDef_Oint(X0) )
| ~ spl0_1901
| ~ spl0_2307 ),
inference(superposition,[],[f22727,f15631]) ).
fof(f15631,plain,
( ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_a) = c_NatArith_Oof__nat(X0,t_a)
| ~ spl0_1901 ),
inference(avatar_component_clause,[],[f15630]) ).
fof(f22939,plain,
( spl0_2309
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2280 ),
inference(avatar_split_clause,[],[f22382,f22378,f19316,f9689,f9668,f22937]) ).
fof(f22937,plain,
( spl0_2309
<=> ! [X10,X40,X0,X12,X39] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X10 = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f22378,plain,
( spl0_2280
<=> ! [X10,X40,X0,X12,X39] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).
fof(f22382,plain,
( ! [X40,X10,X0,X39,X12] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X10 = X12 )
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2280 ),
inference(forward_demodulation,[],[f22381,f19342]) ).
fof(f22381,plain,
( ! [X40,X39,X0,X10,X12] :
( c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0)
| X10 = X12 )
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2280 ),
inference(forward_demodulation,[],[f22379,f19342]) ).
fof(f22379,plain,
( ! [X40,X10,X39,X0,X12] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) )
| ~ spl0_2280 ),
inference(avatar_component_clause,[],[f22378]) ).
fof(f22935,plain,
( spl0_2308
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2279 ),
inference(avatar_split_clause,[],[f22376,f22372,f19316,f9689,f9668,f22933]) ).
fof(f22933,plain,
( spl0_2308
<=> ! [X10,X40,X0,X12,X39] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X39 = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).
fof(f22372,plain,
( spl0_2279
<=> ! [X40,X0,X12,X10,X39] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f22376,plain,
( ! [X40,X10,X0,X39,X12] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X39 = X40 )
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2279 ),
inference(forward_demodulation,[],[f22375,f19342]) ).
fof(f22375,plain,
( ! [X40,X39,X0,X10,X12] :
( c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0)
| X39 = X40 )
| ~ spl0_1228
| ~ spl0_1233
| ~ spl0_2139
| ~ spl0_2279 ),
inference(forward_demodulation,[],[f22373,f19342]) ).
fof(f22373,plain,
( ! [X40,X39,X0,X10,X12] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) )
| ~ spl0_2279 ),
inference(avatar_component_clause,[],[f22372]) ).
fof(f22728,plain,
( ~ spl0_1055
| spl0_2307
| ~ spl0_1497
| ~ spl0_1681 ),
inference(avatar_split_clause,[],[f13900,f13396,f12051,f22726,f8701]) ).
fof(f13396,plain,
( spl0_1681
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X33 = X35
| c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f13900,plain,
( ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_a)
| c_1 = X0
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
| ~ spl0_1497
| ~ spl0_1681 ),
inference(superposition,[],[f13397,f12053]) ).
fof(f13397,plain,
( ! [X0,X35,X33] :
( c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0)
| X33 = X35
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1681 ),
inference(avatar_component_clause,[],[f13396]) ).
fof(f22566,plain,
( spl0_2306
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2305 ),
inference(avatar_split_clause,[],[f22562,f22558,f13801,f13502,f9018,f3835,f22564]) ).
fof(f22558,plain,
( spl0_2305
<=> ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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_2305])]) ).
fof(f22562,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2305 ),
inference(forward_demodulation,[],[f22561,f14546]) ).
fof(f22561,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2305 ),
inference(forward_demodulation,[],[f22559,f14546]) ).
fof(f22559,plain,
( ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2305 ),
inference(avatar_component_clause,[],[f22558]) ).
fof(f22560,plain,
spl0_2305,
inference(avatar_split_clause,[],[f3038,f22558]) ).
fof(f22556,plain,
spl0_2304,
inference(avatar_split_clause,[],[f2968,f22554]) ).
fof(f22554,plain,
( spl0_2304
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f2968,plain,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1502,f1267]) ).
fof(f1502,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f22552,plain,
spl0_2303,
inference(avatar_split_clause,[],[f2963,f22550]) ).
fof(f22550,plain,
( spl0_2303
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f2963,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1036,f1023]) ).
fof(f1036,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f22548,plain,
spl0_2302,
inference(avatar_split_clause,[],[f2962,f22546]) ).
fof(f22546,plain,
( spl0_2302
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f2962,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1035,f1023]) ).
fof(f1035,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f22544,plain,
spl0_2301,
inference(avatar_split_clause,[],[f2910,f22542]) ).
fof(f22542,plain,
( spl0_2301
<=> ! [X11,X0,X23,X39] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(X39,X23,X0) = c_List_Onth(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f2910,plain,
! [X39,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(X39,X23,X0) = c_List_Onth(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X23,X0) ),
inference(definition_unfolding,[],[f597,f660]) ).
fof(f597,axiom,
! [X39,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Otake(X11,X39,X0),X23,X0) = c_List_Onth(X39,X23,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f22540,plain,
spl0_2300,
inference(avatar_split_clause,[],[f2890,f22538]) ).
fof(f22538,plain,
( spl0_2300
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f2890,plain,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0) ),
inference(definition_unfolding,[],[f1014,f1023]) ).
fof(f1014,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X33)),X0) = c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f22536,plain,
spl0_2299,
inference(avatar_split_clause,[],[f1568,f22534]) ).
fof(f22534,plain,
( spl0_2299
<=> ! [X0,X12,X26,X30] :
( ~ c_in(X12,X30,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f1568,axiom,
! [X0,X26,X12,X30] :
( ~ c_in(X12,X30,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f22493,plain,
spl0_2298,
inference(avatar_split_clause,[],[f1541,f22491]) ).
fof(f22491,plain,
( spl0_2298
<=> ! [X0,X30,X2,X26] :
( ~ c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(X26,X2,tc_set(X0))
| c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).
fof(f1541,axiom,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(X26,X2,tc_set(X0))
| c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f22489,plain,
spl0_2297,
inference(avatar_split_clause,[],[f1491,f22487]) ).
fof(f22487,plain,
( spl0_2297
<=> ! [X0,X12,X26,X30] :
( c_in(X12,X26,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(X26,c_insert(X12,X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2297])]) ).
fof(f1491,axiom,
! [X0,X26,X12,X30] :
( c_in(X12,X26,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(X26,c_insert(X12,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f22485,plain,
spl0_2296,
inference(avatar_split_clause,[],[f1231,f22483]) ).
fof(f22483,plain,
( spl0_2296
<=> ! [X12,X33] :
( c_less(c_0,X12,tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).
fof(f1231,axiom,
! [X12,X33] :
( c_less(c_0,X12,tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f22481,plain,
spl0_2295,
inference(avatar_split_clause,[],[f1223,f22479]) ).
fof(f22479,plain,
( spl0_2295
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).
fof(f1223,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f22477,plain,
spl0_2294,
inference(avatar_split_clause,[],[f1220,f22475]) ).
fof(f22475,plain,
( spl0_2294
<=> ! [X12,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_Nat_Opower(X12,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f1220,axiom,
! [X0,X11,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_Nat_Opower(X12,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f22473,plain,
spl0_2293,
inference(avatar_split_clause,[],[f1217,f22471]) ).
fof(f22471,plain,
( spl0_2293
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).
fof(f1217,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f22469,plain,
spl0_2292,
inference(avatar_split_clause,[],[f971,f22467]) ).
fof(f22467,plain,
( spl0_2292
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2292])]) ).
fof(f971,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f22465,plain,
spl0_2291,
inference(avatar_split_clause,[],[f968,f22463]) ).
fof(f22463,plain,
( spl0_2291
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).
fof(f968,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f22461,plain,
spl0_2290,
inference(avatar_split_clause,[],[f963,f22459]) ).
fof(f22459,plain,
( spl0_2290
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2290])]) ).
fof(f963,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f22457,plain,
spl0_2289,
inference(avatar_split_clause,[],[f960,f22455]) ).
fof(f22455,plain,
( spl0_2289
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).
fof(f960,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f22414,plain,
spl0_2288,
inference(avatar_split_clause,[],[f823,f22412]) ).
fof(f22412,plain,
( spl0_2288
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_uminus(X1,X16) != c_Numeral_Onumber__of(X34,X16)
| c_uminus(c_Numeral_Onumber__of(X34,X16),X16) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f823,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_uminus(X1,X16) != c_Numeral_Onumber__of(X34,X16)
| c_uminus(c_Numeral_Onumber__of(X34,X16),X16) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f22410,plain,
spl0_2287,
inference(avatar_split_clause,[],[f724,f22408]) ).
fof(f22408,plain,
( spl0_2287
<=> ! [X12,X10] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f724,axiom,
! [X10,X12] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f22406,plain,
spl0_2286,
inference(avatar_split_clause,[],[f723,f22404]) ).
fof(f22404,plain,
( spl0_2286
<=> ! [X12,X10] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f723,axiom,
! [X10,X12] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f22402,plain,
spl0_2285,
inference(avatar_split_clause,[],[f615,f22400]) ).
fof(f22400,plain,
( spl0_2285
<=> ! [X10,X14,X12,X39] :
( X10 = X12
| c_List_Oremove1(X12,c_List_Olist_OCons(X10,X39,X14),X14) = c_List_Olist_OCons(X10,c_List_Oremove1(X12,X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f615,axiom,
! [X10,X39,X14,X12] :
( X10 = X12
| c_List_Oremove1(X12,c_List_Olist_OCons(X10,X39,X14),X14) = c_List_Olist_OCons(X10,c_List_Oremove1(X12,X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f22398,plain,
spl0_2284,
inference(avatar_split_clause,[],[f598,f22396]) ).
fof(f22396,plain,
( spl0_2284
<=> ! [X50,X9,X23] :
( ~ c_less(c_plus(X23,X9,tc_nat),X50,tc_nat)
| c_plus(X23,X9,tc_nat) = c_List_Onth(c_List_Oupt(X23,X50),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f598,axiom,
! [X50,X9,X23] :
( ~ c_less(c_plus(X23,X9,tc_nat),X50,tc_nat)
| c_plus(X23,X9,tc_nat) = c_List_Onth(c_List_Oupt(X23,X50),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f22394,plain,
spl0_2283,
inference(avatar_split_clause,[],[f591,f22392]) ).
fof(f22392,plain,
( spl0_2283
<=> ! [X11,X40,X0,X39] : c_List_Onth(c_append(X39,X40,X0),c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),X0) = c_List_Onth(X40,X11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).
fof(f591,axiom,
! [X40,X39,X0,X11] : c_List_Onth(c_append(X39,X40,X0),c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),X0) = c_List_Onth(X40,X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f22390,plain,
spl0_2282,
inference(avatar_split_clause,[],[f524,f22388]) ).
fof(f22388,plain,
( spl0_2282
<=> ! [X51,X14,X56,X3] :
( c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist__inter(X51,X56,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f524,axiom,
! [X51,X3,X56,X14] :
( c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist__inter(X51,X56,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f22386,plain,
spl0_2281,
inference(avatar_split_clause,[],[f493,f22384]) ).
fof(f22384,plain,
( spl0_2281
<=> ! [X39,X0,X40] : c_Nat_Osize(c_append(X39,X40,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f493,axiom,
! [X40,X39,X0] : c_Nat_Osize(c_append(X39,X40,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f22380,plain,
spl0_2280,
inference(avatar_split_clause,[],[f411,f22378]) ).
fof(f411,axiom,
! [X40,X10,X39,X0,X12] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f22374,plain,
spl0_2279,
inference(avatar_split_clause,[],[f410,f22372]) ).
fof(f410,axiom,
! [X40,X39,X0,X10,X12] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f22331,plain,
spl0_2278,
inference(avatar_split_clause,[],[f375,f22329]) ).
fof(f22329,plain,
( spl0_2278
<=> ! [X12,X10] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).
fof(f375,axiom,
! [X10,X12] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f22327,plain,
spl0_2277,
inference(avatar_split_clause,[],[f374,f22325]) ).
fof(f22325,plain,
( spl0_2277
<=> ! [X12,X10] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f374,axiom,
! [X10,X12] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f22323,plain,
spl0_2276,
inference(avatar_split_clause,[],[f367,f22321]) ).
fof(f22321,plain,
( spl0_2276
<=> ! [X1,X3] :
( c_0 = X3
| c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f367,axiom,
! [X3,X1] :
( c_0 = X3
| c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f22319,plain,
spl0_2275,
inference(avatar_split_clause,[],[f366,f22317]) ).
fof(f22317,plain,
( spl0_2275
<=> ! [X1,X3] :
( c_0 = X3
| c_div(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(f366,axiom,
! [X3,X1] :
( c_0 = X3
| c_div(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f22315,plain,
spl0_2274,
inference(avatar_split_clause,[],[f186,f22313]) ).
fof(f22313,plain,
( spl0_2274
<=> ! [X16,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_lessequals(c_Finite__Set_OMin(X26,X16),c_Finite__Set_OMax(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f186,axiom,
! [X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_lessequals(c_Finite__Set_OMin(X26,X16),c_Finite__Set_OMax(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f22311,plain,
spl0_2273,
inference(avatar_split_clause,[],[f182,f22309]) ).
fof(f22309,plain,
( spl0_2273
<=> ! [X6,X0,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f182,axiom,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f22307,plain,
spl0_2272,
inference(avatar_split_clause,[],[f12,f22305]) ).
fof(f22305,plain,
( spl0_2272
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f12,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono_0) ).
fof(f22303,plain,
spl0_2271,
inference(avatar_split_clause,[],[f11,f22301]) ).
fof(f22301,plain,
( spl0_2271
<=> ! [X4,X0,X3,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X4,X2,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f11,axiom,
! [X2,X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X4,X2,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono4_0) ).
fof(f22299,plain,
spl0_2270,
inference(avatar_split_clause,[],[f10,f22297]) ).
fof(f22297,plain,
( spl0_2270
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X2,X4,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f10,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X2,X4,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono3_0) ).
fof(f22295,plain,
spl0_2269,
inference(avatar_split_clause,[],[f6,f22293]) ).
fof(f22293,plain,
( spl0_2269
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f6,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono_0) ).
fof(f22252,plain,
spl0_2268,
inference(avatar_split_clause,[],[f5,f22250]) ).
fof(f22250,plain,
( spl0_2268
<=> ! [X4,X0,X3,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X4,X2,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f5,axiom,
! [X2,X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X4,X2,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono4_0) ).
fof(f22248,plain,
spl0_2267,
inference(avatar_split_clause,[],[f4,f22246]) ).
fof(f22246,plain,
( spl0_2267
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X2,X4,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f4,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X2,X4,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono3_0) ).
fof(f22076,plain,
( spl0_2266
| ~ spl0_1063
| ~ spl0_1739 ),
inference(avatar_split_clause,[],[f14210,f13631,f8892,f22074]) ).
fof(f22074,plain,
( spl0_2266
<=> ! [X0] : c_SetInterval_OatLeast(X0,t_a) = c_uminus(c_SetInterval_OlessThan(X0,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f8892,plain,
( spl0_1063
<=> class_Orderings_Olinorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f13631,plain,
( spl0_1739
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f14210,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,t_a) = c_uminus(c_SetInterval_OlessThan(X0,t_a),tc_set(t_a))
| ~ spl0_1063
| ~ spl0_1739 ),
inference(resolution,[],[f13632,f8894]) ).
fof(f8894,plain,
( class_Orderings_Olinorder(t_a)
| ~ spl0_1063 ),
inference(avatar_component_clause,[],[f8892]) ).
fof(f13632,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) )
| ~ spl0_1739 ),
inference(avatar_component_clause,[],[f13631]) ).
fof(f21920,plain,
( spl0_2265
| ~ spl0_1063
| ~ spl0_1738 ),
inference(avatar_split_clause,[],[f14207,f13627,f8892,f21918]) ).
fof(f21918,plain,
( spl0_2265
<=> ! [X0] : c_SetInterval_OatMost(X0,t_a) = c_uminus(c_SetInterval_OgreaterThan(X0,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f13627,plain,
( spl0_1738
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f14207,plain,
( ! [X0] : c_SetInterval_OatMost(X0,t_a) = c_uminus(c_SetInterval_OgreaterThan(X0,t_a),tc_set(t_a))
| ~ spl0_1063
| ~ spl0_1738 ),
inference(resolution,[],[f13628,f8894]) ).
fof(f13628,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) )
| ~ spl0_1738 ),
inference(avatar_component_clause,[],[f13627]) ).
fof(f21802,plain,
( spl0_2264
| ~ spl0_1063
| ~ spl0_1737 ),
inference(avatar_split_clause,[],[f14204,f13623,f8892,f21800]) ).
fof(f21800,plain,
( spl0_2264
<=> ! [X0] : c_uminus(c_SetInterval_OatMost(X0,t_a),tc_set(t_a)) = c_SetInterval_OgreaterThan(X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f13623,plain,
( spl0_1737
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f14204,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,t_a),tc_set(t_a)) = c_SetInterval_OgreaterThan(X0,t_a)
| ~ spl0_1063
| ~ spl0_1737 ),
inference(resolution,[],[f13624,f8894]) ).
fof(f13624,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) )
| ~ spl0_1737 ),
inference(avatar_component_clause,[],[f13623]) ).
fof(f21709,plain,
( spl0_2263
| ~ spl0_1063
| ~ spl0_1736 ),
inference(avatar_split_clause,[],[f14201,f13619,f8892,f21707]) ).
fof(f21707,plain,
( spl0_2263
<=> ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,t_a),tc_set(t_a)) = c_SetInterval_OlessThan(X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f13619,plain,
( spl0_1736
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f14201,plain,
( ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,t_a),tc_set(t_a)) = c_SetInterval_OlessThan(X0,t_a)
| ~ spl0_1063
| ~ spl0_1736 ),
inference(resolution,[],[f13620,f8894]) ).
fof(f13620,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) )
| ~ spl0_1736 ),
inference(avatar_component_clause,[],[f13619]) ).
fof(f21423,plain,
( ~ spl0_32
| spl0_2262
| ~ spl0_1842
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f18373,f18258,f14844,f21421,f3358]) ).
fof(f3358,plain,
( spl0_32
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f14844,plain,
( spl0_1842
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f18258,plain,
( spl0_2066
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f18373,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1842
| ~ spl0_2066 ),
inference(resolution,[],[f18259,f14845]) ).
fof(f14845,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16)
| c_lessequals(X12,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1842 ),
inference(avatar_component_clause,[],[f14844]) ).
fof(f18259,plain,
( ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ spl0_2066 ),
inference(avatar_component_clause,[],[f18258]) ).
fof(f21318,plain,
spl0_2261,
inference(avatar_split_clause,[],[f3196,f21316]) ).
fof(f21316,plain,
( spl0_2261
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f3196,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2993,f1008]) ).
fof(f1008,axiom,
! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f2993,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f207,f1023]) ).
fof(f207,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f21305,plain,
spl0_2260,
inference(avatar_split_clause,[],[f3194,f21303]) ).
fof(f21303,plain,
( spl0_2260
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f3194,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f2991,f1008]) ).
fof(f2991,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0) ),
inference(definition_unfolding,[],[f219,f1023]) ).
fof(f219,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f21301,plain,
spl0_2259,
inference(avatar_split_clause,[],[f3186,f21299]) ).
fof(f21299,plain,
( spl0_2259
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f3186,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2985,f1008]) ).
fof(f2985,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f206,f1023]) ).
fof(f206,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f21297,plain,
spl0_2258,
inference(avatar_split_clause,[],[f3184,f21295]) ).
fof(f21295,plain,
( spl0_2258
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f3184,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f2983,f1008]) ).
fof(f2983,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0) ),
inference(definition_unfolding,[],[f218,f1023]) ).
fof(f218,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f21293,plain,
spl0_2257,
inference(avatar_split_clause,[],[f3152,f21291]) ).
fof(f21291,plain,
( spl0_2257
<=> ! [X0,X10] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f3152,plain,
! [X10,X0] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2959,f1050]) ).
fof(f2959,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0)
| ~ 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f230,f1023]) ).
fof(f230,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0)
| ~ 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f21285,plain,
( spl0_2256
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2255 ),
inference(avatar_split_clause,[],[f21281,f21278,f15101,f10480,f9738,f9306,f9187,f9177,f21283]) ).
fof(f21283,plain,
( spl0_2256
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f21278,plain,
( spl0_2255
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).
fof(f21281,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2255 ),
inference(forward_demodulation,[],[f21279,f16097]) ).
fof(f21279,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_2255 ),
inference(avatar_component_clause,[],[f21278]) ).
fof(f21280,plain,
spl0_2255,
inference(avatar_split_clause,[],[f3151,f21278]) ).
fof(f3151,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2958,f1050]) ).
fof(f2958,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f234,f1023]) ).
fof(f234,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f21276,plain,
spl0_2254,
inference(avatar_split_clause,[],[f3146,f21274]) ).
fof(f21274,plain,
( spl0_2254
<=> ! [X0,X10] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).
fof(f3146,plain,
! [X10,X0] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2955,f1050]) ).
fof(f2955,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0)
| 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f229,f1023]) ).
fof(f229,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0)
| 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f21268,plain,
( spl0_2253
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2251 ),
inference(avatar_split_clause,[],[f21260,f21257,f15101,f10480,f9738,f9306,f9187,f9177,f21266]) ).
fof(f21266,plain,
( spl0_2253
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f21257,plain,
( spl0_2251
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f21260,plain,
( ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2251 ),
inference(forward_demodulation,[],[f21258,f16097]) ).
fof(f21258,plain,
( ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_2251 ),
inference(avatar_component_clause,[],[f21257]) ).
fof(f21264,plain,
( ~ spl0_32
| spl0_2252
| ~ spl0_1843
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f18372,f18258,f14848,f21262,f3358]) ).
fof(f14848,plain,
( spl0_1843
<=> ! [X16,X12,X35,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X10,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f18372,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1843
| ~ spl0_2066 ),
inference(resolution,[],[f18259,f14849]) ).
fof(f14849,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16)
| c_lessequals(X10,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1843 ),
inference(avatar_component_clause,[],[f14848]) ).
fof(f21259,plain,
spl0_2251,
inference(avatar_split_clause,[],[f3145,f21257]) ).
fof(f3145,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2954,f1050]) ).
fof(f2954,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f233,f1023]) ).
fof(f233,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f21255,plain,
( spl0_2250
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f21251,f21248,f13817,f3498,f21253]) ).
fof(f21253,plain,
( spl0_2250
<=> ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f21248,plain,
( spl0_2249
<=> ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f21251,plain,
( ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2249 ),
inference(forward_demodulation,[],[f21249,f14618]) ).
fof(f21249,plain,
( ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2249 ),
inference(avatar_component_clause,[],[f21248]) ).
fof(f21250,plain,
spl0_2249,
inference(avatar_split_clause,[],[f3116,f21248]) ).
fof(f3116,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3115,f1050]) ).
fof(f3115,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3114,f1048]) ).
fof(f3114,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1167,f1050]) ).
fof(f1167,axiom,
! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(f21246,plain,
( spl0_2248
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2247 ),
inference(avatar_split_clause,[],[f21242,f21239,f13817,f3498,f21244]) ).
fof(f21244,plain,
( spl0_2248
<=> ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f21239,plain,
( spl0_2247
<=> ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f21242,plain,
( ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_60
| ~ spl0_1785
| ~ spl0_2247 ),
inference(forward_demodulation,[],[f21240,f14618]) ).
fof(f21240,plain,
( ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2247 ),
inference(avatar_component_clause,[],[f21239]) ).
fof(f21241,plain,
spl0_2247,
inference(avatar_split_clause,[],[f3112,f21239]) ).
fof(f3112,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3111,f1050]) ).
fof(f3111,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3110,f1048]) ).
fof(f3110,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1166,f1050]) ).
fof(f1166,axiom,
! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(f21236,plain,
( spl0_2246
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2245 ),
inference(avatar_split_clause,[],[f21232,f21229,f15101,f10480,f9738,f9306,f9187,f9177,f21234]) ).
fof(f21234,plain,
( spl0_2246
<=> ! [X34,X0] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OMin),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f21229,plain,
( spl0_2245
<=> ! [X34,X0] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f21232,plain,
( ! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OMin),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_1121
| ~ spl0_1123
| ~ spl0_1151
| ~ spl0_1245
| ~ spl0_1334
| ~ spl0_1893
| ~ spl0_2245 ),
inference(forward_demodulation,[],[f21230,f16097]) ).
fof(f21230,plain,
( ! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_2245 ),
inference(avatar_component_clause,[],[f21229]) ).
fof(f21231,plain,
spl0_2245,
inference(avatar_split_clause,[],[f3081,f21229]) ).
fof(f3081,plain,
! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f2892,f1050]) ).
fof(f2892,plain,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0) ),
inference(definition_unfolding,[],[f226,f1023]) ).
fof(f226,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f21220,plain,
spl0_2244,
inference(avatar_split_clause,[],[f3080,f21218]) ).
fof(f21218,plain,
( spl0_2244
<=> ! [X0,X33] :
( c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f3080,plain,
! [X0,X33] :
( c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f2891,f1050]) ).
fof(f2891,plain,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = 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,X33)),X0) ),
inference(definition_unfolding,[],[f225,f1023]) ).
fof(f225,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X33)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f21216,plain,
spl0_2243,
inference(avatar_split_clause,[],[f3042,f21214]) ).
fof(f21214,plain,
( spl0_2243
<=> ! [X11] : c_plus(X11,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),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f3042,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3041,f1050]) ).
fof(f3041,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3040,f1048]) ).
fof(f3040,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3039,f1050]) ).
fof(f3039,plain,
! [X11] : 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),X11,tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2863,f3038]) ).
fof(f2863,plain,
! [X11] : 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),X11,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f775,f1438,f1438]) ).
fof(f775,axiom,
! [X11] : 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),X11,tc_nat) = c_Suc(c_Suc(X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f21199,plain,
( spl0_2242
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2241 ),
inference(avatar_split_clause,[],[f21195,f21192,f13801,f13502,f9018,f3835,f21197]) ).
fof(f21197,plain,
( spl0_2242
<=> ! [X34] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f21192,plain,
( spl0_2241
<=> ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f21195,plain,
( ! [X34] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2241 ),
inference(forward_demodulation,[],[f21193,f14546]) ).
fof(f21193,plain,
( ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) )
| ~ spl0_2241 ),
inference(avatar_component_clause,[],[f21192]) ).
fof(f21194,plain,
spl0_2241,
inference(avatar_split_clause,[],[f2937,f21192]) ).
fof(f2937,plain,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f717,f1438]) ).
fof(f717,axiom,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X34,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f21190,plain,
spl0_2240,
inference(avatar_split_clause,[],[f2868,f21188]) ).
fof(f21188,plain,
( spl0_2240
<=> ! [X23,X0,X12,X9] : c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0) = c_List_Osublist(c_List_Oreplicate(X9,X12,X0),c_SetInterval_OlessThan(X23,tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f2868,plain,
! [X0,X9,X12,X23] : c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0) = c_List_Osublist(c_List_Oreplicate(X9,X12,X0),c_SetInterval_OlessThan(X23,tc_nat),X0),
inference(definition_unfolding,[],[f669,f660]) ).
fof(f669,axiom,
! [X0,X9,X12,X23] : c_List_Otake(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f21186,plain,
spl0_2239,
inference(avatar_split_clause,[],[f2866,f21184]) ).
fof(f21184,plain,
( spl0_2239
<=> ! [X0,X11,X39] : c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) = c_Nat_Osize(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f2866,plain,
! [X39,X0,X11] : c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) = c_Nat_Osize(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f505,f660]) ).
fof(f505,axiom,
! [X39,X0,X11] : c_Nat_Osize(c_List_Otake(X11,X39,X0),tc_List_Olist(X0)) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f21182,plain,
spl0_2238,
inference(avatar_split_clause,[],[f2862,f21180]) ).
fof(f21180,plain,
( spl0_2238
<=> ! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_Relation_OImage(c_Relation_Odiag(X3,X0),c_Inter(X30,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).
fof(f2862,plain,
! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_Relation_OImage(c_Relation_Odiag(X3,X0),c_Inter(X30,X0),X0,X0),
inference(definition_unfolding,[],[f1517,f1267]) ).
fof(f1517,axiom,
! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_inter(X3,c_Inter(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f21177,plain,
( spl0_2237
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2235 ),
inference(avatar_split_clause,[],[f21169,f21166,f13801,f13502,f9018,f3835,f21175]) ).
fof(f21175,plain,
( spl0_2237
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f21166,plain,
( spl0_2235
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
fof(f21169,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2235 ),
inference(forward_demodulation,[],[f21167,f14546]) ).
fof(f21167,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16)
| ~ spl0_2235 ),
inference(avatar_component_clause,[],[f21166]) ).
fof(f21173,plain,
( spl0_2236
| ~ spl0_1345
| ~ spl0_2220 ),
inference(avatar_split_clause,[],[f21110,f20964,f10707,f21171]) ).
fof(f21171,plain,
( spl0_2236
<=> ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
fof(f10707,plain,
( spl0_1345
<=> ! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f21110,plain,
( ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint))
| ~ spl0_1345
| ~ spl0_2220 ),
inference(resolution,[],[f20965,f10708]) ).
fof(f10708,plain,
( ! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) )
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f10707]) ).
fof(f21168,plain,
spl0_2235,
inference(avatar_split_clause,[],[f2861,f21166]) ).
fof(f2861,plain,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16),
inference(definition_unfolding,[],[f100,f1438]) ).
fof(f100,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f21163,plain,
( spl0_2234
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2233 ),
inference(avatar_split_clause,[],[f21159,f21156,f13801,f13502,f9018,f3835,f21161]) ).
fof(f21161,plain,
( spl0_2234
<=> ! [X23,X0,X9,X16] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f21156,plain,
( spl0_2233
<=> ! [X23,X0,X9,X16] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f21159,plain,
( ! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2233 ),
inference(forward_demodulation,[],[f21157,f14546]) ).
fof(f21157,plain,
( ! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16)
| ~ spl0_2233 ),
inference(avatar_component_clause,[],[f21156]) ).
fof(f21158,plain,
spl0_2233,
inference(avatar_split_clause,[],[f2860,f21156]) ).
fof(f2860,plain,
! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16),
inference(definition_unfolding,[],[f101,f1438]) ).
fof(f101,axiom,
! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f21153,plain,
( spl0_2232
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2231 ),
inference(avatar_split_clause,[],[f21149,f21146,f13801,f13502,f9018,f3835,f21151]) ).
fof(f21151,plain,
( spl0_2232
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f21146,plain,
( spl0_2231
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f21149,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2231 ),
inference(forward_demodulation,[],[f21147,f14546]) ).
fof(f21147,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16)
| ~ spl0_2231 ),
inference(avatar_component_clause,[],[f21146]) ).
fof(f21148,plain,
spl0_2231,
inference(avatar_split_clause,[],[f2859,f21146]) ).
fof(f2859,plain,
! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16),
inference(definition_unfolding,[],[f97,f1438]) ).
fof(f97,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f21144,plain,
spl0_2230,
inference(avatar_split_clause,[],[f2848,f21142]) ).
fof(f21142,plain,
( spl0_2230
<=> ! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f2848,plain,
! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)),
inference(definition_unfolding,[],[f1741,f1610]) ).
fof(f1741,axiom,
! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f21140,plain,
spl0_2229,
inference(avatar_split_clause,[],[f2846,f21138]) ).
fof(f21138,plain,
( spl0_2229
<=> ! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f2846,plain,
! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1602,f1610]) ).
fof(f1602,axiom,
! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Ortrancl(X19,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f21107,plain,
( spl0_2228
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2227 ),
inference(avatar_split_clause,[],[f21103,f21100,f13801,f13502,f9018,f3835,f21105]) ).
fof(f21105,plain,
( spl0_2228
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).
fof(f21100,plain,
( spl0_2227
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).
fof(f21103,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2227 ),
inference(forward_demodulation,[],[f21101,f14546]) ).
fof(f21101,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2227 ),
inference(avatar_component_clause,[],[f21100]) ).
fof(f21102,plain,
spl0_2227,
inference(avatar_split_clause,[],[f2839,f21100]) ).
fof(f2839,plain,
! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f921,f1438,f1438]) ).
fof(f921,axiom,
! [X11,X24] : c_plus(X24,c_Suc(X11),tc_nat) = c_Suc(c_plus(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f21016,plain,
( spl0_2226
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2225 ),
inference(avatar_split_clause,[],[f21012,f21008,f13801,f13502,f9018,f3835,f21014]) ).
fof(f21014,plain,
( spl0_2226
<=> ! [X11,X24] : c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat) = c_plus(c_1,c_plus(X24,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f21008,plain,
( spl0_2225
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f21012,plain,
( ! [X11,X24] : c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat) = c_plus(c_1,c_plus(X24,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2225 ),
inference(forward_demodulation,[],[f21011,f14546]) ).
fof(f21011,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2225 ),
inference(forward_demodulation,[],[f21009,f14546]) ).
fof(f21009,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat)
| ~ spl0_2225 ),
inference(avatar_component_clause,[],[f21008]) ).
fof(f21010,plain,
spl0_2225,
inference(avatar_split_clause,[],[f2838,f21008]) ).
fof(f20984,plain,
( spl0_2224
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2223 ),
inference(avatar_split_clause,[],[f20980,f20976,f13801,f13502,f9018,f3835,f20982]) ).
fof(f20982,plain,
( spl0_2224
<=> ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f20976,plain,
( spl0_2223
<=> ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f20980,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2223 ),
inference(forward_demodulation,[],[f20979,f14546]) ).
fof(f20979,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2223 ),
inference(forward_demodulation,[],[f20977,f14546]) ).
fof(f20977,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2223 ),
inference(avatar_component_clause,[],[f20976]) ).
fof(f20978,plain,
spl0_2223,
inference(avatar_split_clause,[],[f2837,f20976]) ).
fof(f2837,plain,
! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f929,f1438,f1438]) ).
fof(f929,axiom,
! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Suc(X24),c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f20974,plain,
spl0_2222,
inference(avatar_split_clause,[],[f2781,f20972]) ).
fof(f20972,plain,
( spl0_2222
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X3,X1,X0),X0) = c_times(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f2781,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X3,X1,X0),X0) = c_times(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f20970,plain,
spl0_2221,
inference(avatar_split_clause,[],[f1735,f20968]) ).
fof(f20968,plain,
( spl0_2221
<=> ! [X26,X0,X16,X1,X30] :
( ~ c_in(X1,X30,X0)
| c_in(c_Sum__Type_OInr(X1,X0,X16),c_Sum__Type_OPlus(X26,X30,X16,X0),tc_sum(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f1735,axiom,
! [X0,X1,X26,X16,X30] :
( ~ c_in(X1,X30,X0)
| c_in(c_Sum__Type_OInr(X1,X0,X16),c_Sum__Type_OPlus(X26,X30,X16,X0),tc_sum(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f20966,plain,
( ~ spl0_32
| spl0_2220
| ~ spl0_1840
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f18366,f18258,f14836,f20964,f3358]) ).
fof(f14836,plain,
( spl0_1840
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f18366,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1840
| ~ spl0_2066 ),
inference(resolution,[],[f18259,f14837]) ).
fof(f14837,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16)
| c_lessequals(X12,X10,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1840 ),
inference(avatar_component_clause,[],[f14836]) ).
fof(f20962,plain,
spl0_2219,
inference(avatar_split_clause,[],[f1734,f20960]) ).
fof(f20960,plain,
( spl0_2219
<=> ! [X30,X0,X16,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Sum__Type_OInl(X3,X0,X16),c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f1734,axiom,
! [X3,X0,X26,X16,X30] :
( ~ c_in(X3,X26,X0)
| c_in(c_Sum__Type_OInl(X3,X0,X16),c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f20958,plain,
spl0_2218,
inference(avatar_split_clause,[],[f1697,f20956]) ).
fof(f20956,plain,
( spl0_2218
<=> ! [X3,X19,X0,X16,X1] :
( c_in(X1,c_Relation_ORange(X19,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f1697,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(X1,c_Relation_ORange(X19,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f20954,plain,
spl0_2217,
inference(avatar_split_clause,[],[f1693,f20952]) ).
fof(f20952,plain,
( spl0_2217
<=> ! [X1,X0,X16,X19,X26] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Main_OImageE__1(X26,X1,X19,X16,X0),X26,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f1693,axiom,
! [X0,X1,X19,X26,X16] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Main_OImageE__1(X26,X1,X19,X16,X0),X26,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f20950,plain,
spl0_2216,
inference(avatar_split_clause,[],[f1692,f20948]) ).
fof(f20948,plain,
( spl0_2216
<=> ! [X38,X0] :
( ~ c_in(X38,c_Relation_OId,tc_prod(X0,X0))
| c_Pair(c_Main_OIdE__1(X38,X0),c_Main_OIdE__1(X38,X0),X0,X0) = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f1692,axiom,
! [X38,X0] :
( ~ c_in(X38,c_Relation_OId,tc_prod(X0,X0))
| c_Pair(c_Main_OIdE__1(X38,X0),c_Main_OIdE__1(X38,X0),X0,X0) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f20946,plain,
spl0_2215,
inference(avatar_split_clause,[],[f1691,f20944]) ).
fof(f20944,plain,
( spl0_2215
<=> ! [X19,X0,X3,X16,X1] :
( c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f1691,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f20942,plain,
spl0_2214,
inference(avatar_split_clause,[],[f1679,f20940]) ).
fof(f20940,plain,
( spl0_2214
<=> ! [X0,X12,X72,X26] :
( c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f1679,axiom,
! [X72,X0,X26,X12] :
( c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f20938,plain,
spl0_2213,
inference(avatar_split_clause,[],[f1667,f20936]) ).
fof(f20936,plain,
( spl0_2213
<=> ! [X0,X29,X39,X26] :
( c_in(X29,X26,X0)
| ~ c_in(X29,c_List_Oset(X39,X0),X0)
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f1667,axiom,
! [X39,X29,X0,X26] :
( c_in(X29,X26,X0)
| ~ c_in(X29,c_List_Oset(X39,X0),X0)
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f20934,plain,
spl0_2212,
inference(avatar_split_clause,[],[f1591,f20932]) ).
fof(f20932,plain,
( spl0_2212
<=> ! [X0,X12,X26] :
( ~ c_lessequals(X26,c_insert(X12,c_emptyset,X0),tc_set(X0))
| c_insert(X12,X26,X0) = c_insert(X12,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f1591,axiom,
! [X0,X26,X12] :
( ~ c_lessequals(X26,c_insert(X12,c_emptyset,X0),tc_set(X0))
| c_insert(X12,X26,X0) = c_insert(X12,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
fof(f20930,plain,
spl0_2211,
inference(avatar_split_clause,[],[f1590,f20928]) ).
fof(f20928,plain,
( spl0_2211
<=> ! [X0,X1,X3,X26] :
( c_lessequals(X26,c_insert(X1,c_emptyset,X0),tc_set(X0))
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f1590,axiom,
! [X3,X0,X1,X26] :
( c_lessequals(X26,c_insert(X1,c_emptyset,X0),tc_set(X0))
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
fof(f20926,plain,
spl0_2210,
inference(avatar_split_clause,[],[f1584,f20924]) ).
fof(f20924,plain,
( spl0_2210
<=> ! [X0,X12,X26,X30] :
( ~ c_in(X12,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f1584,axiom,
! [X0,X26,X12,X30] :
( ~ c_in(X12,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f20915,plain,
spl0_2209,
inference(avatar_split_clause,[],[f1467,f20913]) ).
fof(f20913,plain,
( spl0_2209
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| c_insert(X9,c_emptyset,X0) = c_minus(c_insert(X9,c_emptyset,X0),c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f1467,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| c_insert(X9,c_emptyset,X0) = c_minus(c_insert(X9,c_emptyset,X0),c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f20911,plain,
spl0_2208,
inference(avatar_split_clause,[],[f1459,f20909]) ).
fof(f20909,plain,
( spl0_2208
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X50,X23,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f1459,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X50,X23,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f20907,plain,
spl0_2207,
inference(avatar_split_clause,[],[f1450,f20905]) ).
fof(f20905,plain,
( spl0_2207
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f1450,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f20903,plain,
spl0_2206,
inference(avatar_split_clause,[],[f1447,f20901]) ).
fof(f20901,plain,
( spl0_2206
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X36,X0)
| ~ c_less(X72,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f1447,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X36,X0)
| ~ c_less(X72,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f20899,plain,
spl0_2205,
inference(avatar_split_clause,[],[f1420,f20897]) ).
fof(f20897,plain,
( spl0_2205
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f1420,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f20895,plain,
spl0_2204,
inference(avatar_split_clause,[],[f1415,f20893]) ).
fof(f20893,plain,
( spl0_2204
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_lessequals(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f1415,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_lessequals(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f20891,plain,
spl0_2203,
inference(avatar_split_clause,[],[f1396,f20889]) ).
fof(f20889,plain,
( spl0_2203
<=> ! [X0,X3,X25,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(c_divide(X1,X25,X0),X3,X0) = c_divide(c_times(X1,X3,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f1396,axiom,
! [X3,X0,X1,X25] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(c_divide(X1,X25,X0),X3,X0) = c_divide(c_times(X1,X3,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).
fof(f20887,plain,
spl0_2202,
inference(avatar_split_clause,[],[f1395,f20885]) ).
fof(f20885,plain,
( spl0_2202
<=> ! [X0,X3,X25,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(X3,c_divide(X1,X25,X0),X0) = c_divide(c_times(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f1395,axiom,
! [X3,X0,X1,X25] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(X3,c_divide(X1,X25,X0),X0) = c_divide(c_times(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).
fof(f20883,plain,
spl0_2201,
inference(avatar_split_clause,[],[f1325,f20881]) ).
fof(f20881,plain,
( spl0_2201
<=> ! [X0,X3,X25,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_0 = X25
| c_times(X1,X25,X0) != c_times(X3,X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f1325,axiom,
! [X3,X0,X1,X25] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_0 = X25
| c_times(X1,X25,X0) != c_times(X3,X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
fof(f20879,plain,
spl0_2200,
inference(avatar_split_clause,[],[f1323,f20877]) ).
fof(f20877,plain,
( spl0_2200
<=> ! [X0,X3,X25,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_0 = X25
| c_times(X25,X3,X0) != c_times(X25,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f1323,axiom,
! [X3,X0,X1,X25] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_0 = X25
| c_times(X25,X3,X0) != c_times(X25,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
fof(f20875,plain,
( spl0_2199
| ~ spl0_1345
| ~ spl0_2178 ),
inference(avatar_split_clause,[],[f20824,f20779,f10707,f20873]) ).
fof(f20873,plain,
( spl0_2199
<=> ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f20824,plain,
( ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint))
| ~ spl0_1345
| ~ spl0_2178 ),
inference(resolution,[],[f20780,f10708]) ).
fof(f20871,plain,
spl0_2198,
inference(avatar_split_clause,[],[f1218,f20869]) ).
fof(f20869,plain,
( spl0_2198
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X12,c_0,X0)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f1218,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X12,c_0,X0)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f20867,plain,
spl0_2197,
inference(avatar_split_clause,[],[f1201,f20865]) ).
fof(f20865,plain,
( spl0_2197
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f1201,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f20863,plain,
spl0_2196,
inference(avatar_split_clause,[],[f1199,f20861]) ).
fof(f20861,plain,
( spl0_2196
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_uminus(c_1,X0) = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f1199,axiom,
! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_uminus(c_1,X0) = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f20859,plain,
spl0_2195,
inference(avatar_split_clause,[],[f1160,f20857]) ).
fof(f20857,plain,
( spl0_2195
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X35,X16)
| ~ c_lessequals(X10,X35,X16)
| c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f1160,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X35,X16)
| ~ c_lessequals(X10,X35,X16)
| c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f20855,plain,
spl0_2194,
inference(avatar_split_clause,[],[f1155,f20853]) ).
fof(f20853,plain,
( spl0_2194
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,X35,X16)
| c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f1155,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,X35,X16)
| c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f20851,plain,
spl0_2193,
inference(avatar_split_clause,[],[f1152,f20849]) ).
fof(f20849,plain,
( spl0_2193
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X35,X12,X0)
| ~ c_less(X35,X10,X0)
| c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f1152,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X35,X12,X0)
| ~ c_less(X35,X10,X0)
| c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f20847,plain,
spl0_2192,
inference(avatar_split_clause,[],[f1149,f20845]) ).
fof(f20845,plain,
( spl0_2192
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X12,X35,X0)
| ~ c_less(X10,X35,X0)
| c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f1149,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X12,X35,X0)
| ~ c_less(X10,X35,X0)
| c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f20843,plain,
spl0_2191,
inference(avatar_split_clause,[],[f1131,f20841]) ).
fof(f20841,plain,
( spl0_2191
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Omeet(X3,X1,X0),X0) = c_LOrder_Ojoin(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f1131,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Omeet(X3,X1,X0),X0) = c_LOrder_Ojoin(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f20839,plain,
spl0_2190,
inference(avatar_split_clause,[],[f1122,f20837]) ).
fof(f20837,plain,
( spl0_2190
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Ojoin(X3,X1,X0),X0) = c_LOrder_Omeet(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f1122,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Ojoin(X3,X1,X0),X0) = c_LOrder_Omeet(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f20835,plain,
spl0_2189,
inference(avatar_split_clause,[],[f1108,f20833]) ).
fof(f20833,plain,
( spl0_2189
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_plus(X3,X1,X0),X0) = c_plus(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f1108,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_plus(X3,X1,X0),X0) = c_plus(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f20821,plain,
spl0_2188,
inference(avatar_split_clause,[],[f737,f20819]) ).
fof(f20819,plain,
( spl0_2188
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f737,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f20817,plain,
spl0_2187,
inference(avatar_split_clause,[],[f730,f20815]) ).
fof(f20815,plain,
( spl0_2187
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f730,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f20813,plain,
spl0_2186,
inference(avatar_split_clause,[],[f718,f20811]) ).
fof(f20811,plain,
( spl0_2186
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X75,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f718,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X75,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f20809,plain,
spl0_2185,
inference(avatar_split_clause,[],[f715,f20807]) ).
fof(f20807,plain,
( spl0_2185
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_times(X24,X11,tc_nat),X0) = c_times(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f715,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_times(X24,X11,tc_nat),X0) = c_times(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f20805,plain,
spl0_2184,
inference(avatar_split_clause,[],[f703,f20803]) ).
fof(f20803,plain,
( spl0_2184
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_plus(X24,X11,tc_nat),X0) = c_plus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f703,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_plus(X24,X11,tc_nat),X0) = c_plus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f20801,plain,
spl0_2183,
inference(avatar_split_clause,[],[f675,f20799]) ).
fof(f20799,plain,
( spl0_2183
<=> ! [X12,X0,X11] :
( c_0 = X11
| c_List_Otl(c_List_Oreplicate(X11,X12,X0),X0) = c_List_Oreplicate(c_minus(X11,c_1,tc_nat),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f675,axiom,
! [X0,X11,X12] :
( c_0 = X11
| c_List_Otl(c_List_Oreplicate(X11,X12,X0),X0) = c_List_Oreplicate(c_minus(X11,c_1,tc_nat),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f20797,plain,
spl0_2182,
inference(avatar_split_clause,[],[f593,f20795]) ).
fof(f20795,plain,
( spl0_2182
<=> ! [X23,X0,X10,X39] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Olist__update(X39,X23,X10,X0),X23,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f593,axiom,
! [X39,X0,X10,X23] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Olist__update(X39,X23,X10,X0),X23,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f20793,plain,
spl0_2181,
inference(avatar_split_clause,[],[f527,f20791]) ).
fof(f20791,plain,
( spl0_2181
<=> ! [X0,X23,X10] :
( ~ c_less(X23,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X10,X23,c_List_Onth(X10,X23,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f527,axiom,
! [X10,X0,X23] :
( ~ c_less(X23,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X10,X23,c_List_Onth(X10,X23,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f20789,plain,
spl0_2180,
inference(avatar_split_clause,[],[f486,f20787]) ).
fof(f20787,plain,
( spl0_2180
<=> ! [X0,X11,X39] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(X39,X0) = c_List_Olast(c_List_Odrop(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f486,axiom,
! [X39,X0,X11] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(X39,X0) = c_List_Olast(c_List_Odrop(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f20785,plain,
spl0_2179,
inference(avatar_split_clause,[],[f419,f20783]) ).
fof(f20783,plain,
( spl0_2179
<=> ! [X39,X0,X40,X26] :
( c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f419,axiom,
! [X40,X39,X0,X26] :
( c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f20781,plain,
( ~ spl0_32
| spl0_2178
| ~ spl0_1841
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f18365,f18258,f14840,f20779,f3358]) ).
fof(f14840,plain,
( spl0_1841
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f18365,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1841
| ~ spl0_2066 ),
inference(resolution,[],[f18259,f14841]) ).
fof(f14841,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16)
| c_lessequals(X12,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1841 ),
inference(avatar_component_clause,[],[f14840]) ).
fof(f20777,plain,
spl0_2177,
inference(avatar_split_clause,[],[f418,f20775]) ).
fof(f20775,plain,
( spl0_2177
<=> ! [X40,X0,X39,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f418,axiom,
! [X40,X39,X0,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f20773,plain,
spl0_2176,
inference(avatar_split_clause,[],[f311,f20771]) ).
fof(f20771,plain,
( spl0_2176
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_times(X33,X35,tc_IntDef_Oint),X0) = c_times(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f311,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_times(X33,X35,tc_IntDef_Oint),X0) = c_times(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f20769,plain,
spl0_2175,
inference(avatar_split_clause,[],[f297,f20767]) ).
fof(f20767,plain,
( spl0_2175
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_minus(X33,X35,tc_IntDef_Oint),X0) = c_minus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f297,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_minus(X33,X35,tc_IntDef_Oint),X0) = c_minus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f20765,plain,
spl0_2174,
inference(avatar_split_clause,[],[f296,f20763]) ).
fof(f20763,plain,
( spl0_2174
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_plus(X33,X35,tc_IntDef_Oint),X0) = c_plus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f296,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_plus(X33,X35,tc_IntDef_Oint),X0) = c_plus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f20761,plain,
spl0_2173,
inference(avatar_split_clause,[],[f260,f20759]) ).
fof(f20759,plain,
( spl0_2173
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f260,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f20757,plain,
spl0_2172,
inference(avatar_split_clause,[],[f259,f20755]) ).
fof(f20755,plain,
( spl0_2172
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f259,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f20753,plain,
spl0_2171,
inference(avatar_split_clause,[],[f256,f20751]) ).
fof(f20751,plain,
( spl0_2171
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f256,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f20749,plain,
spl0_2170,
inference(avatar_split_clause,[],[f254,f20747]) ).
fof(f20747,plain,
( spl0_2170
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_minus(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f254,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_minus(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f20745,plain,
spl0_2169,
inference(avatar_split_clause,[],[f253,f20743]) ).
fof(f20743,plain,
( spl0_2169
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f253,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f20741,plain,
spl0_2168,
inference(avatar_split_clause,[],[f200,f20739]) ).
fof(f20739,plain,
( spl0_2168
<=> ! [X9,X11,X24] :
( ~ c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X24,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f200,axiom,
! [X11,X9,X24] :
( ~ c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X24,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f20728,plain,
spl0_2167,
inference(avatar_split_clause,[],[f184,f20726]) ).
fof(f20726,plain,
( spl0_2167
<=> ! [X0,X16,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f184,axiom,
! [X0,X19,X16] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f20724,plain,
spl0_2166,
inference(avatar_split_clause,[],[f183,f20722]) ).
fof(f20722,plain,
( spl0_2166
<=> ! [X0,X16,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| ~ c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f183,axiom,
! [X0,X19,X16] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| ~ c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f20580,plain,
( ~ spl0_1063
| spl0_2165
| ~ spl0_1842
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f18103,f17900,f14844,f20578,f8892]) ).
fof(f18103,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X0,X1,t_a),t_a)
| ~ class_Orderings_Olinorder(t_a) )
| ~ spl0_1842
| ~ spl0_2065 ),
inference(resolution,[],[f17901,f14845]) ).
fof(f20055,plain,
( ~ spl0_1063
| spl0_2164
| ~ spl0_1843
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f18102,f17900,f14848,f20053,f8892]) ).
fof(f18102,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X1,X0,t_a),t_a)
| ~ class_Orderings_Olinorder(t_a) )
| ~ spl0_1843
| ~ spl0_2065 ),
inference(resolution,[],[f17901,f14849]) ).
fof(f19801,plain,
( ~ spl0_1063
| spl0_2163
| ~ spl0_1840
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f18098,f17900,f14836,f19799,f8892]) ).
fof(f18098,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,t_a),X0,t_a)
| ~ class_Orderings_Olinorder(t_a) )
| ~ spl0_1840
| ~ spl0_2065 ),
inference(resolution,[],[f17901,f14837]) ).
fof(f19517,plain,
( spl0_2159
| spl0_2162 ),
inference(avatar_split_clause,[],[f3201,f19515,f19489]) ).
fof(f19489,plain,
( spl0_2159
<=> ! [X33] : c_0 != c_Numeral_Onumber__of(X33,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f19515,plain,
( spl0_2162
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| c_less(c_0,c_Nat_Opower(X12,c_0,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f3201,plain,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_0,X0),X0) ),
inference(inner_rewriting,[],[f1228]) ).
fof(f1228,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f19502,plain,
( ~ spl0_1120
| ~ spl0_2159 ),
inference(avatar_contradiction_clause,[],[f19501]) ).
fof(f19501,plain,
( $false
| ~ spl0_1120
| ~ spl0_2159 ),
inference(trivial_inequality_removal,[],[f19499]) ).
fof(f19499,plain,
( c_0 != c_0
| ~ spl0_1120
| ~ spl0_2159 ),
inference(superposition,[],[f19490,f9174]) ).
fof(f9174,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_1120 ),
inference(avatar_component_clause,[],[f9172]) ).
fof(f9172,plain,
( spl0_1120
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f19490,plain,
( ! [X33] : c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ spl0_2159 ),
inference(avatar_component_clause,[],[f19489]) ).
fof(f19498,plain,
( ~ spl0_1063
| spl0_2161
| ~ spl0_1841
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f18097,f17900,f14840,f19496,f8892]) ).
fof(f18097,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,t_a),X1,t_a)
| ~ class_Orderings_Olinorder(t_a) )
| ~ spl0_1841
| ~ spl0_2065 ),
inference(resolution,[],[f17901,f14841]) ).
fof(f19494,plain,
( spl0_2159
| spl0_2160 ),
inference(avatar_split_clause,[],[f3200,f19492,f19489]) ).
fof(f19492,plain,
( spl0_2160
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_0,X0),c_0,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f3200,plain,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_0,X0),c_0,X0) ),
inference(inner_rewriting,[],[f1211]) ).
fof(f1211,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f19459,plain,
( spl0_2158
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1233
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2051
| ~ spl0_2157 ),
inference(avatar_split_clause,[],[f19455,f19451,f17737,f13801,f13502,f9689,f9018,f3835,f19457]) ).
fof(f19457,plain,
( spl0_2158
<=> ! [X10] :
( c_plus(c_1,c_minus(X10,c_1,tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f17737,plain,
( spl0_2051
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f19451,plain,
( spl0_2157
<=> ! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f19455,plain,
( ! [X10] :
( c_plus(c_1,c_minus(X10,c_1,tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1233
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2051
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f19454,f17740]) ).
fof(f17740,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_1233
| ~ spl0_2051 ),
inference(superposition,[],[f17738,f9690]) ).
fof(f17738,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat)
| ~ spl0_2051 ),
inference(avatar_component_clause,[],[f17737]) ).
fof(f19454,plain,
( ! [X10] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f19452,f14546]) ).
fof(f19452,plain,
( ! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_2157 ),
inference(avatar_component_clause,[],[f19451]) ).
fof(f19453,plain,
spl0_2157,
inference(avatar_split_clause,[],[f3092,f19451]) ).
fof(f3092,plain,
! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ),
inference(forward_demodulation,[],[f2912,f2842]) ).
fof(f2912,plain,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X10 ),
inference(definition_unfolding,[],[f918,f1438,f1438]) ).
fof(f918,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_Suc(c_minus(X10,c_Suc(c_0),tc_nat)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f19449,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2940,f19447]) ).
fof(f19447,plain,
( spl0_2156
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f2940,plain,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1503,f1267]) ).
fof(f1503,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f19445,plain,
spl0_2155,
inference(avatar_split_clause,[],[f2939,f19443]) ).
fof(f19443,plain,
( spl0_2155
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f2939,plain,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1504,f1267]) ).
fof(f1504,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f19441,plain,
spl0_2154,
inference(avatar_split_clause,[],[f2935,f19439]) ).
fof(f19439,plain,
( spl0_2154
<=> ! [X6,X0,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f2935,plain,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
inference(definition_unfolding,[],[f1652,f1267]) ).
fof(f1652,axiom,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_inter(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f19437,plain,
spl0_2153,
inference(avatar_split_clause,[],[f2934,f19435]) ).
fof(f19435,plain,
( spl0_2153
<=> ! [X6,X0,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f2934,plain,
! [X0,X6,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
inference(definition_unfolding,[],[f1651,f1267]) ).
fof(f1651,axiom,
! [X0,X6,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_inter(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f19431,plain,
spl0_2152,
inference(avatar_split_clause,[],[f2927,f19429]) ).
fof(f19429,plain,
( spl0_2152
<=> ! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f2927,plain,
! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f913,f1438,f1438]) ).
fof(f913,axiom,
! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Suc(X11),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f19425,plain,
spl0_2151,
inference(avatar_split_clause,[],[f2925,f19423]) ).
fof(f19423,plain,
( spl0_2151
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f2925,plain,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f915,f1438,f1438]) ).
fof(f915,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Suc(X24),c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f19419,plain,
spl0_2150,
inference(avatar_split_clause,[],[f2920,f19417]) ).
fof(f19417,plain,
( spl0_2150
<=> ! [X0,X3,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f2920,plain,
! [X3,X0,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1571,f1267]) ).
fof(f1571,axiom,
! [X3,X0,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
fof(f19415,plain,
spl0_2149,
inference(avatar_split_clause,[],[f2918,f19413]) ).
fof(f19413,plain,
( spl0_2149
<=> ! [X0,X30,X1,X26] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),c_insert(X1,X30,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f2918,plain,
! [X0,X1,X26,X30] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),c_insert(X1,X30,X0),X0,X0) ),
inference(definition_unfolding,[],[f1558,f1267]) ).
fof(f1558,axiom,
! [X0,X1,X26,X30] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_inter(X26,c_insert(X1,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f19409,plain,
spl0_2148,
inference(avatar_split_clause,[],[f2914,f19407]) ).
fof(f19407,plain,
( spl0_2148
<=> ! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f2914,plain,
! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f914,f1438,f1438]) ).
fof(f914,axiom,
! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Suc(X11),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f19403,plain,
spl0_2147,
inference(avatar_split_clause,[],[f2909,f19401]) ).
fof(f19401,plain,
( spl0_2147
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f2909,plain,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f916,f1438,f1438]) ).
fof(f916,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Suc(X24),c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f19393,plain,
( spl0_2146
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2145 ),
inference(avatar_split_clause,[],[f19389,f19386,f13801,f13502,f9018,f3835,f19391]) ).
fof(f19391,plain,
( spl0_2146
<=> ! [X24,X14] :
( c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_plus(c_1,X24,tc_nat),X14)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f19386,plain,
( spl0_2145
<=> ! [X24,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f19389,plain,
( ! [X14,X24] :
( c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_plus(c_1,X24,tc_nat),X14)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2145 ),
inference(forward_demodulation,[],[f19387,f14546]) ).
fof(f19387,plain,
( ! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) )
| ~ spl0_2145 ),
inference(avatar_component_clause,[],[f19386]) ).
fof(f19388,plain,
spl0_2145,
inference(avatar_split_clause,[],[f2896,f19386]) ).
fof(f2896,plain,
! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) ),
inference(definition_unfolding,[],[f696,f1438]) ).
fof(f696,axiom,
! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_NatArith_Oof__nat(c_Suc(X24),X14) = c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f19380,plain,
( spl0_2144
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2143 ),
inference(avatar_split_clause,[],[f19376,f19373,f13801,f13502,f9018,f3835,f19378]) ).
fof(f19378,plain,
( spl0_2144
<=> ! [X11,X0,X12,X39] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_plus(c_1,X11,tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f19373,plain,
( spl0_2143
<=> ! [X11,X0,X12,X39] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f19376,plain,
( ! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_plus(c_1,X11,tc_nat),X0)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2143 ),
inference(forward_demodulation,[],[f19374,f14546]) ).
fof(f19374,plain,
( ! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0)
| ~ spl0_2143 ),
inference(avatar_component_clause,[],[f19373]) ).
fof(f19375,plain,
spl0_2143,
inference(avatar_split_clause,[],[f2856,f19373]) ).
fof(f2856,plain,
! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0),
inference(definition_unfolding,[],[f587,f1438]) ).
fof(f587,axiom,
! [X39,X0,X11,X12] : c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Suc(X11),X0) = c_List_Onth(X39,X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f19371,plain,
( spl0_2142
| ~ spl0_1187
| ~ spl0_1740
| ~ spl0_2127 ),
inference(avatar_split_clause,[],[f19120,f19019,f13635,f9499,f19368]) ).
fof(f19368,plain,
( spl0_2142
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f9499,plain,
( spl0_1187
<=> class_Orderings_Oorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f13635,plain,
( spl0_1740
<=> ! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f19019,plain,
( spl0_2127
<=> c_less(c_0,c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f19120,plain,
( ~ class_Orderings_Oorder(t_a)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,t_a)
| ~ spl0_1740
| ~ spl0_2127 ),
inference(resolution,[],[f19021,f13636]) ).
fof(f13636,plain,
( ! [X0,X11,X24] :
( ~ c_less(X11,X24,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) )
| ~ spl0_1740 ),
inference(avatar_component_clause,[],[f13635]) ).
fof(f19021,plain,
( c_less(c_0,c_1,t_a)
| ~ spl0_2127 ),
inference(avatar_component_clause,[],[f19019]) ).
fof(f19353,plain,
( spl0_2141
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2140 ),
inference(avatar_split_clause,[],[f19349,f19346,f13801,f13502,f9018,f3835,f19351]) ).
fof(f19351,plain,
( spl0_2141
<=> ! [X11,X0,X12,X39] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_plus(c_1,X11,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f19346,plain,
( spl0_2140
<=> ! [X11,X0,X12,X39] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f19349,plain,
( ! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_plus(c_1,X11,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2140 ),
inference(forward_demodulation,[],[f19347,f14546]) ).
fof(f19347,plain,
( ! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0)
| ~ spl0_2140 ),
inference(avatar_component_clause,[],[f19346]) ).
fof(f19348,plain,
spl0_2140,
inference(avatar_split_clause,[],[f2855,f19346]) ).
fof(f2855,plain,
! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0),
inference(definition_unfolding,[],[f466,f1438]) ).
fof(f466,axiom,
! [X39,X0,X11,X12] : c_List_Odrop(c_Suc(X11),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(X11,X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f19318,plain,
( spl0_2139
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2138 ),
inference(avatar_split_clause,[],[f19314,f19311,f13801,f13502,f9018,f3835,f19316]) ).
fof(f19311,plain,
( spl0_2138
<=> ! [X11,X12,X14] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f19314,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2138 ),
inference(forward_demodulation,[],[f19312,f14546]) ).
fof(f19312,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14)
| ~ spl0_2138 ),
inference(avatar_component_clause,[],[f19311]) ).
fof(f19313,plain,
spl0_2138,
inference(avatar_split_clause,[],[f2854,f19311]) ).
fof(f2854,plain,
! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14),
inference(definition_unfolding,[],[f617,f1438]) ).
fof(f617,axiom,
! [X11,X14,X12] : c_List_Oreplicate(c_Suc(X11),X12,X14) = c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f19217,plain,
( spl0_2137
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2136 ),
inference(avatar_split_clause,[],[f19213,f19210,f13801,f13502,f9018,f3835,f19215]) ).
fof(f19215,plain,
( spl0_2137
<=> ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_plus(c_1,X24,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f19210,plain,
( spl0_2136
<=> ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f19213,plain,
( ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_plus(c_1,X24,tc_nat),X11,tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2136 ),
inference(forward_demodulation,[],[f19211,f14546]) ).
fof(f19211,plain,
( ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat)
| ~ spl0_2136 ),
inference(avatar_component_clause,[],[f19210]) ).
fof(f19212,plain,
spl0_2136,
inference(avatar_split_clause,[],[f2853,f19210]) ).
fof(f2853,plain,
! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),
inference(definition_unfolding,[],[f993,f1438]) ).
fof(f993,axiom,
! [X11,X24] : c_times(c_Suc(X24),X11,tc_nat) = c_plus(X11,c_times(X24,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f19119,plain,
( spl0_2135
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2134 ),
inference(avatar_split_clause,[],[f19115,f19112,f13801,f13502,f9018,f3835,f19117]) ).
fof(f19117,plain,
( spl0_2135
<=> ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f19112,plain,
( spl0_2134
<=> ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f19115,plain,
( ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2134 ),
inference(forward_demodulation,[],[f19113,f14546]) ).
fof(f19113,plain,
( ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2134 ),
inference(avatar_component_clause,[],[f19112]) ).
fof(f19114,plain,
spl0_2134,
inference(avatar_split_clause,[],[f2852,f19112]) ).
fof(f2852,plain,
! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f951,f1438]) ).
fof(f951,axiom,
! [X11,X24] : c_times(X24,c_Suc(X11),tc_nat) = c_plus(X24,c_times(X24,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f19063,plain,
( spl0_2133
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2132 ),
inference(avatar_split_clause,[],[f19059,f19056,f13801,f13502,f9018,f3835,f19061]) ).
fof(f19061,plain,
( spl0_2133
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f19056,plain,
( spl0_2132
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f19059,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2132 ),
inference(forward_demodulation,[],[f19057,f14546]) ).
fof(f19057,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2132 ),
inference(avatar_component_clause,[],[f19056]) ).
fof(f19058,plain,
spl0_2132,
inference(avatar_split_clause,[],[f2851,f19056]) ).
fof(f2851,plain,
! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1239,f1438]) ).
fof(f1239,axiom,
! [X38,X11] : c_Nat_Opower(X38,c_Suc(X11),tc_nat) = c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f19039,plain,
( spl0_2131
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2130 ),
inference(avatar_split_clause,[],[f19035,f19032,f13801,f13502,f9018,f3835,f19037]) ).
fof(f19037,plain,
( spl0_2131
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f19032,plain,
( spl0_2130
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f19035,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_IntDef_Oint)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2130 ),
inference(forward_demodulation,[],[f19033,f14546]) ).
fof(f19033,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_2130 ),
inference(avatar_component_clause,[],[f19032]) ).
fof(f19034,plain,
spl0_2130,
inference(avatar_split_clause,[],[f2850,f19032]) ).
fof(f2850,plain,
! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f359,f1438]) ).
fof(f359,axiom,
! [X38,X11] : c_Nat_Opower(X38,c_Suc(X11),tc_IntDef_Oint) = c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f19030,plain,
spl0_2129,
inference(avatar_split_clause,[],[f2849,f19028]) ).
fof(f19028,plain,
( spl0_2129
<=> ! [X0,X30,X26] : c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f2849,plain,
! [X0,X26,X30] : c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)),
inference(definition_unfolding,[],[f1480,f1267]) ).
fof(f1480,axiom,
! [X0,X26,X30] : c_inter(X26,X30,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f19026,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1702,f19024]) ).
fof(f19024,plain,
( spl0_2128
<=> ! [X0,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Pair(X3,X3,X0,X0),c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f1702,axiom,
! [X3,X0,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Pair(X3,X3,X0,X0),c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f19022,plain,
( ~ spl0_1127
| spl0_114
| spl0_2127
| ~ spl0_1510
| ~ spl0_1632 ),
inference(avatar_split_clause,[],[f13250,f12848,f12128,f19019,f3767,f9203]) ).
fof(f12128,plain,
( spl0_1510
<=> c_1 = c_HOL_Oabs(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f12848,plain,
( spl0_1632
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_less(c_0,c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f13250,plain,
( c_less(c_0,c_1,t_a)
| c_0 = c_1
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1510
| ~ spl0_1632 ),
inference(superposition,[],[f12849,f12130]) ).
fof(f12130,plain,
( c_1 = c_HOL_Oabs(c_1,t_a)
| ~ spl0_1510 ),
inference(avatar_component_clause,[],[f12128]) ).
fof(f12849,plain,
( ! [X3,X0] :
( c_less(c_0,c_HOL_Oabs(X3,X0),X0)
| c_0 = X3
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1632 ),
inference(avatar_component_clause,[],[f12848]) ).
fof(f19017,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1668,f19015]) ).
fof(f19015,plain,
( spl0_2126
<=> ! [X0,X39,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_Main_Oin__listsI__1(X26,X39,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f1668,axiom,
! [X39,X0,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_Main_Oin__listsI__1(X26,X39,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f19013,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1569,f19011]) ).
fof(f19011,plain,
( spl0_2125
<=> ! [X0,X3,X26] : c_insert(X3,X26,X0) = c_insert(X3,c_minus(X26,c_insert(X3,c_emptyset,X0),tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f1569,axiom,
! [X3,X0,X26] : c_insert(X3,X26,X0) = c_insert(X3,c_minus(X26,c_insert(X3,c_emptyset,X0),tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f19009,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1544,f19007]) ).
fof(f19007,plain,
( spl0_2124
<=> ! [X0,X30,X26] : c_Union(c_union(X26,X30,tc_set(X0)),X0) = c_union(c_Union(X26,X0),c_Union(X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f1544,axiom,
! [X0,X26,X30] : c_Union(c_union(X26,X30,tc_set(X0)),X0) = c_union(c_Union(X26,X0),c_Union(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f19005,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1490,f19003]) ).
fof(f19003,plain,
( spl0_2123
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f1490,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f19001,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1479,f18999]) ).
fof(f18999,plain,
( spl0_2122
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f1479,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f18997,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1478,f18995]) ).
fof(f18995,plain,
( spl0_2121
<=> ! [X0,X30,X26] :
( c_lessequals(X30,X26,tc_set(X0))
| ~ c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f1478,axiom,
! [X0,X26,X30] :
( c_lessequals(X30,X26,tc_set(X0))
| ~ c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f18993,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1468,f18991]) ).
fof(f18991,plain,
( spl0_2120
<=> ! [X0,X30,X26] : c_uminus(c_minus(X26,X30,tc_set(X0)),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),X30,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f1468,axiom,
! [X0,X26,X30] : c_uminus(c_minus(X26,X30,tc_set(X0)),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f18989,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1254,f18987]) ).
fof(f18987,plain,
( spl0_2119
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f1254,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f18985,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1253,f18983]) ).
fof(f18983,plain,
( spl0_2118
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f1253,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f18981,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1088,f18979]) ).
fof(f18979,plain,
( spl0_2117
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f1088,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f18976,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1087,f18974]) ).
fof(f18974,plain,
( spl0_2116
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f1087,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f18972,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1086,f18970]) ).
fof(f18970,plain,
( spl0_2115
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f1086,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f18968,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1085,f18966]) ).
fof(f18966,plain,
( spl0_2114
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f1085,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f18964,plain,
spl0_2113,
inference(avatar_split_clause,[],[f1083,f18962]) ).
fof(f18962,plain,
( spl0_2113
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f1083,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f18960,plain,
spl0_2112,
inference(avatar_split_clause,[],[f1082,f18958]) ).
fof(f18958,plain,
( spl0_2112
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f1082,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f18956,plain,
spl0_2111,
inference(avatar_split_clause,[],[f1081,f18954]) ).
fof(f18954,plain,
( spl0_2111
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f1081,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f18952,plain,
spl0_2110,
inference(avatar_split_clause,[],[f1080,f18950]) ).
fof(f18950,plain,
( spl0_2110
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f1080,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f18948,plain,
spl0_2109,
inference(avatar_split_clause,[],[f1040,f18946]) ).
fof(f18946,plain,
( spl0_2109
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f1040,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f18944,plain,
spl0_2108,
inference(avatar_split_clause,[],[f1039,f18942]) ).
fof(f18942,plain,
( spl0_2108
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f1039,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f18940,plain,
spl0_2107,
inference(avatar_split_clause,[],[f1032,f18938]) ).
fof(f18938,plain,
( spl0_2107
<=> ! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f1032,axiom,
! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f18935,plain,
spl0_2106,
inference(avatar_split_clause,[],[f1031,f18933]) ).
fof(f18933,plain,
( spl0_2106
<=> ! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f1031,axiom,
! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f18931,plain,
spl0_2105,
inference(avatar_split_clause,[],[f1013,f18929]) ).
fof(f18929,plain,
( spl0_2105
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f1013,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f18927,plain,
spl0_2104,
inference(avatar_split_clause,[],[f1010,f18925]) ).
fof(f18925,plain,
( spl0_2104
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0) = c_plus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f1010,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0) = c_plus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f18923,plain,
spl0_2103,
inference(avatar_split_clause,[],[f865,f18921]) ).
fof(f18921,plain,
( spl0_2103
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(c_1,X16),X3,X16)
| c_less(c_uminus(X3,X16),c_1,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f865,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(c_1,X16),X3,X16)
| c_less(c_uminus(X3,X16),c_1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f18919,plain,
spl0_2102,
inference(avatar_split_clause,[],[f864,f18917]) ).
fof(f18917,plain,
( spl0_2102
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(X3,X16),c_1,X16)
| c_less(c_uminus(c_1,X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f864,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(X3,X16),c_1,X16)
| c_less(c_uminus(c_1,X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f18915,plain,
spl0_2101,
inference(avatar_split_clause,[],[f861,f18913]) ).
fof(f18913,plain,
( spl0_2101
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(c_1,X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_1,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f861,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(c_1,X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f18911,plain,
spl0_2100,
inference(avatar_split_clause,[],[f860,f18909]) ).
fof(f18909,plain,
( spl0_2100
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_1,X16)
| c_lessequals(c_uminus(c_1,X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f860,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_1,X16)
| c_lessequals(c_uminus(c_1,X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f18907,plain,
spl0_2099,
inference(avatar_split_clause,[],[f854,f18905]) ).
fof(f18905,plain,
( spl0_2099
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(X1,c_uminus(c_1,X16),X16)
| c_less(c_1,c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f854,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(X1,c_uminus(c_1,X16),X16)
| c_less(c_1,c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f18903,plain,
spl0_2098,
inference(avatar_split_clause,[],[f853,f18901]) ).
fof(f18901,plain,
( spl0_2098
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_1,c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f853,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_1,c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f18899,plain,
spl0_2097,
inference(avatar_split_clause,[],[f838,f18897]) ).
fof(f18897,plain,
( spl0_2097
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(X1,c_uminus(c_1,X16),X16)
| c_lessequals(c_1,c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f838,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(X1,c_uminus(c_1,X16),X16)
| c_lessequals(c_1,c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f18894,plain,
spl0_2096,
inference(avatar_split_clause,[],[f837,f18892]) ).
fof(f18892,plain,
( spl0_2096
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_1,c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f837,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_1,c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f18890,plain,
spl0_2095,
inference(avatar_split_clause,[],[f826,f18888]) ).
fof(f18888,plain,
( spl0_2095
<=> ! [X16,X33] :
( ~ class_Ring__and__Field_Ofield(X16)
| ~ class_Numeral_Onumber(X16)
| c_HOL_Oinverse(c_Numeral_Onumber__of(X33,X16),X16) = c_divide(c_1,c_Numeral_Onumber__of(X33,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f826,axiom,
! [X16,X33] :
( ~ class_Ring__and__Field_Ofield(X16)
| ~ class_Numeral_Onumber(X16)
| c_HOL_Oinverse(c_Numeral_Onumber__of(X33,X16),X16) = c_divide(c_1,c_Numeral_Onumber__of(X33,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).
fof(f18886,plain,
spl0_2094,
inference(avatar_split_clause,[],[f763,f18884]) ).
fof(f18884,plain,
( spl0_2094
<=> ! [X34,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,X0) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f763,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,X0) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f18882,plain,
spl0_2093,
inference(avatar_split_clause,[],[f674,f18880]) ).
fof(f18880,plain,
( spl0_2093
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Otl(c_append(X39,X40,X0),X0) = c_append(c_List_Otl(X39,X0),X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f674,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Otl(c_append(X39,X40,X0),X0) = c_append(c_List_Otl(X39,X0),X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f18878,plain,
spl0_2092,
inference(avatar_split_clause,[],[f658,f18876]) ).
fof(f18876,plain,
( spl0_2092
<=> ! [X0,X12,X26] :
( ~ c_in(c_0,X26,tc_nat)
| c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f658,axiom,
! [X0,X26,X12] :
( ~ c_in(c_0,X26,tc_nat)
| c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f18873,plain,
spl0_2091,
inference(avatar_split_clause,[],[f621,f18871]) ).
fof(f18871,plain,
( spl0_2091
<=> ! [X0,X40,X10] : c_List_Olist_OCons(X10,X40,X0) = c_List_Orev(c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f621,axiom,
! [X40,X10,X0] : c_List_Olist_OCons(X10,X40,X0) = c_List_Orev(c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f18869,plain,
spl0_2090,
inference(avatar_split_clause,[],[f618,f18867]) ).
fof(f18867,plain,
( spl0_2090
<=> ! [X12,X39,X14] : c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f618,axiom,
! [X39,X14,X12] : c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f18865,plain,
spl0_2089,
inference(avatar_split_clause,[],[f607,f18863]) ).
fof(f18863,plain,
( spl0_2089
<=> ! [X12,X39,X14] :
( ~ c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Oremdups(X39,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f607,axiom,
! [X39,X14,X12] :
( ~ c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Oremdups(X39,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f18861,plain,
spl0_2088,
inference(avatar_split_clause,[],[f595,f18859]) ).
fof(f18859,plain,
( spl0_2088
<=> ! [X0,X11,X39] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_in(c_List_Onth(X39,X11,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f595,axiom,
! [X39,X0,X11] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_in(c_List_Onth(X39,X11,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f18857,plain,
spl0_2087,
inference(avatar_split_clause,[],[f594,f18855]) ).
fof(f18855,plain,
( spl0_2087
<=> ! [X0,X12,X50,X23,X39] :
( X23 = X50
| c_List_Onth(c_List_Olist__update(X39,X23,X12,X0),X50,X0) = c_List_Onth(X39,X50,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f594,axiom,
! [X50,X39,X0,X12,X23] :
( X23 = X50
| c_List_Onth(c_List_Olist__update(X39,X23,X12,X0),X50,X0) = c_List_Onth(X39,X50,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f18853,plain,
( spl0_2086
| ~ spl0_1399
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17576,f17299,f11039,f18851]) ).
fof(f18851,plain,
( spl0_2086
<=> ! [X0] : c_Set_Ocontents(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f11039,plain,
( spl0_1399
<=> ! [X0,X10] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f17576,plain,
( ! [X0] : c_Set_Ocontents(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0
| ~ spl0_1399
| ~ spl0_1988 ),
inference(superposition,[],[f11040,f17300]) ).
fof(f11040,plain,
( ! [X10,X0] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10
| ~ spl0_1399 ),
inference(avatar_component_clause,[],[f11039]) ).
fof(f18849,plain,
spl0_2085,
inference(avatar_split_clause,[],[f512,f18847]) ).
fof(f18847,plain,
( spl0_2085
<=> ! [X0,X12,X19] : ~ c_in(c_Pair(X12,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f512,axiom,
! [X0,X19,X12] : ~ c_in(c_Pair(X12,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f18845,plain,
spl0_2084,
inference(avatar_split_clause,[],[f499,f18843]) ).
fof(f18843,plain,
( spl0_2084
<=> ! [X0,X39] :
( c_List_Oremdups(X39,X0) = X39
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f499,axiom,
! [X39,X0] :
( c_List_Oremdups(X39,X0) = X39
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f18841,plain,
spl0_2083,
inference(avatar_split_clause,[],[f439,f18839]) ).
fof(f18839,plain,
( spl0_2083
<=> ! [X39,X0,X40] : c_List_Oconcat(c_append(X39,X40,tc_List_Olist(X0)),X0) = c_append(c_List_Oconcat(X39,X0),c_List_Oconcat(X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f439,axiom,
! [X40,X39,X0] : c_List_Oconcat(c_append(X39,X40,tc_List_Olist(X0)),X0) = c_append(c_List_Oconcat(X39,X0),c_List_Oconcat(X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f18837,plain,
spl0_2082,
inference(avatar_split_clause,[],[f432,f18835]) ).
fof(f18835,plain,
( spl0_2082
<=> ! [X12,X39,X14] :
( c_List_Olist_ONil = X39
| c_List_Obutlast(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Obutlast(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f432,axiom,
! [X39,X14,X12] :
( c_List_Olist_ONil = X39
| c_List_Obutlast(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Obutlast(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f18833,plain,
spl0_2081,
inference(avatar_split_clause,[],[f413,f18831]) ).
fof(f18831,plain,
( spl0_2081
<=> ! [X0,X10] :
( c_List_Olist_ONil = X10
| c_append(c_List_Obutlast(X10,X0),c_List_Olist_OCons(c_List_Olast(X10,X0),c_List_Olist_ONil,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f413,axiom,
! [X10,X0] :
( c_List_Olist_ONil = X10
| c_append(c_List_Obutlast(X10,X0),c_List_Olist_OCons(c_List_Olast(X10,X0),c_List_Olist_ONil,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f18829,plain,
spl0_2080,
inference(avatar_split_clause,[],[f409,f18827]) ).
fof(f18827,plain,
( spl0_2080
<=> ! [X0,X40,X19] : ~ c_in(c_Pair(c_List_Olist_ONil,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f409,axiom,
! [X40,X0,X19] : ~ c_in(c_Pair(c_List_Olist_ONil,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f18825,plain,
spl0_2079,
inference(avatar_split_clause,[],[f401,f18823]) ).
fof(f18823,plain,
( spl0_2079
<=> ! [X29,X41,X0] :
( c_List_Olist_ONil = X29
| c_List_Olist_ONil != c_List_Oconcat(X41,X0)
| ~ c_in(X29,c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f401,axiom,
! [X41,X29,X0] :
( c_List_Olist_ONil = X29
| c_List_Olist_ONil != c_List_Oconcat(X41,X0)
| ~ c_in(X29,c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f18821,plain,
spl0_2078,
inference(avatar_split_clause,[],[f400,f18819]) ).
fof(f18819,plain,
( spl0_2078
<=> ! [X0,X39,X19] : ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f400,axiom,
! [X39,X0,X19] : ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f18817,plain,
spl0_2077,
inference(avatar_split_clause,[],[f205,f18815]) ).
fof(f18815,plain,
( spl0_2077
<=> ! [X0,X11] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f205,axiom,
! [X0,X11] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f18813,plain,
spl0_2076,
inference(avatar_split_clause,[],[f197,f18811]) ).
fof(f18811,plain,
( spl0_2076
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X11,X24,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f197,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X11,X24,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f18809,plain,
( spl0_2075
| ~ spl0_1899
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17573,f17299,f15280,f18807]) ).
fof(f18807,plain,
( spl0_2075
<=> ! [X0] : c_Finite__Set_OMax(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f15280,plain,
( spl0_1899
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f17573,plain,
( ! [X0] : c_Finite__Set_OMax(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0
| ~ spl0_1899
| ~ spl0_1988 ),
inference(superposition,[],[f15281,f17300]) ).
fof(f15281,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_a),t_a) = X0
| ~ spl0_1899 ),
inference(avatar_component_clause,[],[f15280]) ).
fof(f18805,plain,
spl0_2074,
inference(avatar_split_clause,[],[f196,f18803]) ).
fof(f18803,plain,
( spl0_2074
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X24,X11,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f196,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X24,X11,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f18801,plain,
spl0_2073,
inference(avatar_split_clause,[],[f195,f18799]) ).
fof(f18799,plain,
( spl0_2073
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(c_plus(X24,X11,tc_nat),X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f195,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(c_plus(X24,X11,tc_nat),X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f18797,plain,
spl0_2072,
inference(avatar_split_clause,[],[f166,f18795]) ).
fof(f18795,plain,
( spl0_2072
<=> ! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMin(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f166,axiom,
! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMin(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f18793,plain,
spl0_2071,
inference(avatar_split_clause,[],[f151,f18791]) ).
fof(f18791,plain,
( spl0_2071
<=> ! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMax(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f151,axiom,
! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMax(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f18789,plain,
spl0_2070,
inference(avatar_split_clause,[],[f7,f18787]) ).
fof(f18787,plain,
( spl0_2070
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_times(X3,X1,X0),c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_times(X3,X1,X0),c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro2_0) ).
fof(f18785,plain,
spl0_2069,
inference(avatar_split_clause,[],[f1,f18783]) ).
fof(f18783,plain,
( spl0_2069
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_plus(X3,X1,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_plus(X3,X1,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro2_0) ).
fof(f18737,plain,
( spl0_2068
| ~ spl0_1900
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17572,f17299,f15473,f18735]) ).
fof(f18735,plain,
( spl0_2068
<=> ! [X0] : c_Finite__Set_OMin(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f15473,plain,
( spl0_1900
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f17572,plain,
( ! [X0] : c_Finite__Set_OMin(c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) = X0
| ~ spl0_1900
| ~ spl0_1988 ),
inference(superposition,[],[f15474,f17300]) ).
fof(f15474,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_a),t_a) = X0
| ~ spl0_1900 ),
inference(avatar_component_clause,[],[f15473]) ).
fof(f18432,plain,
( spl0_2067
| ~ spl0_1590
| ~ spl0_2066 ),
inference(avatar_split_clause,[],[f18367,f18258,f12676,f18430]) ).
fof(f18367,plain,
( ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1590
| ~ spl0_2066 ),
inference(resolution,[],[f18259,f12677]) ).
fof(f18260,plain,
( ~ spl0_1055
| spl0_2066
| ~ spl0_1908
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f18105,f17900,f16164,f18258,f8701]) ).
fof(f16164,plain,
( spl0_1908
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f18105,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
| ~ spl0_1908
| ~ spl0_2065 ),
inference(resolution,[],[f17901,f16165]) ).
fof(f16165,plain,
( ! [X0,X35,X33] :
( ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1908 ),
inference(avatar_component_clause,[],[f16164]) ).
fof(f17902,plain,
( ~ spl0_1198
| spl0_2065
| ~ spl0_1856
| ~ spl0_2050 ),
inference(avatar_split_clause,[],[f17799,f17733,f14900,f17900,f9544]) ).
fof(f9544,plain,
( spl0_1198
<=> class_Orderings_Oord(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f14900,plain,
( spl0_1856
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f17733,plain,
( spl0_2050
<=> ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f17799,plain,
( ! [X0] :
( c_lessequals(X0,X0,t_a)
| ~ class_Orderings_Oord(t_a) )
| ~ spl0_1856
| ~ spl0_2050 ),
inference(resolution,[],[f17734,f14901]) ).
fof(f14901,plain,
( ! [X72,X0,X36,X23] :
( ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0)
| c_lessequals(X23,X36,X0)
| ~ class_Orderings_Oord(X0) )
| ~ spl0_1856 ),
inference(avatar_component_clause,[],[f14900]) ).
fof(f17734,plain,
( ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a)
| ~ spl0_2050 ),
inference(avatar_component_clause,[],[f17733]) ).
fof(f17825,plain,
spl0_2064,
inference(avatar_split_clause,[],[f3199,f17823]) ).
fof(f17823,plain,
( spl0_2064
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f3199,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3198,f1009]) ).
fof(f1009,axiom,
! [X10] : c_Numeral_Obin__add(X10,c_Numeral_OPls) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3198,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f2995,f2790]) ).
fof(f2790,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f1020,f1023]) ).
fof(f1020,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(f2995,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f211,f1023]) ).
fof(f211,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f17821,plain,
spl0_2063,
inference(avatar_split_clause,[],[f3192,f17819]) ).
fof(f17819,plain,
( spl0_2063
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f3192,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3191,f1009]) ).
fof(f3191,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2989,f2790]) ).
fof(f2989,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f215,f1023]) ).
fof(f215,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f17817,plain,
spl0_2062,
inference(avatar_split_clause,[],[f3189,f17815]) ).
fof(f17815,plain,
( spl0_2062
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f3189,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3188,f1009]) ).
fof(f3188,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f2987,f2790]) ).
fof(f2987,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f210,f1023]) ).
fof(f210,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f17813,plain,
spl0_2061,
inference(avatar_split_clause,[],[f3182,f17811]) ).
fof(f17811,plain,
( spl0_2061
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f3182,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3181,f1009]) ).
fof(f3181,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f2981,f2790]) ).
fof(f2981,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f214,f1023]) ).
fof(f214,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f17809,plain,
spl0_2060,
inference(avatar_split_clause,[],[f3163,f17807]) ).
fof(f17807,plain,
( spl0_2060
<=> ! [X11,X24] :
( c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f3163,plain,
! [X11,X24] :
( c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2967,f2791]) ).
fof(f2967,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f991,f1438]) ).
fof(f991,axiom,
! [X11,X24] :
( ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f17805,plain,
spl0_2059,
inference(avatar_split_clause,[],[f3079,f17803]) ).
fof(f17803,plain,
( spl0_2059
<=> ! [X34,X0] :
( c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f3079,plain,
! [X0,X34] :
( c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f224,f1050]) ).
fof(f224,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f17798,plain,
spl0_2058,
inference(avatar_split_clause,[],[f3078,f17796]) ).
fof(f17796,plain,
( spl0_2058
<=> ! [X0,X33] :
( c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X33),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f3078,plain,
! [X0,X33] :
( c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X33),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f223,f1050]) ).
fof(f223,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f17794,plain,
spl0_2057,
inference(avatar_split_clause,[],[f3051,f17792]) ).
fof(f17792,plain,
( spl0_2057
<=> ! [X0,X19] : c_List_Olistset(c_List_Olist_ONil,X0) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f3051,plain,
! [X0,X19] : c_List_Olistset(c_List_Olist_ONil,X0) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0),tc_List_Olist(X0)),
inference(forward_demodulation,[],[f530,f533]) ).
fof(f533,axiom,
! [X14] : c_List_Olistset(c_List_Olist_ONil,X14) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f530,axiom,
! [X0,X19] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X0)) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X0)),tc_List_Olist(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f17790,plain,
spl0_2056,
inference(avatar_split_clause,[],[f3048,f17788]) ).
fof(f17788,plain,
( spl0_2056
<=> ! [X0,X55,X3] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f3048,plain,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_1,tc_nat),
inference(forward_demodulation,[],[f2872,f2791]) ).
fof(f2872,plain,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f521,f1438]) ).
fof(f521,axiom,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f17786,plain,
spl0_2055,
inference(avatar_split_clause,[],[f3044,f17784]) ).
fof(f17784,plain,
( spl0_2055
<=> ! [X3,X0,X30,X2] : c_union(c_insert(X3,X30,X0),X2,X0) = c_union(X30,c_insert(X3,X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f3044,plain,
! [X2,X3,X0,X30] : c_union(c_insert(X3,X30,X0),X2,X0) = c_union(X30,c_insert(X3,X2,X0),X0),
inference(forward_demodulation,[],[f1537,f1538]) ).
fof(f1538,axiom,
! [X3,X0,X26,X30] : c_union(X26,c_insert(X3,X30,X0),X0) = c_insert(X3,c_union(X26,X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f1537,axiom,
! [X2,X3,X0,X30] : c_union(c_insert(X3,X30,X0),X2,X0) = c_insert(X3,c_union(X30,X2,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f17782,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2949,f17780]) ).
fof(f17780,plain,
( spl0_2054
<=> ! [X0,X11,X10] :
( c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f2949,plain,
! [X10,X0,X11] :
( c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ),
inference(definition_unfolding,[],[f664,f660]) ).
fof(f664,axiom,
! [X10,X0,X11] :
( c_List_Otake(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f17762,plain,
( spl0_2053
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2052 ),
inference(avatar_split_clause,[],[f17758,f17755,f13801,f13502,f9018,f3835,f17760]) ).
fof(f17760,plain,
( spl0_2053
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_plus(c_1,X36,tc_nat),X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f17755,plain,
( spl0_2052
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f17758,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_plus(c_1,X36,tc_nat),X72,tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2052 ),
inference(forward_demodulation,[],[f17756,f14546]) ).
fof(f17756,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat)
| ~ spl0_2052 ),
inference(avatar_component_clause,[],[f17755]) ).
fof(f17757,plain,
spl0_2052,
inference(avatar_split_clause,[],[f2843,f17755]) ).
fof(f17739,plain,
( spl0_2051
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2049 ),
inference(avatar_split_clause,[],[f17731,f17728,f13801,f13502,f9018,f3835,f17737]) ).
fof(f17728,plain,
( spl0_2049
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f17731,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2049 ),
inference(forward_demodulation,[],[f17729,f14546]) ).
fof(f17729,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat)
| ~ spl0_2049 ),
inference(avatar_component_clause,[],[f17728]) ).
fof(f17735,plain,
( spl0_2050
| ~ spl0_1321
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17578,f17299,f10397,f17733]) ).
fof(f10397,plain,
( spl0_1321
<=> ! [X0,X12,X26] : c_in(X12,c_insert(X12,X26,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f17578,plain,
( ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_a),t_a)
| ~ spl0_1321
| ~ spl0_1988 ),
inference(superposition,[],[f10398,f17300]) ).
fof(f10398,plain,
( ! [X0,X26,X12] : c_in(X12,c_insert(X12,X26,X0),X0)
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f10397]) ).
fof(f17730,plain,
spl0_2049,
inference(avatar_split_clause,[],[f2842,f17728]) ).
fof(f17706,plain,
( spl0_2048
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2047 ),
inference(avatar_split_clause,[],[f17702,f17699,f13801,f13502,f9018,f3835,f17704]) ).
fof(f17704,plain,
( spl0_2048
<=> ! [X0,X11,X39] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_plus(c_1,X11,tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f17699,plain,
( spl0_2047
<=> ! [X0,X11,X39] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f17702,plain,
( ! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_plus(c_1,X11,tc_nat),X39,X0)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_2047 ),
inference(forward_demodulation,[],[f17700,f14546]) ).
fof(f17700,plain,
( ! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0)
| ~ spl0_2047 ),
inference(avatar_component_clause,[],[f17699]) ).
fof(f17701,plain,
spl0_2047,
inference(avatar_split_clause,[],[f2841,f17699]) ).
fof(f2841,plain,
! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0),
inference(definition_unfolding,[],[f632,f1438]) ).
fof(f632,axiom,
! [X39,X0,X11] : c_List_Orotate(c_Suc(X11),X39,X0) = c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f17697,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1748,f17695]) ).
fof(f17695,plain,
( spl0_2046
<=> ! [X0,X85,X16,X86] :
( ~ c_Wellfounded__Recursion_Owf(X85,X16)
| ~ c_Wellfounded__Recursion_Owf(X86,X0)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X86,X85,X0,X16),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f1748,axiom,
! [X0,X86,X16,X85] :
( ~ c_Wellfounded__Recursion_Owf(X85,X16)
| ~ c_Wellfounded__Recursion_Owf(X86,X0)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X86,X85,X0,X16),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f17693,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1746,f17691]) ).
fof(f17691,plain,
( spl0_2045
<=> ! [X0,X84,X16,X83] :
( ~ c_Relation_Otrans(X83,X16)
| ~ c_Relation_Otrans(X84,X0)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X84,X83,X0,X16),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f1746,axiom,
! [X83,X0,X16,X84] :
( ~ c_Relation_Otrans(X83,X16)
| ~ c_Relation_Otrans(X84,X0)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X84,X83,X0,X16),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f17689,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1701,f17687]) ).
fof(f17687,plain,
( spl0_2044
<=> ! [X25,X0,X26] :
( c_in(c_Main_OdiagE__1(X26,X25,X0),X26,X0)
| ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f1701,axiom,
! [X0,X26,X25] :
( c_in(c_Main_OdiagE__1(X26,X25,X0),X26,X0)
| ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f17685,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1616,f17683]) ).
fof(f17683,plain,
( spl0_2043
<=> ! [X0,X12,X19,X10] :
( c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f1616,axiom,
! [X10,X0,X19,X12] :
( c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f17681,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1613,f17679]) ).
fof(f17679,plain,
( spl0_2042
<=> ! [X0,X12,X19,X10] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f1613,axiom,
! [X10,X0,X19,X12] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f17677,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1551,f17675]) ).
fof(f17675,plain,
( spl0_2041
<=> ! [X0,X29,X2,X26] :
( ~ c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| c_in(X26,c_Union(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f1551,axiom,
! [X2,X29,X0,X26] :
( ~ c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| c_in(X26,c_Union(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f17672,plain,
spl0_2040,
inference(avatar_split_clause,[],[f1538,f17670]) ).
fof(f17670,plain,
( spl0_2040
<=> ! [X0,X3,X26,X30] : c_union(X26,c_insert(X3,X30,X0),X0) = c_insert(X3,c_union(X26,X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f17668,plain,
spl0_2039,
inference(avatar_split_clause,[],[f1534,f17666]) ).
fof(f17666,plain,
( spl0_2039
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f1534,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f17664,plain,
spl0_2038,
inference(avatar_split_clause,[],[f1514,f17662]) ).
fof(f17662,plain,
( spl0_2038
<=> ! [X0,X29,X2,X26] :
( c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| ~ c_in(X26,c_Inter(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f1514,axiom,
! [X2,X29,X0,X26] :
( c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| ~ c_in(X26,c_Inter(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f17660,plain,
spl0_2037,
inference(avatar_split_clause,[],[f1487,f17658]) ).
fof(f17658,plain,
( spl0_2037
<=> ! [X0,X30,X26] : c_minus(X26,X30,tc_set(X0)) = c_minus(c_minus(X26,X30,tc_set(X0)),X30,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f1487,axiom,
! [X0,X26,X30] : c_minus(X26,X30,tc_set(X0)) = c_minus(c_minus(X26,X30,tc_set(X0)),X30,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f17656,plain,
spl0_2036,
inference(avatar_split_clause,[],[f1466,f17654]) ).
fof(f17654,plain,
( spl0_2036
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f1466,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f17652,plain,
spl0_2035,
inference(avatar_split_clause,[],[f1465,f17650]) ).
fof(f17650,plain,
( spl0_2035
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f1465,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f17648,plain,
spl0_2034,
inference(avatar_split_clause,[],[f1455,f17646]) ).
fof(f17646,plain,
( spl0_2034
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f1455,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f17644,plain,
spl0_2033,
inference(avatar_split_clause,[],[f1454,f17642]) ).
fof(f17642,plain,
( spl0_2033
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f1454,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f17640,plain,
spl0_2032,
inference(avatar_split_clause,[],[f1442,f17638]) ).
fof(f17638,plain,
( spl0_2032
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,c_plus(X72,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f1442,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,c_plus(X72,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f17636,plain,
spl0_2031,
inference(avatar_split_clause,[],[f1435,f17634]) ).
fof(f17634,plain,
( spl0_2031
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X36,X72,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f1435,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X36,X72,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f17632,plain,
( spl0_2030
| ~ spl0_1265
| ~ spl0_1988 ),
inference(avatar_split_clause,[],[f17577,f17299,f9822,f17630]) ).
fof(f17630,plain,
( spl0_2030
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f9822,plain,
( spl0_1265
<=> ! [X0,X3,X26] : c_emptyset != c_insert(X3,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f17577,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,t_a)
| ~ spl0_1265
| ~ spl0_1988 ),
inference(superposition,[],[f9823,f17300]) ).
fof(f9823,plain,
( ! [X3,X0,X26] : c_emptyset != c_insert(X3,X26,X0)
| ~ spl0_1265 ),
inference(avatar_component_clause,[],[f9822]) ).
fof(f17628,plain,
spl0_2029,
inference(avatar_split_clause,[],[f1433,f17626]) ).
fof(f17626,plain,
( spl0_2029
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f1433,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f17624,plain,
spl0_2028,
inference(avatar_split_clause,[],[f1432,f17622]) ).
fof(f17622,plain,
( spl0_2028
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f1432,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f17620,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1427,f17618]) ).
fof(f17618,plain,
( spl0_2027
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1427,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f17616,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1426,f17614]) ).
fof(f17614,plain,
( spl0_2026
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1426,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f17612,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1384,f17610]) ).
fof(f17610,plain,
( spl0_2025
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_uminus(c_times(X3,X1,X0),X0) = c_times(X3,c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f1384,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_uminus(c_times(X3,X1,X0),X0) = c_times(X3,c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f17608,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1383,f17606]) ).
fof(f17606,plain,
( spl0_2024
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(c_uminus(X3,X0),X1,X0) = c_uminus(c_times(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1383,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(c_uminus(X3,X0),X1,X0) = c_uminus(c_times(X3,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f17604,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1361,f17602]) ).
fof(f17602,plain,
( spl0_2023
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(X3,X1,X0) = c_times(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1361,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(X3,X1,X0) = c_times(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f17600,plain,
spl0_2022,
inference(avatar_split_clause,[],[f1316,f17598]) ).
fof(f17598,plain,
( spl0_2022
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_divide(c_uminus(X3,X0),X1,X0) = c_uminus(c_divide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f1316,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_divide(c_uminus(X3,X0),X1,X0) = c_uminus(c_divide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__minus__left_0) ).
fof(f17596,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1206,f17594]) ).
fof(f17594,plain,
( spl0_2021
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f1206,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f17592,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1200,f17590]) ).
fof(f17590,plain,
( spl0_2020
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1200,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f17571,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1198,f17569]) ).
fof(f17569,plain,
( spl0_2019
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1198,axiom,
! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f17567,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1103,f17565]) ).
fof(f17565,plain,
( spl0_2018
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1103,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f17563,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1102,f17561]) ).
fof(f17561,plain,
( spl0_2017
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1102,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f17559,plain,
spl0_2016,
inference(avatar_split_clause,[],[f974,f17557]) ).
fof(f17557,plain,
( spl0_2016
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f974,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f17555,plain,
spl0_2015,
inference(avatar_split_clause,[],[f954,f17553]) ).
fof(f17553,plain,
( spl0_2015
<=> ! [X9,X11,X24] :
( X11 = X24
| c_0 = X9
| c_times(X11,X9,tc_nat) != c_times(X24,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f954,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_0 = X9
| c_times(X11,X9,tc_nat) != c_times(X24,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f17551,plain,
spl0_2014,
inference(avatar_split_clause,[],[f952,f17549]) ).
fof(f17549,plain,
( spl0_2014
<=> ! [X9,X11,X24] :
( X11 = X24
| c_0 = X9
| c_times(X9,X11,tc_nat) != c_times(X9,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f952,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_0 = X9
| c_times(X9,X11,tc_nat) != c_times(X9,X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f17547,plain,
spl0_2013,
inference(avatar_split_clause,[],[f931,f17545]) ).
fof(f17545,plain,
( spl0_2013
<=> ! [X9,X50,X23] : c_minus(c_minus(X23,X50,tc_nat),X9,tc_nat) = c_minus(X23,c_plus(X50,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f17543,plain,
spl0_2012,
inference(avatar_split_clause,[],[f922,f17541]) ).
fof(f17541,plain,
( spl0_2012
<=> ! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f922,axiom,
! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f17539,plain,
spl0_2011,
inference(avatar_split_clause,[],[f757,f17537]) ).
fof(f17537,plain,
( spl0_2011
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f757,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f17535,plain,
spl0_2010,
inference(avatar_split_clause,[],[f754,f17533]) ).
fof(f17533,plain,
( spl0_2010
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f754,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f17522,plain,
spl0_2009,
inference(avatar_split_clause,[],[f741,f17520]) ).
fof(f17520,plain,
( spl0_2009
<=> ! [X34] :
( c_0 != c_Numeral_Onumber__of(X34,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f741,axiom,
! [X34] :
( c_0 != c_Numeral_Onumber__of(X34,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f17518,plain,
spl0_2008,
inference(avatar_split_clause,[],[f721,f17516]) ).
fof(f17516,plain,
( spl0_2008
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f721,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f17514,plain,
spl0_2007,
inference(avatar_split_clause,[],[f695,f17512]) ).
fof(f17512,plain,
( spl0_2007
<=> ! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X24,X11,tc_nat),X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f695,axiom,
! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X24,X11,tc_nat),X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f17510,plain,
spl0_2006,
inference(avatar_split_clause,[],[f643,f17508]) ).
fof(f17508,plain,
( spl0_2006
<=> ! [X39,X0,X40] : c_List_Oset(c_append(X39,X40,X0),X0) = c_union(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f643,axiom,
! [X40,X39,X0] : c_List_Oset(c_append(X39,X40,X0),X0) = c_union(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f17506,plain,
spl0_2005,
inference(avatar_split_clause,[],[f633,f17504]) ).
fof(f17504,plain,
( spl0_2005
<=> ! [X0,X11,X10] :
( c_List_Orotate(X11,X10,X0) = X10
| c_0 != c_Divides_Oop_Amod(X11,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f633,axiom,
! [X10,X0,X11] :
( c_List_Orotate(X11,X10,X0) = X10
| c_0 != c_Divides_Oop_Amod(X11,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f17502,plain,
spl0_2004,
inference(avatar_split_clause,[],[f619,f17500]) ).
fof(f17500,plain,
( spl0_2004
<=> ! [X40,X0,X39] : c_List_Orev(c_append(X39,X40,X0),X0) = c_append(c_List_Orev(X40,X0),c_List_Orev(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f619,axiom,
! [X40,X39,X0] : c_List_Orev(c_append(X39,X40,X0),X0) = c_append(c_List_Orev(X40,X0),c_List_Orev(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f17498,plain,
spl0_2003,
inference(avatar_split_clause,[],[f602,f17496]) ).
fof(f17496,plain,
( spl0_2003
<=> ! [X40,X14,X12,X39] : c_append(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Olist_OCons(X12,c_append(X39,X40,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f602,axiom,
! [X40,X39,X14,X12] : c_append(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Olist_OCons(X12,c_append(X39,X40,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f17494,plain,
spl0_2002,
inference(avatar_split_clause,[],[f590,f17492]) ).
fof(f17492,plain,
( spl0_2002
<=> ! [X40,X0,X10,X39] : c_List_Onth(c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f590,axiom,
! [X40,X39,X10,X0] : c_List_Onth(c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f17490,plain,
spl0_2001,
inference(avatar_split_clause,[],[f585,f17488]) ).
fof(f17488,plain,
( spl0_2001
<=> ! [X49,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Osublist(X39,X49,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f585,axiom,
! [X39,X0,X49,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Osublist(X39,X49,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f17486,plain,
spl0_2000,
inference(avatar_split_clause,[],[f584,f17484]) ).
fof(f17484,plain,
( spl0_2000
<=> ! [X10,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Oremove1(X10,X39,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f584,axiom,
! [X39,X0,X10,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Oremove1(X10,X39,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f17472,plain,
spl0_1999,
inference(avatar_split_clause,[],[f495,f17470]) ).
fof(f17470,plain,
( spl0_1999
<=> ! [X0,X11,X39] : c_Nat_Osize(c_List_Odrop(X11,X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f495,axiom,
! [X39,X0,X11] : c_Nat_Osize(c_List_Odrop(X11,X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f17468,plain,
spl0_1998,
inference(avatar_split_clause,[],[f471,f17466]) ).
fof(f17466,plain,
( spl0_1998
<=> ! [X23,X0,X12,X9] : c_List_Odrop(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_minus(X9,X23,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f471,axiom,
! [X0,X9,X12,X23] : c_List_Odrop(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_minus(X9,X23,tc_nat),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f17464,plain,
spl0_1997,
inference(avatar_split_clause,[],[f468,f17462]) ).
fof(f17462,plain,
( spl0_1997
<=> ! [X24,X11,X0,X39] : c_List_Odrop(X11,c_List_Odrop(X24,X39,X0),X0) = c_List_Odrop(c_plus(X11,X24,tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f468,axiom,
! [X39,X0,X11,X24] : c_List_Odrop(X11,c_List_Odrop(X24,X39,X0),X0) = c_List_Odrop(c_plus(X11,X24,tc_nat),X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f17460,plain,
spl0_1996,
inference(avatar_split_clause,[],[f448,f17458]) ).
fof(f17458,plain,
( spl0_1996
<=> ! [X12,X39,X14] :
( ~ c_List_Odistinct(X39,X14)
| c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| c_in(X12,c_List_Oset(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f448,axiom,
! [X39,X14,X12] :
( ~ c_List_Odistinct(X39,X14)
| c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| c_in(X12,c_List_Oset(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f17456,plain,
spl0_1995,
inference(avatar_split_clause,[],[f441,f17454]) ).
fof(f17454,plain,
( spl0_1995
<=> ! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f441,axiom,
! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f17452,plain,
spl0_1994,
inference(avatar_split_clause,[],[f412,f17450]) ).
fof(f17450,plain,
( spl0_1994
<=> ! [X42,X40,X0,X39] : c_append(c_append(X39,X40,X0),X42,X0) = c_append(X39,c_append(X40,X42,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f412,axiom,
! [X40,X39,X0,X42] : c_append(c_append(X39,X40,X0),X42,X0) = c_append(X39,c_append(X40,X42,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f17448,plain,
spl0_1993,
inference(avatar_split_clause,[],[f402,f17446]) ).
fof(f17446,plain,
( spl0_1993
<=> ! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_ONil__eq__concat__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f402,axiom,
! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_ONil__eq__concat__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f17444,plain,
spl0_1992,
inference(avatar_split_clause,[],[f389,f17442]) ).
fof(f17442,plain,
( spl0_1992
<=> ! [X1,X3] : c_Divides_Oop_Amod(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f389,axiom,
! [X3,X1] : c_Divides_Oop_Amod(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f17440,plain,
spl0_1991,
inference(avatar_split_clause,[],[f133,f17438]) ).
fof(f17438,plain,
( spl0_1991
<=> ! [X9,X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f133,axiom,
! [X11,X9,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f17436,plain,
spl0_1990,
inference(avatar_split_clause,[],[f131,f17434]) ).
fof(f17434,plain,
( spl0_1990
<=> ! [X9,X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f131,axiom,
! [X11,X9,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f17413,plain,
spl0_1989,
inference(avatar_split_clause,[],[f111,f17411]) ).
fof(f17411,plain,
( spl0_1989
<=> ! [X11,X24] :
( ~ c_less(c_1,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_div(X24,X11,tc_nat),X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f111,axiom,
! [X11,X24] :
( ~ c_less(c_1,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_div(X24,X11,tc_nat),X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f17301,plain,
( spl0_1988
| ~ spl0_1187
| ~ spl0_1637 ),
inference(avatar_split_clause,[],[f13272,f12868,f9499,f17299]) ).
fof(f12868,plain,
( spl0_1637
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f13272,plain,
( ! [X0] : c_insert(X0,c_emptyset,t_a) = c_SetInterval_OatLeastAtMost(X0,X0,t_a)
| ~ spl0_1187
| ~ spl0_1637 ),
inference(resolution,[],[f12869,f9501]) ).
fof(f9501,plain,
( class_Orderings_Oorder(t_a)
| ~ spl0_1187 ),
inference(avatar_component_clause,[],[f9499]) ).
fof(f12869,plain,
( ! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) )
| ~ spl0_1637 ),
inference(avatar_component_clause,[],[f12868]) ).
fof(f17167,plain,
( spl0_1987
| ~ spl0_1127
| ~ spl0_1624 ),
inference(avatar_split_clause,[],[f13152,f12816,f9203,f17165]) ).
fof(f17165,plain,
( spl0_1987
<=> ! [X0] : c_HOL_Oabs(X0,t_a) = c_HOL_Oabs(c_uminus(X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f12816,plain,
( spl0_1624
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f13152,plain,
( ! [X0] : c_HOL_Oabs(X0,t_a) = c_HOL_Oabs(c_uminus(X0,t_a),t_a)
| ~ spl0_1127
| ~ spl0_1624 ),
inference(resolution,[],[f12817,f9205]) ).
fof(f9205,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9203]) ).
fof(f12817,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) )
| ~ spl0_1624 ),
inference(avatar_component_clause,[],[f12816]) ).
fof(f17080,plain,
( spl0_1986
| ~ spl0_1127
| ~ spl0_1622 ),
inference(avatar_split_clause,[],[f13145,f12808,f9203,f17078]) ).
fof(f17078,plain,
( spl0_1986
<=> ! [X0] : c_HOL_Oabs(X0,t_a) = c_HOL_Oabs(c_HOL_Oabs(X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f12808,plain,
( spl0_1622
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f13145,plain,
( ! [X0] : c_HOL_Oabs(X0,t_a) = c_HOL_Oabs(c_HOL_Oabs(X0,t_a),t_a)
| ~ spl0_1127
| ~ spl0_1622 ),
inference(resolution,[],[f12809,f9205]) ).
fof(f12809,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) )
| ~ spl0_1622 ),
inference(avatar_component_clause,[],[f12808]) ).
fof(f16901,plain,
( spl0_1985
| ~ spl0_1050
| ~ spl0_1592 ),
inference(avatar_split_clause,[],[f13001,f12684,f8599,f16899]) ).
fof(f12684,plain,
( spl0_1592
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f13001,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,t_a) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_a)
| ~ spl0_1050
| ~ spl0_1592 ),
inference(resolution,[],[f12685,f8601]) ).
fof(f12685,plain,
( ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) )
| ~ spl0_1592 ),
inference(avatar_component_clause,[],[f12684]) ).
fof(f16532,plain,
( spl0_1983
| ~ spl0_1984
| ~ spl0_1055
| ~ spl0_1585 ),
inference(avatar_split_clause,[],[f12985,f12654,f8701,f16529,f16525]) ).
fof(f16525,plain,
( spl0_1983
<=> c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f16529,plain,
( spl0_1984
<=> class_Numeral_Onumber__ring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f12654,plain,
( spl0_1585
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f12985,plain,
( ~ class_Numeral_Onumber__ring(t_a)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,t_a),t_a)
| ~ spl0_1055
| ~ spl0_1585 ),
inference(resolution,[],[f12655,f8703]) ).
fof(f8703,plain,
( class_Ring__and__Field_Oordered__idom(t_a)
| ~ spl0_1055 ),
inference(avatar_component_clause,[],[f8701]) ).
fof(f12655,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) )
| ~ spl0_1585 ),
inference(avatar_component_clause,[],[f12654]) ).
fof(f16489,plain,
spl0_1982,
inference(avatar_split_clause,[],[f3155,f16487]) ).
fof(f16487,plain,
( spl0_1982
<=> ! [X0,X10] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f3155,plain,
! [X10,X0] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2961,f1008]) ).
fof(f2961,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f228,f1023]) ).
fof(f228,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f16485,plain,
spl0_1981,
inference(avatar_split_clause,[],[f3150,f16483]) ).
fof(f16483,plain,
( spl0_1981
<=> ! [X0,X10] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f3150,plain,
! [X10,X0] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2957,f1008]) ).
fof(f2957,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f227,f1023]) ).
fof(f227,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f16481,plain,
spl0_1980,
inference(avatar_split_clause,[],[f3043,f16479]) ).
fof(f16479,plain,
( spl0_1980
<=> ! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f3043,plain,
! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2865,f2791]) ).
fof(f2865,plain,
! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat),
inference(definition_unfolding,[],[f764,f1438]) ).
fof(f764,axiom,
! [X75] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f16477,plain,
spl0_1979,
inference(avatar_split_clause,[],[f2966,f16475]) ).
fof(f16475,plain,
( spl0_1979
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f2966,plain,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0) ),
inference(definition_unfolding,[],[f666,f660]) ).
fof(f666,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Otake(X11,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f16468,plain,
( spl0_1978
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f16464,f16461,f13801,f13502,f9018,f3835,f16466]) ).
fof(f16466,plain,
( spl0_1978
<=> ! [X34] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f16461,plain,
( spl0_1977
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f16464,plain,
( ! [X34] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1977 ),
inference(forward_demodulation,[],[f16462,f14546]) ).
fof(f16462,plain,
( ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1977 ),
inference(avatar_component_clause,[],[f16461]) ).
fof(f16463,plain,
spl0_1977,
inference(avatar_split_clause,[],[f2932,f16461]) ).
fof(f2932,plain,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f716,f1438]) ).
fof(f716,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f16459,plain,
spl0_1976,
inference(avatar_split_clause,[],[f2930,f16457]) ).
fof(f16457,plain,
( spl0_1976
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f2930,plain,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1500,f1267]) ).
fof(f1500,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f16455,plain,
spl0_1975,
inference(avatar_split_clause,[],[f2929,f16453]) ).
fof(f16453,plain,
( spl0_1975
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f2929,plain,
! [X0,X26,X25,X30] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1501,f1267]) ).
fof(f1501,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f16451,plain,
spl0_1974,
inference(avatar_split_clause,[],[f2899,f16449]) ).
fof(f16449,plain,
( spl0_1974
<=> ! [X11,X24] :
( X11 = X24
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f2899,plain,
! [X11,X24] :
( X11 = X24
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f911,f1438,f1438]) ).
fof(f911,axiom,
! [X11,X24] :
( X11 = X24
| c_Suc(X11) != c_Suc(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f16447,plain,
spl0_1973,
inference(avatar_split_clause,[],[f2847,f16445]) ).
fof(f16445,plain,
( spl0_1973
<=> ! [X0,X11,X10] : c_append(c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Odrop(X11,X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f2847,plain,
! [X10,X0,X11] : c_append(c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Odrop(X11,X10,X0),X0) = X10,
inference(definition_unfolding,[],[f429,f660]) ).
fof(f429,axiom,
! [X10,X0,X11] : c_append(c_List_Otake(X11,X10,X0),c_List_Odrop(X11,X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f16443,plain,
spl0_1972,
inference(avatar_split_clause,[],[f1720,f16441]) ).
fof(f16441,plain,
( spl0_1972
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnionE__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f1720,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnionE__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f16439,plain,
spl0_1971,
inference(avatar_split_clause,[],[f1717,f16437]) ).
fof(f16437,plain,
( spl0_1971
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInterI__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f1717,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInterI__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f16435,plain,
spl0_1970,
inference(avatar_split_clause,[],[f1680,f16433]) ).
fof(f16433,plain,
( spl0_1970
<=> ! [X0,X12,X26,X72] :
( c_in(X12,X26,X0)
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f1680,axiom,
! [X72,X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f16431,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1669,f16429]) ).
fof(f16429,plain,
( spl0_1969
<=> ! [X0,X39,X26] :
( ~ c_in(c_Main_Oin__listsI__1(X26,X39,X0),X26,X0)
| c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f1669,axiom,
! [X39,X0,X26] :
( ~ c_in(c_Main_Oin__listsI__1(X26,X39,X0),X26,X0)
| c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f16427,plain,
( spl0_1968
| ~ spl0_1187
| ~ spl0_1741
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f14603,f14448,f13639,f9499,f16424]) ).
fof(f16424,plain,
( spl0_1968
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f13639,plain,
( spl0_1741
<=> ! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f14448,plain,
( spl0_1789
<=> c_lessequals(c_0,c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f14603,plain,
( ~ class_Orderings_Oorder(t_a)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,t_a)
| ~ spl0_1741
| ~ spl0_1789 ),
inference(resolution,[],[f14450,f13640]) ).
fof(f13640,plain,
( ! [X0,X11,X24] :
( ~ c_lessequals(X11,X24,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) )
| ~ spl0_1741 ),
inference(avatar_component_clause,[],[f13639]) ).
fof(f14450,plain,
( c_lessequals(c_0,c_1,t_a)
| ~ spl0_1789 ),
inference(avatar_component_clause,[],[f14448]) ).
fof(f16422,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1664,f16420]) ).
fof(f16420,plain,
( spl0_1967
<=> ! [X24,X78] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_IntDef_Oint)
| c_times(X78,c_Main_Ozmod__eq__0D__dest__1(X78,X24),tc_IntDef_Oint) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f1664,axiom,
! [X78,X24] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_IntDef_Oint)
| c_times(X78,c_Main_Ozmod__eq__0D__dest__1(X78,X24),tc_IntDef_Oint) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f16418,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1648,f16416]) ).
fof(f16416,plain,
( spl0_1966
<=> ! [X24,X78] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_nat)
| c_times(X78,c_Main_Omod__eq__0D__dest__1(X78,X24),tc_nat) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f1648,axiom,
! [X78,X24] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_nat)
| c_times(X78,c_Main_Omod__eq__0D__dest__1(X78,X24),tc_nat) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f16414,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1621,f16412]) ).
fof(f16412,plain,
( spl0_1965
<=> ! [X12,X10] :
( ~ c_less(X12,X10,tc_nat)
| c_in(c_Pair(X12,X10,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f1621,axiom,
! [X10,X12] :
( ~ c_less(X12,X10,tc_nat)
| c_in(c_Pair(X12,X10,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(f16410,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1620,f16408]) ).
fof(f16408,plain,
( spl0_1964
<=> ! [X12,X10] :
( c_less(X12,X10,tc_nat)
| ~ c_in(c_Pair(X12,X10,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f1620,axiom,
! [X10,X12] :
( c_less(X12,X10,tc_nat)
| ~ c_in(c_Pair(X12,X10,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(f16406,plain,
spl0_1963,
inference(avatar_split_clause,[],[f1577,f16404]) ).
fof(f16404,plain,
( spl0_1963
<=> ! [X0,X3,X1,X26] :
( X1 = X3
| c_in(X3,X26,X0)
| ~ c_in(X3,c_insert(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f1577,axiom,
! [X3,X0,X1,X26] :
( X1 = X3
| c_in(X3,X26,X0)
| ~ c_in(X3,c_insert(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f16402,plain,
spl0_1962,
inference(avatar_split_clause,[],[f1552,f16400]) ).
fof(f16400,plain,
( spl0_1962
<=> ! [X3,X0,X30] : c_Union(c_insert(X3,X30,tc_set(X0)),X0) = c_union(X3,c_Union(X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f1552,axiom,
! [X3,X0,X30] : c_Union(c_insert(X3,X30,tc_set(X0)),X0) = c_union(X3,c_Union(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f16398,plain,
spl0_1961,
inference(avatar_split_clause,[],[f1549,f16396]) ).
fof(f16396,plain,
( spl0_1961
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnion__iff__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f1549,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnion__iff__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f16394,plain,
spl0_1960,
inference(avatar_split_clause,[],[f1515,f16392]) ).
fof(f16392,plain,
( spl0_1960
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInter__iff__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f1515,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInter__iff__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f16390,plain,
spl0_1959,
inference(avatar_split_clause,[],[f1382,f16388]) ).
fof(f16388,plain,
( spl0_1959
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_0 = X3
| c_0 = X1
| c_times(X3,X1,X0) != c_0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f1382,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_0 = X3
| c_0 = X1
| c_times(X3,X1,X0) != c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f16386,plain,
spl0_1958,
inference(avatar_split_clause,[],[f1369,f16384]) ).
fof(f16384,plain,
( spl0_1958
<=> ! [X25,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X3
| c_0 = X25
| c_times(X3,X25,X0) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f1369,axiom,
! [X3,X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X3
| c_0 = X25
| c_times(X3,X25,X0) != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
fof(f16380,plain,
spl0_1957,
inference(avatar_split_clause,[],[f1365,f16378]) ).
fof(f16378,plain,
( spl0_1957
<=> ! [X25,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X3
| c_0 = X25
| c_times(X25,X3,X0) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f1365,axiom,
! [X3,X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X3
| c_0 = X25
| c_times(X25,X3,X0) != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f16376,plain,
spl0_1956,
inference(avatar_split_clause,[],[f1257,f16374]) ).
fof(f16374,plain,
( spl0_1956
<=> ! [X15,X3,X0,X16,X76,X1] :
( X1 = X76
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f1257,axiom,
! [X3,X0,X1,X76,X16,X15] :
( X1 = X76
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f16372,plain,
spl0_1955,
inference(avatar_split_clause,[],[f1256,f16370]) ).
fof(f16370,plain,
( spl0_1955
<=> ! [X15,X0,X16,X76,X3,X1] :
( X3 = X15
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f1256,axiom,
! [X3,X0,X1,X16,X76,X15] :
( X3 = X15
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f16368,plain,
spl0_1954,
inference(avatar_split_clause,[],[f1243,f16366]) ).
fof(f16366,plain,
( spl0_1954
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f1243,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f16364,plain,
spl0_1953,
inference(avatar_split_clause,[],[f1242,f16362]) ).
fof(f16362,plain,
( spl0_1953
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X11,tc_nat)
| c_0 != c_Nat_Opower(X3,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f1242,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X11,tc_nat)
| c_0 != c_Nat_Opower(X3,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f16360,plain,
spl0_1952,
inference(avatar_split_clause,[],[f1162,f16358]) ).
fof(f16358,plain,
( spl0_1952
<=> ! [X16,X12,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X12,X10,X16) = c_Orderings_Omax(X12,c_Orderings_Omax(X12,X10,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f1162,axiom,
! [X10,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X12,X10,X16) = c_Orderings_Omax(X12,c_Orderings_Omax(X12,X10,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f16356,plain,
spl0_1951,
inference(avatar_split_clause,[],[f1157,f16354]) ).
fof(f16354,plain,
( spl0_1951
<=> ! [X16,X12,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X12,X10,X16) = c_Orderings_Omin(X12,c_Orderings_Omin(X12,X10,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f1157,axiom,
! [X10,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X12,X10,X16) = c_Orderings_Omin(X12,c_Orderings_Omin(X12,X10,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f16352,plain,
spl0_1950,
inference(avatar_split_clause,[],[f1140,f16350]) ).
fof(f16350,plain,
( spl0_1950
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Opprt(X3,X0),c_OrderedGroup_Opprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f1140,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Opprt(X3,X0),c_OrderedGroup_Opprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f16348,plain,
spl0_1949,
inference(avatar_split_clause,[],[f1136,f16346]) ).
fof(f16346,plain,
( spl0_1949
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_OrderedGroup_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f1136,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_OrderedGroup_Onprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f16344,plain,
spl0_1948,
inference(avatar_split_clause,[],[f1130,f16342]) ).
fof(f16342,plain,
( spl0_1948
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f1130,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f16340,plain,
( spl0_1947
| ~ spl0_1187
| ~ spl0_1750
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f14602,f14448,f13675,f9499,f16337]) ).
fof(f16337,plain,
( spl0_1947
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f13675,plain,
( spl0_1750
<=> ! [X9,X0,X72] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X72,X9,X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f14602,plain,
( ~ class_Orderings_Oorder(t_a)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,t_a)
| ~ spl0_1750
| ~ spl0_1789 ),
inference(resolution,[],[f14450,f13676]) ).
fof(f13676,plain,
( ! [X72,X0,X9] :
( ~ c_lessequals(X72,X9,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) )
| ~ spl0_1750 ),
inference(avatar_component_clause,[],[f13675]) ).
fof(f16335,plain,
spl0_1946,
inference(avatar_split_clause,[],[f1129,f16333]) ).
fof(f16333,plain,
( spl0_1946
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f1129,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f16331,plain,
spl0_1945,
inference(avatar_split_clause,[],[f1126,f16329]) ).
fof(f16329,plain,
( spl0_1945
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f1126,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f16327,plain,
spl0_1944,
inference(avatar_split_clause,[],[f1125,f16325]) ).
fof(f16325,plain,
( spl0_1944
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f1125,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f16323,plain,
spl0_1943,
inference(avatar_split_clause,[],[f1089,f16321]) ).
fof(f16321,plain,
( spl0_1943
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X25,X3,X0) != c_plus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f1089,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X25,X3,X0) != c_plus(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f16319,plain,
spl0_1942,
inference(avatar_split_clause,[],[f1084,f16317]) ).
fof(f16317,plain,
( spl0_1942
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X3,X1,X0) != c_plus(X3,X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f1084,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X3,X1,X0) != c_plus(X3,X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f16315,plain,
spl0_1941,
inference(avatar_split_clause,[],[f1005,f16313]) ).
fof(f16313,plain,
( spl0_1941
<=> ! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(X33)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f1005,axiom,
! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(X33)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f16311,plain,
spl0_1940,
inference(avatar_split_clause,[],[f979,f16309]) ).
fof(f16309,plain,
( spl0_1940
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f979,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f16307,plain,
spl0_1939,
inference(avatar_split_clause,[],[f978,f16305]) ).
fof(f16305,plain,
( spl0_1939
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f978,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f16303,plain,
spl0_1938,
inference(avatar_split_clause,[],[f977,f16301]) ).
fof(f16301,plain,
( spl0_1938
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f977,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f16299,plain,
spl0_1937,
inference(avatar_split_clause,[],[f976,f16297]) ).
fof(f16297,plain,
( spl0_1937
<=> ! [X9,X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f976,axiom,
! [X11,X9,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f16291,plain,
spl0_1936,
inference(avatar_split_clause,[],[f970,f16289]) ).
fof(f16289,plain,
( spl0_1936
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f970,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f16287,plain,
spl0_1935,
inference(avatar_split_clause,[],[f969,f16285]) ).
fof(f16285,plain,
( spl0_1935
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f969,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f16283,plain,
spl0_1934,
inference(avatar_split_clause,[],[f967,f16281]) ).
fof(f16281,plain,
( spl0_1934
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f967,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f16279,plain,
spl0_1933,
inference(avatar_split_clause,[],[f966,f16277]) ).
fof(f16277,plain,
( spl0_1933
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f966,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f16275,plain,
spl0_1932,
inference(avatar_split_clause,[],[f965,f16273]) ).
fof(f16273,plain,
( spl0_1932
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f965,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f16271,plain,
spl0_1931,
inference(avatar_split_clause,[],[f964,f16269]) ).
fof(f16269,plain,
( spl0_1931
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f964,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f16267,plain,
spl0_1930,
inference(avatar_split_clause,[],[f962,f16265]) ).
fof(f16265,plain,
( spl0_1930
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f962,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f16263,plain,
spl0_1929,
inference(avatar_split_clause,[],[f961,f16261]) ).
fof(f16261,plain,
( spl0_1929
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f961,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f16259,plain,
spl0_1928,
inference(avatar_split_clause,[],[f821,f16257]) ).
fof(f16257,plain,
( spl0_1928
<=> ! [X16,X1] :
( ~ class_HOL_Oone(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_1 != c_uminus(X1,X16)
| c_uminus(c_1,X16) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f821,axiom,
! [X1,X16] :
( ~ class_HOL_Oone(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_1 != c_uminus(X1,X16)
| c_uminus(c_1,X16) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f16255,plain,
spl0_1927,
inference(avatar_split_clause,[],[f762,f16253]) ).
fof(f16253,plain,
( spl0_1927
<=> ! [X34,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f762,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f16242,plain,
spl0_1926,
inference(avatar_split_clause,[],[f714,f16240]) ).
fof(f16240,plain,
( spl0_1926
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X24,X11,tc_nat)
| c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f714,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X24,X11,tc_nat)
| c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f16238,plain,
spl0_1925,
inference(avatar_split_clause,[],[f713,f16236]) ).
fof(f16236,plain,
( spl0_1925
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(X24,X11,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f713,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(X24,X11,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f16234,plain,
spl0_1924,
inference(avatar_split_clause,[],[f711,f16232]) ).
fof(f16232,plain,
( spl0_1924
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f711,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f16230,plain,
spl0_1923,
inference(avatar_split_clause,[],[f710,f16228]) ).
fof(f16228,plain,
( spl0_1923
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f710,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f16226,plain,
spl0_1922,
inference(avatar_split_clause,[],[f654,f16224]) ).
fof(f16224,plain,
( spl0_1922
<=> ! [X0,X12,X39] :
( c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = X39
| c_List_Orev(X39,X0) != c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f654,axiom,
! [X39,X0,X12] :
( c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = X39
| c_List_Orev(X39,X0) != c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
fof(f16222,plain,
spl0_1921,
inference(avatar_split_clause,[],[f650,f16220]) ).
fof(f16220,plain,
( spl0_1921
<=> ! [X12,X0,X11] :
( c_0 = X11
| c_insert(X12,c_emptyset,X0) = c_List_Oset(c_List_Oreplicate(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f650,axiom,
! [X0,X11,X12] :
( c_0 = X11
| c_insert(X12,c_emptyset,X0) = c_List_Oset(c_List_Oreplicate(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f16218,plain,
spl0_1920,
inference(avatar_split_clause,[],[f604,f16216]) ).
fof(f16216,plain,
( spl0_1920
<=> ! [X10,X40,X14,X12] :
( X10 = X12
| c_List_Oop_Amem(X12,X40,X14)
| ~ c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f604,axiom,
! [X40,X10,X14,X12] :
( X10 = X12
| c_List_Oop_Amem(X12,X40,X14)
| ~ c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f16214,plain,
spl0_1919,
inference(avatar_split_clause,[],[f534,f16212]) ).
fof(f16212,plain,
( spl0_1919
<=> ! [X57,X14,X26] : c_List_Olistset(c_List_Olist_OCons(X26,X57,tc_set(X14)),X14) = c_List_Oset__Cons(X26,c_List_Olistset(X57,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f534,axiom,
! [X57,X26,X14] : c_List_Olistset(c_List_Olist_OCons(X26,X57,tc_set(X14)),X14) = c_List_Oset__Cons(X26,c_List_Olistset(X57,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f16210,plain,
spl0_1918,
inference(avatar_split_clause,[],[f526,f16208]) ).
fof(f16208,plain,
( spl0_1918
<=> ! [X23,X0,X12,X10] :
( ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X23,tc_nat)
| c_List_Olist__update(X10,X23,X12,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f526,axiom,
! [X10,X0,X12,X23] :
( ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X23,tc_nat)
| c_List_Olist__update(X10,X23,X12,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f16206,plain,
spl0_1917,
inference(avatar_split_clause,[],[f506,f16204]) ).
fof(f16204,plain,
( spl0_1917
<=> ! [X0,X39] : c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f506,axiom,
! [X39,X0] : c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f16198,plain,
spl0_1916,
inference(avatar_split_clause,[],[f494,f16196]) ).
fof(f16196,plain,
( spl0_1916
<=> ! [X0,X39] : c_Nat_Osize(c_List_Obutlast(X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f494,axiom,
! [X39,X0] : c_Nat_Osize(c_List_Obutlast(X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f16194,plain,
spl0_1915,
inference(avatar_split_clause,[],[f490,f16192]) ).
fof(f16192,plain,
( spl0_1915
<=> ! [X50,X23] :
( ~ c_less(X23,X50,tc_nat)
| c_List_Olast(c_List_Oupt(X23,X50),tc_nat) = c_minus(X50,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f490,axiom,
! [X50,X23] :
( ~ c_less(X23,X50,tc_nat)
| c_List_Olast(c_List_Oupt(X23,X50),tc_nat) = c_minus(X50,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f16190,plain,
spl0_1914,
inference(avatar_split_clause,[],[f438,f16188]) ).
fof(f16188,plain,
( spl0_1914
<=> ! [X12,X39,X14] : c_List_Oconcat(c_List_Olist_OCons(X12,X39,tc_List_Olist(X14)),X14) = c_append(X12,c_List_Oconcat(X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f438,axiom,
! [X39,X14,X12] : c_List_Oconcat(c_List_Olist_OCons(X12,X39,tc_List_Olist(X14)),X14) = c_append(X12,c_List_Oconcat(X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f16186,plain,
spl0_1913,
inference(avatar_split_clause,[],[f350,f16184]) ).
fof(f16184,plain,
( spl0_1913
<=> ! [X37,X19] : c_IntDiv_OnegateSnd(c_Pair(X37,X19,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X37,c_uminus(X19,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f16182,plain,
spl0_1912,
inference(avatar_split_clause,[],[f325,f16180]) ).
fof(f16180,plain,
( spl0_1912
<=> ! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f325,axiom,
! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f16178,plain,
spl0_1911,
inference(avatar_split_clause,[],[f309,f16176]) ).
fof(f309,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f16174,plain,
spl0_1910,
inference(avatar_split_clause,[],[f308,f16172]) ).
fof(f16172,plain,
( spl0_1910
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f308,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f16170,plain,
spl0_1909,
inference(avatar_split_clause,[],[f305,f16168]) ).
fof(f16168,plain,
( spl0_1909
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f305,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f16166,plain,
spl0_1908,
inference(avatar_split_clause,[],[f304,f16164]) ).
fof(f304,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f16162,plain,
spl0_1907,
inference(avatar_split_clause,[],[f175,f16160]) ).
fof(f16160,plain,
( spl0_1907
<=> ! [X0,X30,X31] :
( ~ c_in(X30,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X30,X31,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f175,axiom,
! [X31,X0,X30] :
( ~ c_in(X30,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X30,X31,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f16140,plain,
spl0_1906,
inference(avatar_split_clause,[],[f92,f16138]) ).
fof(f16138,plain,
( spl0_1906
<=> ! [X18,X0,X21,X16,X17,X22] :
( X18 = X22
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f92,axiom,
! [X21,X0,X18,X16,X17,X22] :
( X18 = X22
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f16136,plain,
spl0_1905,
inference(avatar_split_clause,[],[f91,f16134]) ).
fof(f16134,plain,
( spl0_1905
<=> ! [X17,X0,X18,X22,X16,X21] :
( X17 = X21
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f91,axiom,
! [X21,X0,X18,X16,X17,X22] :
( X17 = X21
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f15894,plain,
( spl0_1904
| ~ spl0_1231
| ~ spl0_1551 ),
inference(avatar_split_clause,[],[f12594,f12297,f9680,f15892]) ).
fof(f15892,plain,
( spl0_1904
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f12297,plain,
( spl0_1551
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f12594,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_a),t_a)
| ~ spl0_1231
| ~ spl0_1551 ),
inference(resolution,[],[f12298,f9682]) ).
fof(f12298,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) )
| ~ spl0_1551 ),
inference(avatar_component_clause,[],[f12297]) ).
fof(f15832,plain,
( spl0_1903
| ~ spl0_1231
| ~ spl0_1547 ),
inference(avatar_split_clause,[],[f12576,f12281,f9680,f15830]) ).
fof(f15830,plain,
( spl0_1903
<=> ! [X0] : c_uminus(X0,t_a) = c_minus(c_0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f12281,plain,
( spl0_1547
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f12576,plain,
( ! [X0] : c_uminus(X0,t_a) = c_minus(c_0,X0,t_a)
| ~ spl0_1231
| ~ spl0_1547 ),
inference(resolution,[],[f12282,f9682]) ).
fof(f12282,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) )
| ~ spl0_1547 ),
inference(avatar_component_clause,[],[f12281]) ).
fof(f15729,plain,
( spl0_1902
| ~ spl0_1231
| ~ spl0_1545 ),
inference(avatar_split_clause,[],[f12570,f12273,f9680,f15727]) ).
fof(f15727,plain,
( spl0_1902
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f12273,plain,
( spl0_1545
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f12570,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,t_a),X0,t_a)
| ~ spl0_1231
| ~ spl0_1545 ),
inference(resolution,[],[f12274,f9682]) ).
fof(f12274,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) )
| ~ spl0_1545 ),
inference(avatar_component_clause,[],[f12273]) ).
fof(f15632,plain,
( spl0_1901
| ~ spl0_1050
| ~ spl0_1518 ),
inference(avatar_split_clause,[],[f12466,f12161,f8599,f15630]) ).
fof(f12161,plain,
( spl0_1518
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f12466,plain,
( ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_a) = c_NatArith_Oof__nat(X0,t_a)
| ~ spl0_1050
| ~ spl0_1518 ),
inference(resolution,[],[f12162,f8601]) ).
fof(f12162,plain,
( ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) )
| ~ spl0_1518 ),
inference(avatar_component_clause,[],[f12161]) ).
fof(f15475,plain,
( spl0_1900
| ~ spl0_1063
| ~ spl0_1513 ),
inference(avatar_split_clause,[],[f12455,f12141,f8892,f15473]) ).
fof(f12141,plain,
( spl0_1513
<=> ! [X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f12455,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_a),t_a) = X0
| ~ spl0_1063
| ~ spl0_1513 ),
inference(resolution,[],[f12142,f8894]) ).
fof(f12142,plain,
( ! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 )
| ~ spl0_1513 ),
inference(avatar_component_clause,[],[f12141]) ).
fof(f15282,plain,
( spl0_1899
| ~ spl0_1063
| ~ spl0_1512 ),
inference(avatar_split_clause,[],[f12452,f12137,f8892,f15280]) ).
fof(f12137,plain,
( spl0_1512
<=> ! [X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f12452,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_a),t_a) = X0
| ~ spl0_1063
| ~ spl0_1512 ),
inference(resolution,[],[f12138,f8894]) ).
fof(f12138,plain,
( ! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 )
| ~ spl0_1512 ),
inference(avatar_component_clause,[],[f12137]) ).
fof(f15124,plain,
spl0_1898,
inference(avatar_split_clause,[],[f3109,f15122]) ).
fof(f15122,plain,
( spl0_1898
<=> ! [X75] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f3109,plain,
! [X75] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2933,f2791]) ).
fof(f2933,plain,
! [X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f765,f1438,f1438]) ).
fof(f765,axiom,
! [X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f15120,plain,
( spl0_1897
| ~ spl0_1155
| ~ spl0_1627
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f14600,f14448,f12828,f9343,f15117]) ).
fof(f15117,plain,
( spl0_1897
<=> c_0 = c_OrderedGroup_Onprt(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f14600,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_0 = c_OrderedGroup_Onprt(c_1,t_a)
| ~ spl0_1627
| ~ spl0_1789 ),
inference(resolution,[],[f14450,f12829]) ).
fof(f15115,plain,
spl0_1896,
inference(avatar_split_clause,[],[f3093,f15113]) ).
fof(f15113,plain,
( spl0_1896
<=> ! [X11,X23] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X23,X11,tc_nat),tc_nat),X11,tc_nat)
| ~ c_less(c_0,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f3093,plain,
! [X11,X23] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X23,X11,tc_nat),tc_nat),X11,tc_nat)
| ~ c_less(c_0,X11,tc_nat) ),
inference(forward_demodulation,[],[f2913,f2842]) ).
fof(f2913,plain,
! [X11,X23] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X23,tc_nat),tc_nat),tc_nat),X11,tc_nat) ),
inference(definition_unfolding,[],[f930,f1438]) ).
fof(f930,axiom,
! [X11,X23] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X11,c_Suc(X23),tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f15111,plain,
spl0_1895,
inference(avatar_split_clause,[],[f3047,f15109]) ).
fof(f15109,plain,
( spl0_1895
<=> ! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f3047,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f3046,f1050]) ).
fof(f3046,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f3045,f1048]) ).
fof(f3045,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f777,f1050]) ).
fof(f777,axiom,
! [X10] : c_div(c_plus(X10,X10,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) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f15107,plain,
spl0_1894,
inference(avatar_split_clause,[],[f3035,f15105]) ).
fof(f15105,plain,
( spl0_1894
<=> ! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33),X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f3035,plain,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33),X33),
inference(forward_demodulation,[],[f1022,f1021]) ).
fof(f1021,axiom,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33) = c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f1022,axiom,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f15103,plain,
spl0_1893,
inference(avatar_split_clause,[],[f3032,f15101]) ).
fof(f3032,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2833,f2806]) ).
fof(f2806,plain,
! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin),
inference(definition_unfolding,[],[f1006,f1007]) ).
fof(f1007,axiom,
! [X33] : c_Numeral_Obin__pred(X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f1006,axiom,
! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__pred(X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2833,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f1018,f1023,f1007,f1023]) ).
fof(f1018,axiom,
! [X33] : c_Numeral_Obin__minus(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X33)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f15099,plain,
spl0_1892,
inference(avatar_split_clause,[],[f2943,f15097]) ).
fof(f15097,plain,
( spl0_1892
<=> ! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f2943,plain,
! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f747,f1023]) ).
fof(f747,axiom,
! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X34),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f15095,plain,
spl0_1891,
inference(avatar_split_clause,[],[f2941,f15093]) ).
fof(f15093,plain,
( spl0_1891
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f2941,plain,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f748,f1023]) ).
fof(f748,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f15063,plain,
( spl0_1890
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1889 ),
inference(avatar_split_clause,[],[f15059,f15056,f13801,f13502,f9018,f3835,f15061]) ).
fof(f15061,plain,
( spl0_1890
<=> ! [X50,X23] :
( c_List_Olist_ONil = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| c_lessequals(X23,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f15056,plain,
( spl0_1889
<=> ! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f15059,plain,
( ! [X50,X23] :
( c_List_Olist_ONil = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| c_lessequals(X23,X50,tc_nat) )
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1889 ),
inference(forward_demodulation,[],[f15057,f14546]) ).
fof(f15057,plain,
( ! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) )
| ~ spl0_1889 ),
inference(avatar_component_clause,[],[f15056]) ).
fof(f15058,plain,
spl0_1889,
inference(avatar_split_clause,[],[f2928,f15056]) ).
fof(f2928,plain,
! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f677,f1438]) ).
fof(f677,axiom,
! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Suc(X50)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f15054,plain,
spl0_1888,
inference(avatar_split_clause,[],[f2889,f15052]) ).
fof(f2889,plain,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) ),
inference(definition_unfolding,[],[f1011,f1023]) ).
fof(f1011,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f15045,plain,
( spl0_1887
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1886 ),
inference(avatar_split_clause,[],[f15041,f15038,f13801,f13502,f9018,f3835,f15043]) ).
fof(f15043,plain,
( spl0_1887
<=> ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_plus(c_1,X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f15038,plain,
( spl0_1886
<=> ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f15041,plain,
( ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_plus(c_1,X24,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1886 ),
inference(forward_demodulation,[],[f15039,f14546]) ).
fof(f15039,plain,
( ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat)
| ~ spl0_1886 ),
inference(avatar_component_clause,[],[f15038]) ).
fof(f15040,plain,
spl0_1886,
inference(avatar_split_clause,[],[f2834,f15038]) ).
fof(f2834,plain,
! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1421,f1438]) ).
fof(f1421,axiom,
! [X24] : c_SetInterval_OatLeastLessThan(X24,c_Suc(X24),tc_nat) = c_insert(X24,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f15036,plain,
spl0_1885,
inference(avatar_split_clause,[],[f2832,f15034]) ).
fof(f15034,plain,
( spl0_1885
<=> ! [X0,X30,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_minus(X30,X26,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f2832,plain,
! [X0,X26,X30] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_minus(X30,X26,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1483,f1267]) ).
fof(f1483,axiom,
! [X0,X26,X30] : c_emptyset = c_inter(X26,c_minus(X30,X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f15032,plain,
spl0_1884,
inference(avatar_split_clause,[],[f2821,f15030]) ).
fof(f15030,plain,
( spl0_1884
<=> ! [X77,X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f2821,plain,
! [X0,X77] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0),
inference(definition_unfolding,[],[f1600,f1610]) ).
fof(f1600,axiom,
! [X0,X77] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X77,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f15028,plain,
spl0_1883,
inference(avatar_split_clause,[],[f2820,f15026]) ).
fof(f15026,plain,
( spl0_1883
<=> ! [X77,X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f2820,plain,
! [X0,X77] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0),
inference(definition_unfolding,[],[f1601,f1610]) ).
fof(f1601,axiom,
! [X0,X77] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X77,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f15021,plain,
( spl0_1882
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1881 ),
inference(avatar_split_clause,[],[f15017,f15014,f13801,f13502,f9018,f3835,f15019]) ).
fof(f15019,plain,
( spl0_1882
<=> ! [X11] : c_plus(c_1,X11,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f15014,plain,
( spl0_1881
<=> ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f15017,plain,
( ! [X11] : c_plus(c_1,X11,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),X11)
| ~ spl0_129
| ~ spl0_1090
| ~ spl0_1707
| ~ spl0_1781
| ~ spl0_1881 ),
inference(forward_demodulation,[],[f15015,f14546]) ).
fof(f15015,plain,
( ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11)
| ~ spl0_1881 ),
inference(avatar_component_clause,[],[f15014]) ).
fof(f15016,plain,
spl0_1881,
inference(avatar_split_clause,[],[f2816,f15014]) ).
fof(f2816,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11),
inference(definition_unfolding,[],[f57,f1438,f1438]) ).
fof(f57,axiom,
! [X11] : c_Suc(X11) = c_Binomial_Obinomial(c_Suc(X11),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f15012,plain,
spl0_1880,
inference(avatar_split_clause,[],[f1732,f15010]) ).
fof(f15010,plain,
( spl0_1880
<=> ! [X0,X30,X26] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(X30,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f1732,axiom,
! [X0,X26,X30] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(X30,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f15008,plain,
( spl0_1879
| ~ spl0_1155
| ~ spl0_1631
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f14599,f14448,f12844,f9343,f15005]) ).
fof(f15005,plain,
( spl0_1879
<=> c_1 = c_OrderedGroup_Opprt(c_1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f12844,plain,
( spl0_1631
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f14599,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_a)
| c_1 = c_OrderedGroup_Opprt(c_1,t_a)
| ~ spl0_1631
| ~ spl0_1789 ),
inference(resolution,[],[f14450,f12845]) ).
fof(f12845,plain,
( ! [X10,X0] :
( ~ c_lessequals(c_0,X10,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 )
| ~ spl0_1631 ),
inference(avatar_component_clause,[],[f12844]) ).
fof(f15003,plain,
spl0_1878,
inference(avatar_split_clause,[],[f1729,f15001]) ).
fof(f15001,plain,
( spl0_1878
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f1729,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f14999,plain,
spl0_1877,
inference(avatar_split_clause,[],[f1725,f14997]) ).
fof(f14997,plain,
( spl0_1877
<=> ! [X0,X30,X26] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_less(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f1725,axiom,
! [X0,X26,X30] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_less(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f14995,plain,
spl0_1876,
inference(avatar_split_clause,[],[f1721,f14993]) ).
fof(f14993,plain,
( spl0_1876
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnionE__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f1721,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnionE__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f14991,plain,
spl0_1875,
inference(avatar_split_clause,[],[f1718,f14989]) ).
fof(f14989,plain,
( spl0_1875
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInterI__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f1718,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInterI__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f14987,plain,
spl0_1874,
inference(avatar_split_clause,[],[f1650,f14985]) ).
fof(f14985,plain,
( spl0_1874
<=> ! [X0,X3,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f1650,axiom,
! [X3,X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f14983,plain,
spl0_1873,
inference(avatar_split_clause,[],[f1619,f14981]) ).
fof(f14981,plain,
( spl0_1873
<=> ! [X3,X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_in(c_Pair(X3,X3,X0,X0),X19,tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f1619,axiom,
! [X3,X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_in(c_Pair(X3,X3,X0,X0),X19,tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f14979,plain,
spl0_1872,
inference(avatar_split_clause,[],[f1583,f14977]) ).
fof(f14977,plain,
( spl0_1872
<=> ! [X0,X12,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f1583,axiom,
! [X0,X26,X12,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f14975,plain,
spl0_1871,
inference(avatar_split_clause,[],[f1550,f14973]) ).
fof(f14973,plain,
( spl0_1871
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnion__iff__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f1550,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnion__iff__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f14971,plain,
spl0_1870,
inference(avatar_split_clause,[],[f1546,f14969]) ).
fof(f14969,plain,
( spl0_1870
<=> ! [X29,X0,X26] :
( c_emptyset = X29
| c_emptyset != c_Union(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f1546,axiom,
! [X29,X0,X26] :
( c_emptyset = X29
| c_emptyset != c_Union(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f14967,plain,
spl0_1869,
inference(avatar_split_clause,[],[f1540,f14965]) ).
fof(f14965,plain,
( spl0_1869
<=> ! [X2,X0,X30,X26] :
( c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f1540,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f14950,plain,
spl0_1868,
inference(avatar_split_clause,[],[f1539,f14948]) ).
fof(f14948,plain,
( spl0_1868
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X26,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f1539,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X26,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f14946,plain,
spl0_1867,
inference(avatar_split_clause,[],[f1525,f14944]) ).
fof(f14944,plain,
( spl0_1867
<=> ! [X0,X30,X26] : c_union(X26,X30,X0) = c_union(X26,c_minus(X30,X26,tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f1525,axiom,
! [X0,X26,X30] : c_union(X26,X30,X0) = c_union(X26,c_minus(X30,X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f14942,plain,
spl0_1866,
inference(avatar_split_clause,[],[f1524,f14940]) ).
fof(f14940,plain,
( spl0_1866
<=> ! [X0,X30,X26] : c_union(c_minus(X30,X26,tc_set(X0)),X26,X0) = c_union(X30,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f1524,axiom,
! [X0,X26,X30] : c_union(c_minus(X30,X26,tc_set(X0)),X26,X0) = c_union(X30,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f14938,plain,
spl0_1865,
inference(avatar_split_clause,[],[f1516,f14936]) ).
fof(f14936,plain,
( spl0_1865
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInter__iff__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f1516,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInter__iff__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f14934,plain,
spl0_1864,
inference(avatar_split_clause,[],[f1510,f14932]) ).
fof(f14932,plain,
( spl0_1864
<=> ! [X29,X0,X26] :
( c_UNIV = X29
| c_UNIV != c_Inter(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f1510,axiom,
! [X29,X0,X26] :
( c_UNIV = X29
| c_UNIV != c_Inter(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f14930,plain,
spl0_1863,
inference(avatar_split_clause,[],[f1449,f14928]) ).
fof(f14928,plain,
( spl0_1863
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f1449,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f14926,plain,
spl0_1862,
inference(avatar_split_clause,[],[f1448,f14924]) ).
fof(f14924,plain,
( spl0_1862
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f1448,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f14922,plain,
spl0_1861,
inference(avatar_split_clause,[],[f1446,f14920]) ).
fof(f14920,plain,
( spl0_1861
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f1446,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f14918,plain,
spl0_1860,
inference(avatar_split_clause,[],[f1445,f14916]) ).
fof(f14916,plain,
( spl0_1860
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f1445,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f14914,plain,
spl0_1859,
inference(avatar_split_clause,[],[f1419,f14912]) ).
fof(f14912,plain,
( spl0_1859
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f1419,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f14910,plain,
( spl0_1858
| ~ spl0_1231
| ~ spl0_1466 ),
inference(avatar_split_clause,[],[f11985,f11655,f9680,f14908]) ).
fof(f11655,plain,
( spl0_1466
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f11985,plain,
( ! [X0] : c_uminus(c_uminus(X0,t_a),t_a) = X0
| ~ spl0_1231
| ~ spl0_1466 ),
inference(resolution,[],[f11656,f9682]) ).
fof(f11656,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 )
| ~ spl0_1466 ),
inference(avatar_component_clause,[],[f11655]) ).
fof(f14906,plain,
spl0_1857,
inference(avatar_split_clause,[],[f1418,f14904]) ).
fof(f14904,plain,
( spl0_1857
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f1418,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f14902,plain,
spl0_1856,
inference(avatar_split_clause,[],[f1414,f14900]) ).
fof(f1414,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f14898,plain,
spl0_1855,
inference(avatar_split_clause,[],[f1413,f14896]) ).
fof(f14896,plain,
( spl0_1855
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f1413,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f14894,plain,
spl0_1854,
inference(avatar_split_clause,[],[f1394,f14892]) ).
fof(f1394,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(X3,c_HOL_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
fof(f14890,plain,
spl0_1853,
inference(avatar_split_clause,[],[f1322,f14888]) ).
fof(f1322,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_0 = X3
| c_1 = c_times(c_HOL_Oinverse(X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f14886,plain,
spl0_1852,
inference(avatar_split_clause,[],[f1281,f14884]) ).
fof(f14884,plain,
( spl0_1852
<=> ! [X0,X1,X3] :
( X1 = X3
| ~ c_in(c_Pair(X3,X1,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f1281,axiom,
! [X3,X0,X1] :
( X1 = X3
| ~ c_in(c_Pair(X3,X1,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f14882,plain,
spl0_1851,
inference(avatar_split_clause,[],[f1261,f14880]) ).
fof(f1261,axiom,
! [X0,X16,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f14878,plain,
spl0_1850,
inference(avatar_split_clause,[],[f1259,f14876]) ).
fof(f14876,plain,
( spl0_1850
<=> ! [X16,X0,X10] : c_Pair(c_fst(X10,X0,X16),c_snd(X10,X0,X16),X0,X16) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f1259,axiom,
! [X10,X0,X16] : c_Pair(c_fst(X10,X0,X16),c_snd(X10,X0,X16),X0,X16) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f14874,plain,
spl0_1849,
inference(avatar_split_clause,[],[f1255,f14872]) ).
fof(f14872,plain,
( spl0_1849
<=> ! [X0,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f1255,axiom,
! [X3,X0] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f14870,plain,
spl0_1848,
inference(avatar_split_clause,[],[f1252,f14868]) ).
fof(f14868,plain,
( spl0_1848
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f1252,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f14866,plain,
spl0_1847,
inference(avatar_split_clause,[],[f1241,f14864]) ).
fof(f14864,plain,
( spl0_1847
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_0 != c_Nat_Opower(X3,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f1241,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_0 != c_Nat_Opower(X3,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f14862,plain,
spl0_1846,
inference(avatar_split_clause,[],[f1233,f14860]) ).
fof(f14860,plain,
( spl0_1846
<=> ! [X12,X33] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f1233,axiom,
! [X12,X33] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f14858,plain,
spl0_1845,
inference(avatar_split_clause,[],[f1189,f14856]) ).
fof(f14856,plain,
( spl0_1845
<=> ! [X11,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_less(c_0,X11,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f1189,axiom,
! [X11,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_less(c_0,X11,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f14854,plain,
spl0_1844,
inference(avatar_split_clause,[],[f1176,f14852]) ).
fof(f14852,plain,
( spl0_1844
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f1176,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f14850,plain,
spl0_1843,
inference(avatar_split_clause,[],[f1159,f14848]) ).
fof(f1159,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X10,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f14846,plain,
spl0_1842,
inference(avatar_split_clause,[],[f1158,f14844]) ).
fof(f1158,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f14842,plain,
spl0_1841,
inference(avatar_split_clause,[],[f1154,f14840]) ).
fof(f1154,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f14838,plain,
spl0_1840,
inference(avatar_split_clause,[],[f1153,f14836]) ).
fof(f1153,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f14834,plain,
spl0_1839,
inference(avatar_split_clause,[],[f1151,f14832]) ).
fof(f14832,plain,
( spl0_1839
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X10,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f1151,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X10,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f14830,plain,
spl0_1838,
inference(avatar_split_clause,[],[f1150,f14828]) ).
fof(f14828,plain,
( spl0_1838
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X12,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f1150,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X12,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f14826,plain,
( ~ spl0_1837
| ~ spl0_112
| ~ spl0_1628 ),
inference(avatar_split_clause,[],[f13549,f12832,f3758,f14823]) ).
fof(f14823,plain,
( spl0_1837
<=> c_lessequals(c_1,c_HOL_Oabs(v_c,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f12832,plain,
( spl0_1628
<=> ! [X0] : c_times(c_1,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f13549,plain,
( ~ c_lessequals(c_1,c_HOL_Oabs(v_c,t_a),t_a)
| ~ spl0_112
| ~ spl0_1628 ),
inference(superposition,[],[f3759,f12833]) ).
fof(f12833,plain,
( ! [X0] : c_times(c_1,X0,t_a) = X0
| ~ spl0_1628 ),
inference(avatar_component_clause,[],[f12832]) ).
fof(f14821,plain,
spl0_1836,
inference(avatar_split_clause,[],[f1148,f14819]) ).
fof(f14819,plain,
( spl0_1836
<=> ! [X0,X12,X35,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X10,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f1148,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X10,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f14817,plain,
spl0_1835,
inference(avatar_split_clause,[],[f1147,f14815]) ).
fof(f14815,plain,
( spl0_1835
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X12,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f1147,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X12,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f14813,plain,
spl0_1834,
inference(avatar_split_clause,[],[f1143,f14811]) ).
fof(f14811,plain,
( spl0_1834
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_0,c_plus(X3,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f1143,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_0,c_plus(X3,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f14809,plain,
spl0_1833,
inference(avatar_split_clause,[],[f1142,f14807]) ).
fof(f14807,plain,
( spl0_1833
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_0,c_plus(X3,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f1142,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_0,c_plus(X3,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f14805,plain,
spl0_1832,
inference(avatar_split_clause,[],[f1109,f14803]) ).
fof(f1109,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X3,X1,X0),X0) = c_minus(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f14801,plain,
spl0_1831,
inference(avatar_split_clause,[],[f1106,f14799]) ).
fof(f14799,plain,
( spl0_1831
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Omeet(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f1106,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Omeet(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f14797,plain,
spl0_1830,
inference(avatar_split_clause,[],[f1104,f14795]) ).
fof(f14795,plain,
( spl0_1830
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Ojoin(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f1104,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Ojoin(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f14793,plain,
spl0_1829,
inference(avatar_split_clause,[],[f1101,f14791]) ).
fof(f14791,plain,
( spl0_1829
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f1101,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f14789,plain,
spl0_1828,
inference(avatar_split_clause,[],[f1100,f14787]) ).
fof(f14787,plain,
( spl0_1828
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f1100,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f14785,plain,
spl0_1827,
inference(avatar_split_clause,[],[f1098,f14783]) ).
fof(f1098,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,X1,X0) = c_minus(X3,c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f14774,plain,
spl0_1826,
inference(avatar_split_clause,[],[f1097,f14772]) ).
fof(f1097,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f14770,plain,
spl0_1825,
inference(avatar_split_clause,[],[f1096,f14768]) ).
fof(f14768,plain,
( spl0_1825
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f1096,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f14766,plain,
spl0_1824,
inference(avatar_split_clause,[],[f1095,f14764]) ).
fof(f14764,plain,
( spl0_1824
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f1095,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f14762,plain,
spl0_1823,
inference(avatar_split_clause,[],[f1094,f14760]) ).
fof(f14760,plain,
( spl0_1823
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f1094,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f14758,plain,
spl0_1822,
inference(avatar_split_clause,[],[f1078,f14756]) ).
fof(f14756,plain,
( spl0_1822
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_uminus(X3,X0) = c_HOL_Oabs(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f1078,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_uminus(X3,X0) = c_HOL_Oabs(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f14754,plain,
spl0_1821,
inference(avatar_split_clause,[],[f1004,f14752]) ).
fof(f14752,plain,
( spl0_1821
<=> ! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f1004,axiom,
! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f14750,plain,
spl0_1820,
inference(avatar_split_clause,[],[f1003,f14748]) ).
fof(f14748,plain,
( spl0_1820
<=> ! [X34,X33,X10] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),c_Numeral_OBit(X33,X10)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f1003,axiom,
! [X10,X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),c_Numeral_OBit(X33,X10)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f14746,plain,
spl0_1819,
inference(avatar_split_clause,[],[f939,f14744]) ).
fof(f14744,plain,
( spl0_1819
<=> ! [X11,X10] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(X11,c_minus(X10,X11,tc_nat),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f939,axiom,
! [X10,X11] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(X11,c_minus(X10,X11,tc_nat),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f14742,plain,
spl0_1818,
inference(avatar_split_clause,[],[f938,f14740]) ).
fof(f14740,plain,
( spl0_1818
<=> ! [X11,X10] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(c_minus(X10,X11,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f938,axiom,
! [X10,X11] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(c_minus(X10,X11,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f14738,plain,
spl0_1817,
inference(avatar_split_clause,[],[f746,f14736]) ).
fof(f14736,plain,
( spl0_1817
<=> ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f746,axiom,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f14734,plain,
( ~ spl0_1127
| spl0_1816
| ~ spl0_1369
| ~ spl0_1521 ),
inference(avatar_split_clause,[],[f12541,f12173,f10880,f14731,f9203]) ).
fof(f14731,plain,
( spl0_1816
<=> c_lessequals(c_0,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f10880,plain,
( spl0_1369
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f12173,plain,
( spl0_1521
<=> c_0 = c_HOL_Oabs(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f12541,plain,
( c_lessequals(c_0,c_0,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1369
| ~ spl0_1521 ),
inference(superposition,[],[f10881,f12175]) ).
fof(f12175,plain,
( c_0 = c_HOL_Oabs(c_0,t_a)
| ~ spl0_1521 ),
inference(avatar_component_clause,[],[f12173]) ).
fof(f10881,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1369 ),
inference(avatar_component_clause,[],[f10880]) ).
fof(f14729,plain,
spl0_1815,
inference(avatar_split_clause,[],[f693,f14727]) ).
fof(f14727,plain,
( spl0_1815
<=> ! [X11,X10] :
( ~ c_lessequals(X10,X11,tc_nat)
| c_minus(X11,c_minus(X11,X10,tc_nat),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f693,axiom,
! [X10,X11] :
( ~ c_lessequals(X10,X11,tc_nat)
| c_minus(X11,c_minus(X11,X10,tc_nat),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f14725,plain,
spl0_1814,
inference(avatar_split_clause,[],[f659,f14723]) ).
fof(f14723,plain,
( spl0_1814
<=> ! [X0,X12,X26] :
( c_in(c_0,X26,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f659,axiom,
! [X0,X26,X12] :
( c_in(c_0,X26,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f14721,plain,
spl0_1813,
inference(avatar_split_clause,[],[f642,f14719]) ).
fof(f14719,plain,
( spl0_1813
<=> ! [X12,X39,X14] : c_List_Oset(c_List_Olist_OCons(X12,X39,X14),X14) = c_insert(X12,c_List_Oset(X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f642,axiom,
! [X39,X14,X12] : c_List_Oset(c_List_Olist_OCons(X12,X39,X14),X14) = c_insert(X12,c_List_Oset(X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f14717,plain,
spl0_1812,
inference(avatar_split_clause,[],[f636,f14715]) ).
fof(f14715,plain,
( spl0_1812
<=> ! [X0,X11,X10] :
( c_List_Orotate(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f636,axiom,
! [X10,X0,X11] :
( c_List_Orotate(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f14713,plain,
spl0_1811,
inference(avatar_split_clause,[],[f596,f14711]) ).
fof(f14711,plain,
( spl0_1811
<=> ! [X10,X11,X0,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Oreplicate(X11,X10,X0),X23,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f596,axiom,
! [X10,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Oreplicate(X11,X10,X0),X23,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f14709,plain,
spl0_1810,
inference(avatar_split_clause,[],[f498,f14707]) ).
fof(f14707,plain,
( spl0_1810
<=> ! [X23,X0,X12,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Olist__update(X39,X23,X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f498,axiom,
! [X39,X0,X12,X23] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Olist__update(X39,X23,X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f14705,plain,
spl0_1809,
inference(avatar_split_clause,[],[f485,f14703]) ).
fof(f14703,plain,
( spl0_1809
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_List_Olast(c_append(X39,X40,X0),X0) = c_List_Olast(X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f485,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_List_Olast(c_append(X39,X40,X0),X0) = c_List_Olast(X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f14701,plain,
spl0_1808,
inference(avatar_split_clause,[],[f483,f14699]) ).
fof(f14699,plain,
( spl0_1808
<=> ! [X0,X12,X39] :
( c_List_Olist_ONil = X39
| c_List_Olast(c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olast(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f483,axiom,
! [X39,X0,X12] :
( c_List_Olist_ONil = X39
| c_List_Olast(c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olast(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f14697,plain,
spl0_1807,
inference(avatar_split_clause,[],[f475,f14695]) ).
fof(f14695,plain,
( spl0_1807
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Ohd(c_append(X39,X40,X0),X0) = c_List_Ohd(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f475,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Ohd(c_append(X39,X40,X0),X0) = c_List_Ohd(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f14693,plain,
spl0_1806,
inference(avatar_split_clause,[],[f474,f14691]) ).
fof(f14691,plain,
( spl0_1806
<=> ! [X0,X10] :
( c_List_Olist_ONil = X10
| c_List_Olist_OCons(c_List_Ohd(X10,X0),c_List_Otl(X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f474,axiom,
! [X10,X0] :
( c_List_Olist_ONil = X10
| c_List_Olist_OCons(c_List_Ohd(X10,X0),c_List_Otl(X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f14689,plain,
spl0_1805,
inference(avatar_split_clause,[],[f472,f14687]) ).
fof(f14687,plain,
( spl0_1805
<=> ! [X50,X24,X23] : c_List_Odrop(X24,c_List_Oupt(X23,X50),tc_nat) = c_List_Oupt(c_plus(X23,X24,tc_nat),X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f472,axiom,
! [X50,X24,X23] : c_List_Odrop(X24,c_List_Oupt(X23,X50),tc_nat) = c_List_Oupt(c_plus(X23,X24,tc_nat),X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f14685,plain,
spl0_1804,
inference(avatar_split_clause,[],[f470,f14683]) ).
fof(f14683,plain,
( spl0_1804
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = c_List_Odrop(X11,X39,X0)
| ~ c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f470,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = c_List_Odrop(X11,X39,X0)
| ~ c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f14681,plain,
spl0_1803,
inference(avatar_split_clause,[],[f469,f14679]) ).
fof(f14679,plain,
( spl0_1803
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil != c_List_Odrop(X11,X39,X0)
| c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f469,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil != c_List_Odrop(X11,X39,X0)
| c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f14677,plain,
spl0_1802,
inference(avatar_split_clause,[],[f369,f14675]) ).
fof(f14675,plain,
( spl0_1802
<=> ! [X1,X3] : c_div(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X3,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f369,axiom,
! [X3,X1] : c_div(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X3,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f14673,plain,
spl0_1801,
inference(avatar_split_clause,[],[f310,f14671]) ).
fof(f310,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_uminus(X35,tc_IntDef_Oint),X0) = c_uminus(c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f14669,plain,
spl0_1800,
inference(avatar_split_clause,[],[f199,f14667]) ).
fof(f14667,plain,
( spl0_1800
<=> ! [X9,X11,X24] :
( c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f199,axiom,
! [X11,X9,X24] :
( c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f14665,plain,
spl0_1799,
inference(avatar_split_clause,[],[f198,f14663]) ).
fof(f14663,plain,
( spl0_1799
<=> ! [X9,X11,X24] :
( c_Divides_Oop_Advd(X9,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f198,axiom,
! [X11,X9,X24] :
( c_Divides_Oop_Advd(X9,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f14661,plain,
spl0_1798,
inference(avatar_split_clause,[],[f185,f14659]) ).
fof(f14659,plain,
( spl0_1798
<=> ! [X0,X3,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f185,axiom,
! [X3,X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f14657,plain,
spl0_1797,
inference(avatar_split_clause,[],[f181,f14655]) ).
fof(f14655,plain,
( spl0_1797
<=> ! [X6,X0,X32] :
( c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f181,axiom,
! [X0,X6,X32] :
( c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f14653,plain,
spl0_1796,
inference(avatar_split_clause,[],[f180,f14651]) ).
fof(f14651,plain,
( spl0_1796
<=> ! [X6,X0,X32] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f180,axiom,
! [X0,X6,X32] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f14649,plain,
( ~ spl0_1127
| ~ spl0_1795
| ~ spl0_1379
| ~ spl0_1521 ),
inference(avatar_split_clause,[],[f12540,f12173,f10939,f14646,f9203]) ).
fof(f10939,plain,
( spl0_1379
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f12540,plain,
( ~ c_less(c_0,c_0,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1379
| ~ spl0_1521 ),
inference(superposition,[],[f10940,f12175]) ).
fof(f10940,plain,
( ! [X0] :
( ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1379 ),
inference(avatar_component_clause,[],[f10939]) ).
fof(f14644,plain,
spl0_1794,
inference(avatar_split_clause,[],[f179,f14642]) ).
fof(f14642,plain,
( spl0_1794
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f179,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f14640,plain,
spl0_1793,
inference(avatar_split_clause,[],[f178,f14638]) ).
fof(f14638,plain,
( spl0_1793
<=> ! [X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f178,axiom,
! [X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f14636,plain,
spl0_1792,
inference(avatar_split_clause,[],[f170,f14634]) ).
fof(f14634,plain,
( spl0_1792
<=> ! [X0,X26] :
( c_emptyset = X26
| c_0 != c_Finite__Set_Ocard(X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f170,axiom,
! [X0,X26] :
( c_emptyset = X26
| c_0 != c_Finite__Set_Ocard(X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f14632,plain,
spl0_1791,
inference(avatar_split_clause,[],[f117,f14630]) ).
fof(f14630,plain,
( spl0_1791
<=> ! [X11,X10] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X10,X11,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f117,axiom,
! [X10,X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X10,X11,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f14628,plain,
spl0_1790,
inference(avatar_split_clause,[],[f115,f14626]) ).
fof(f14626,plain,
( spl0_1790
<=> ! [X11,X10] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X11,X10,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f115,axiom,
! [X10,X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X11,X10,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f14451,plain,
( ~ spl0_1127
| spl0_1789
| ~ spl0_1368
| ~ spl0_1510 ),
inference(avatar_split_clause,[],[f12511,f12128,f10876,f14448,f9203]) ).
fof(f10876,plain,
( spl0_1368
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f12511,plain,
( c_lessequals(c_0,c_1,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1368
| ~ spl0_1510 ),
inference(superposition,[],[f10877,f12130]) ).
fof(f10877,plain,
( ! [X3,X0] :
( c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1368 ),
inference(avatar_component_clause,[],[f10876]) ).
fof(f14319,plain,
( ~ spl0_1127
| ~ spl0_1788
| ~ spl0_1370
| ~ spl0_1510 ),
inference(avatar_split_clause,[],[f12510,f12128,f10884,f14316,f9203]) ).
fof(f14316,plain,
( spl0_1788
<=> c_less(c_1,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f10884,plain,
( spl0_1370
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f12510,plain,
( ~ c_less(c_1,c_0,t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1370
| ~ spl0_1510 ),
inference(superposition,[],[f10885,f12130]) ).
fof(f10885,plain,
( ! [X3,X0] :
( ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1370 ),
inference(avatar_component_clause,[],[f10884]) ).
fof(f13827,plain,
spl0_1787,
inference(avatar_split_clause,[],[f3154,f13825]) ).
fof(f13825,plain,
( spl0_1787
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f3154,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f3153,f1009]) ).
fof(f3153,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2960,f2790]) ).
fof(f2960,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f232,f1023]) ).
fof(f232,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f13823,plain,
spl0_1786,
inference(avatar_split_clause,[],[f3084,f13821]) ).
fof(f13821,plain,
( spl0_1786
<=> ! [X0] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X0)
| ~ class_Power_Orecpower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f3084,plain,
! [X0] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f3083,f1050]) ).
fof(f3083,plain,
! [X0] :
( 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),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f3082,f1048]) ).
fof(f3082,plain,
! [X0] :
( 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),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f772,f1050]) ).
fof(f772,axiom,
! [X0] :
( ~ class_Power_Orecpower(X0)
| 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),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f13819,plain,
spl0_1785,
inference(avatar_split_clause,[],[f3077,f13817]) ).
fof(f3077,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f3076,f1050]) ).
fof(f3076,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f3075,f1048]) ).
fof(f3075,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f222,f1050]) ).
fof(f222,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f13815,plain,
spl0_1784,
inference(avatar_split_clause,[],[f2901,f13813]) ).
fof(f13813,plain,
( spl0_1784
<=> ! [X0,X30,X26] :
( c_UNIV = X26
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f2901,plain,
! [X0,X26,X30] :
( c_UNIV = X26
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1492,f1267]) ).
fof(f1492,axiom,
! [X0,X26,X30] :
( c_UNIV = X26
| c_UNIV != c_inter(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f13811,plain,
spl0_1783,
inference(avatar_split_clause,[],[f2900,f13809]) ).
fof(f13809,plain,
( spl0_1783
<=> ! [X0,X30,X26] :
( c_UNIV = X30
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f2900,plain,
! [X0,X26,X30] :
( c_UNIV = X30
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1493,f1267]) ).
fof(f1493,axiom,
! [X0,X26,X30] :
( c_UNIV = X30
| c_UNIV != c_inter(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f13807,plain,
spl0_1782,
inference(avatar_split_clause,[],[f2895,f13805]) ).
fof(f13805,plain,
( spl0_1782
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f2895,plain,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ),
inference(definition_unfolding,[],[f1240,f1438]) ).
fof(f1240,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Suc(X11),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f13803,plain,
spl0_1781,
inference(avatar_split_clause,[],[f2827,f13801]) ).
fof(f2827,plain,
! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f266,f1438]) ).
fof(f266,axiom,
! [X24] : c_IntDef_Oint(c_Suc(X24)) = c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f13799,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2824,f13797]) ).
fof(f13797,plain,
( spl0_1780
<=> ! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),X26,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f2824,plain,
! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),X26,X0,X0),
inference(definition_unfolding,[],[f1472,f1267]) ).
fof(f1472,axiom,
! [X0,X26] : c_emptyset = c_inter(c_uminus(X26,tc_set(X0)),X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f13795,plain,
( ~ spl0_1779
| ~ spl0_112
| ~ spl0_1660 ),
inference(avatar_split_clause,[],[f13750,f13065,f3758,f13792]) ).
fof(f13065,plain,
( spl0_1660
<=> ! [X0] : c_0 = c_times(c_0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f13750,plain,
( ~ c_lessequals(c_1,c_0,t_a)
| ~ spl0_112
| ~ spl0_1660 ),
inference(superposition,[],[f3759,f13066]) ).
fof(f13066,plain,
( ! [X0] : c_0 = c_times(c_0,X0,t_a)
| ~ spl0_1660 ),
inference(avatar_component_clause,[],[f13065]) ).
fof(f13790,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2823,f13788]) ).
fof(f13788,plain,
( spl0_1778
<=> ! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_uminus(X26,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f2823,plain,
! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_uminus(X26,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1473,f1267]) ).
fof(f1473,axiom,
! [X0,X26] : c_emptyset = c_inter(X26,c_uminus(X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f13786,plain,
spl0_1777,
inference(avatar_split_clause,[],[f1731,f13784]) ).
fof(f13784,plain,
( spl0_1777
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(c_Main_OsubsetI__1(X26,X30,X0),X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f1731,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(c_Main_OsubsetI__1(X26,X30,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f13782,plain,
spl0_1776,
inference(avatar_split_clause,[],[f1730,f13780]) ).
fof(f13780,plain,
( spl0_1776
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| c_in(c_Main_OsubsetI__1(X26,X30,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f1730,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| c_in(c_Main_OsubsetI__1(X26,X30,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f13778,plain,
spl0_1775,
inference(avatar_split_clause,[],[f1670,f13776]) ).
fof(f13776,plain,
( spl0_1775
<=> ! [X0,X39] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f1670,axiom,
! [X39,X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f13774,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1623,f13772]) ).
fof(f13772,plain,
( spl0_1774
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Datatype__Universe_ONumb(X12,X0,X16) != c_Datatype__Universe_ONumb(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1623,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Datatype__Universe_ONumb(X12,X0,X16) != c_Datatype__Universe_ONumb(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f13770,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1622,f13768]) ).
fof(f13768,plain,
( spl0_1773
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Datatype__Universe_OLeaf(X12,X0,X16) != c_Datatype__Universe_OLeaf(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1622,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Datatype__Universe_OLeaf(X12,X0,X16) != c_Datatype__Universe_OLeaf(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f13766,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1597,f13764]) ).
fof(f13764,plain,
( spl0_1772
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Sum__Type_OInr(X12,X16,X0) != c_Sum__Type_OInr(X10,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1597,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Sum__Type_OInr(X12,X16,X0) != c_Sum__Type_OInr(X10,X16,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f13762,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1595,f13760]) ).
fof(f13760,plain,
( spl0_1771
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Sum__Type_OInl(X12,X0,X16) != c_Sum__Type_OInl(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1595,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Sum__Type_OInl(X12,X0,X16) != c_Sum__Type_OInl(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f13758,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1589,f13756]) ).
fof(f13756,plain,
( spl0_1770
<=> ! [X0,X3,X1,X26] :
( X1 = X3
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1589,axiom,
! [X3,X0,X1,X26] :
( X1 = X3
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
fof(f13754,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1582,f13752]) ).
fof(f13752,plain,
( spl0_1769
<=> ! [X0,X12,X26,X30] :
( c_in(X12,X30,X0)
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f1582,axiom,
! [X0,X26,X12,X30] :
( c_in(X12,X30,X0)
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f13749,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1570,f13747]) ).
fof(f13747,plain,
( spl0_1768
<=> ! [X0,X12,X26] : c_insert(X12,X26,X0) = c_insert(X12,c_insert(X12,X26,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1570,axiom,
! [X0,X26,X12] : c_insert(X12,X26,X0) = c_insert(X12,c_insert(X12,X26,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f13745,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1564,f13743]) ).
fof(f13743,plain,
( spl0_1767
<=> ! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_Oempty__Union__conv__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f1564,axiom,
! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_Oempty__Union__conv__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f13741,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1547,f13739]) ).
fof(f13739,plain,
( spl0_1766
<=> ! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_OUnion__empty__conv__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1547,axiom,
! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_OUnion__empty__conv__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f13737,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1522,f13735]) ).
fof(f13735,plain,
( spl0_1765
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_in(X26,c_Pow(X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1522,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_in(X26,c_Pow(X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f13733,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1521,f13731]) ).
fof(f13731,plain,
( spl0_1764
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(X26,c_Pow(X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1521,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(X26,c_Pow(X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f13729,plain,
spl0_1763,
inference(avatar_split_clause,[],[f1511,f13727]) ).
fof(f13727,plain,
( spl0_1763
<=> ! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__2__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f1511,axiom,
! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__2__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f13725,plain,
spl0_1762,
inference(avatar_split_clause,[],[f1508,f13723]) ).
fof(f13723,plain,
( spl0_1762
<=> ! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__1__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f1508,axiom,
! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__1__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f13721,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1489,f13719]) ).
fof(f13719,plain,
( spl0_1761
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1489,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f13717,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1488,f13715]) ).
fof(f13715,plain,
( spl0_1760
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f1488,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f13713,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1486,f13711]) ).
fof(f13711,plain,
( spl0_1759
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_emptyset = c_minus(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1486,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_emptyset = c_minus(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f13709,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1485,f13707]) ).
fof(f13707,plain,
( spl0_1758
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| c_emptyset != c_minus(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1485,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| c_emptyset != c_minus(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f13705,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1475,f13703]) ).
fof(f13703,plain,
( spl0_1757
<=> ! [X0,X30,X26] :
( X26 = X30
| c_uminus(X26,tc_set(X0)) != c_uminus(X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1475,axiom,
! [X0,X26,X30] :
( X26 = X30
| c_uminus(X26,tc_set(X0)) != c_uminus(X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f13701,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1464,f13699]) ).
fof(f13699,plain,
( spl0_1756
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X23,X9,X0)
| c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f1464,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X23,X9,X0)
| c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f13697,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1463,f13695]) ).
fof(f13695,plain,
( spl0_1755
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1463,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f13693,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1462,f13691]) ).
fof(f13691,plain,
( spl0_1754
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OlessThan(X12,X0) != c_SetInterval_OlessThan(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1462,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OlessThan(X12,X0) != c_SetInterval_OlessThan(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f13689,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1453,f13687]) ).
fof(f13687,plain,
( spl0_1753
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X9,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f1453,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X9,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f13685,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1452,f13683]) ).
fof(f13683,plain,
( spl0_1752
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f1452,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f13681,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1451,f13679]) ).
fof(f13679,plain,
( spl0_1751
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OgreaterThan(X12,X0) != c_SetInterval_OgreaterThan(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f1451,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OgreaterThan(X12,X0) != c_SetInterval_OgreaterThan(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f13677,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1444,f13675]) ).
fof(f1444,axiom,
! [X72,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X72,X9,X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f13673,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1440,f13671]) ).
fof(f13671,plain,
( spl0_1749
<=> ! [X36,X72] : c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f1440,axiom,
! [X72,X36] : c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f13669,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1437,f13667]) ).
fof(f13667,plain,
( spl0_1748
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f1437,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f13665,plain,
spl0_1747,
inference(avatar_split_clause,[],[f1431,f13663]) ).
fof(f13663,plain,
( spl0_1747
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X9,X0)
| c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1431,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X9,X0)
| c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f13661,plain,
spl0_1746,
inference(avatar_split_clause,[],[f1430,f13659]) ).
fof(f13659,plain,
( spl0_1746
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f1430,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f13657,plain,
spl0_1745,
inference(avatar_split_clause,[],[f1429,f13655]) ).
fof(f13655,plain,
( spl0_1745
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatMost(X12,X0) != c_SetInterval_OatMost(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f1429,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatMost(X12,X0) != c_SetInterval_OatMost(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f13653,plain,
spl0_1744,
inference(avatar_split_clause,[],[f1425,f13651]) ).
fof(f13651,plain,
( spl0_1744
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X9,X23,X0)
| c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f1425,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X9,X23,X0)
| c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f13649,plain,
spl0_1743,
inference(avatar_split_clause,[],[f1424,f13647]) ).
fof(f13647,plain,
( spl0_1743
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f1424,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f13645,plain,
spl0_1742,
inference(avatar_split_clause,[],[f1423,f13643]) ).
fof(f13643,plain,
( spl0_1742
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatLeast(X12,X0) != c_SetInterval_OatLeast(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f1423,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatLeast(X12,X0) != c_SetInterval_OatLeast(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f13641,plain,
spl0_1741,
inference(avatar_split_clause,[],[f1417,f13639]) ).
fof(f1417,axiom,
! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f13637,plain,
spl0_1740,
inference(avatar_split_clause,[],[f1412,f13635]) ).
fof(f1412,axiom,
! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f13633,plain,
spl0_1739,
inference(avatar_split_clause,[],[f1411,f13631]) ).
fof(f1411,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f13629,plain,
spl0_1738,
inference(avatar_split_clause,[],[f1410,f13627]) ).
fof(f1410,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f13625,plain,
spl0_1737,
inference(avatar_split_clause,[],[f1409,f13623]) ).
fof(f1409,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f13621,plain,
spl0_1736,
inference(avatar_split_clause,[],[f1408,f13619]) ).
fof(f1408,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f13617,plain,
spl0_1735,
inference(avatar_split_clause,[],[f1196,f13615]) ).
fof(f13615,plain,
( spl0_1735
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f1196,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f13613,plain,
spl0_1734,
inference(avatar_split_clause,[],[f1195,f13611]) ).
fof(f13611,plain,
( spl0_1734
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f1195,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f13609,plain,
spl0_1733,
inference(avatar_split_clause,[],[f1194,f13607]) ).
fof(f13607,plain,
( spl0_1733
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f1194,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f13605,plain,
spl0_1732,
inference(avatar_split_clause,[],[f1193,f13603]) ).
fof(f13603,plain,
( spl0_1732
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f1193,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f13601,plain,
spl0_1731,
inference(avatar_split_clause,[],[f1190,f13599]) ).
fof(f13599,plain,
( spl0_1731
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f1190,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f13597,plain,
spl0_1730,
inference(avatar_split_clause,[],[f1183,f13595]) ).
fof(f13595,plain,
( spl0_1730
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f1183,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f13593,plain,
spl0_1729,
inference(avatar_split_clause,[],[f1182,f13591]) ).
fof(f13591,plain,
( spl0_1729
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f1182,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f13589,plain,
spl0_1728,
inference(avatar_split_clause,[],[f1181,f13587]) ).
fof(f13587,plain,
( spl0_1728
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f1181,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f13585,plain,
spl0_1727,
inference(avatar_split_clause,[],[f1180,f13583]) ).
fof(f13583,plain,
( spl0_1727
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f1180,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f13581,plain,
spl0_1726,
inference(avatar_split_clause,[],[f1177,f13579]) ).
fof(f13579,plain,
( spl0_1726
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f1177,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f13577,plain,
spl0_1725,
inference(avatar_split_clause,[],[f1171,f13575]) ).
fof(f13575,plain,
( spl0_1725
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f1171,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f13573,plain,
spl0_1724,
inference(avatar_split_clause,[],[f1170,f13571]) ).
fof(f13571,plain,
( spl0_1724
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f1170,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f13569,plain,
spl0_1723,
inference(avatar_split_clause,[],[f1169,f13567]) ).
fof(f13567,plain,
( spl0_1723
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f1169,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f13565,plain,
spl0_1722,
inference(avatar_split_clause,[],[f1168,f13563]) ).
fof(f13563,plain,
( spl0_1722
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f1168,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f13561,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1128,f13559]) ).
fof(f13559,plain,
( spl0_1721
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_0,X3,X0)
| c_less(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f1128,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_0,X3,X0)
| c_less(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f13557,plain,
spl0_1720,
inference(avatar_split_clause,[],[f1127,f13555]) ).
fof(f13555,plain,
( spl0_1720
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(c_0,X3,X0)
| ~ c_less(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f1127,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(c_0,X3,X0)
| ~ c_less(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f13553,plain,
spl0_1719,
inference(avatar_split_clause,[],[f1124,f13551]) ).
fof(f13551,plain,
( spl0_1719
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f1124,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f13548,plain,
spl0_1718,
inference(avatar_split_clause,[],[f1123,f13546]) ).
fof(f13546,plain,
( spl0_1718
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f1123,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f13544,plain,
spl0_1717,
inference(avatar_split_clause,[],[f1121,f13542]) ).
fof(f13542,plain,
( spl0_1717
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_uminus(X3,X0) != c_uminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f1121,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_uminus(X3,X0) != c_uminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f13540,plain,
spl0_1716,
inference(avatar_split_clause,[],[f1118,f13538]) ).
fof(f13538,plain,
( spl0_1716
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f1118,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f13536,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1117,f13534]) ).
fof(f13534,plain,
( spl0_1715
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f1117,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f13532,plain,
spl0_1714,
inference(avatar_split_clause,[],[f1116,f13530]) ).
fof(f13530,plain,
( spl0_1714
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f1116,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f13528,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1115,f13526]) ).
fof(f13526,plain,
( spl0_1713
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f1115,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f13524,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1061,f13522]) ).
fof(f13522,plain,
( spl0_1712
<=> ! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(X35,X0) = c_times(X35,c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f1061,axiom,
! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(X35,X0) = c_times(X35,c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f13520,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1060,f13518]) ).
fof(f13518,plain,
( spl0_1711
<=> ! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X35,X0) = c_uminus(X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f1060,axiom,
! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X35,X0) = c_uminus(X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f13516,plain,
spl0_1710,
inference(avatar_split_clause,[],[f980,f13514]) ).
fof(f13514,plain,
( spl0_1710
<=> ! [X9,X11,X24] :
( X11 = X24
| c_plus(X24,X9,tc_nat) != c_plus(X11,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f980,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_plus(X24,X9,tc_nat) != c_plus(X11,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f13512,plain,
spl0_1709,
inference(avatar_split_clause,[],[f975,f13510]) ).
fof(f13510,plain,
( spl0_1709
<=> ! [X9,X11,X24] :
( X11 = X24
| c_plus(X9,X24,tc_nat) != c_plus(X9,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f975,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_plus(X9,X24,tc_nat) != c_plus(X9,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f13508,plain,
spl0_1708,
inference(avatar_split_clause,[],[f959,f13506]) ).
fof(f13506,plain,
( spl0_1708
<=> ! [X11,X24] :
( c_0 = X24
| c_0 = X11
| c_0 != c_times(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f959,axiom,
! [X11,X24] :
( c_0 = X24
| c_0 = X11
| c_0 != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f13504,plain,
spl0_1707,
inference(avatar_split_clause,[],[f744,f13502]) ).
fof(f744,axiom,
! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),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(f13500,plain,
spl0_1706,
inference(avatar_split_clause,[],[f707,f13498]) ).
fof(f707,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f13496,plain,
spl0_1705,
inference(avatar_split_clause,[],[f701,f13494]) ).
fof(f13494,plain,
( spl0_1705
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f701,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f13492,plain,
spl0_1704,
inference(avatar_split_clause,[],[f700,f13490]) ).
fof(f13490,plain,
( spl0_1704
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f700,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f13488,plain,
spl0_1703,
inference(avatar_split_clause,[],[f678,f13486]) ).
fof(f13486,plain,
( spl0_1703
<=> ! [X50,X23] :
( c_0 = X50
| c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X23,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f678,axiom,
! [X50,X23] :
( c_0 = X50
| c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X23,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f13484,plain,
spl0_1702,
inference(avatar_split_clause,[],[f637,f13482]) ).
fof(f13482,plain,
( spl0_1702
<=> ! [X42,X40,X0,X39] :
( X40 = X42
| c_append(X39,X40,X0) != c_append(X39,X42,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f637,axiom,
! [X40,X39,X0,X42] :
( X40 = X42
| c_append(X39,X40,X0) != c_append(X39,X42,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f13480,plain,
spl0_1701,
inference(avatar_split_clause,[],[f631,f13478]) ).
fof(f13478,plain,
( spl0_1701
<=> ! [X0,X10] :
( c_List_Orotate1(X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f631,axiom,
! [X10,X0] :
( c_List_Orotate1(X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f13476,plain,
spl0_1700,
inference(avatar_split_clause,[],[f520,f13474]) ).
fof(f13474,plain,
( spl0_1700
<=> ! [X55,X54,X0,X3,X15] :
( X54 = X55
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f520,axiom,
! [X3,X0,X54,X55,X15] :
( X54 = X55
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f13472,plain,
spl0_1699,
inference(avatar_split_clause,[],[f519,f13470]) ).
fof(f13470,plain,
( spl0_1699
<=> ! [X55,X54,X0,X3,X15] :
( X3 = X15
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f519,axiom,
! [X3,X0,X54,X55,X15] :
( X3 = X15
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f13468,plain,
spl0_1698,
inference(avatar_split_clause,[],[f504,f13466]) ).
fof(f13466,plain,
( spl0_1698
<=> ! [X0,X11,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate(X11,X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f504,axiom,
! [X39,X0,X11] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate(X11,X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f13464,plain,
spl0_1697,
inference(avatar_split_clause,[],[f446,f13462]) ).
fof(f13462,plain,
( spl0_1697
<=> ! [X12,X39,X14] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| ~ c_in(X12,c_List_Oset(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f446,axiom,
! [X39,X14,X12] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| ~ c_in(X12,c_List_Oset(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f13460,plain,
spl0_1696,
inference(avatar_split_clause,[],[f424,f13458]) ).
fof(f13458,plain,
( spl0_1696
<=> ! [X42,X40,X0,X39] :
( X40 = X42
| c_append(X40,X39,X0) != c_append(X42,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f424,axiom,
! [X40,X39,X0,X42] :
( X40 = X42
| c_append(X40,X39,X0) != c_append(X42,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f13456,plain,
spl0_1695,
inference(avatar_split_clause,[],[f387,f13454]) ).
fof(f13454,plain,
( spl0_1695
<=> ! [X1,X3] : c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f387,axiom,
! [X3,X1] : c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f13452,plain,
spl0_1694,
inference(avatar_split_clause,[],[f386,f13450]) ).
fof(f13450,plain,
( spl0_1694
<=> ! [X1,X3] : c_Divides_Oop_Amod(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f386,axiom,
! [X3,X1] : c_Divides_Oop_Amod(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f13448,plain,
spl0_1693,
inference(avatar_split_clause,[],[f379,f13446]) ).
fof(f13446,plain,
( spl0_1693
<=> ! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f379,axiom,
! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f13443,plain,
( spl0_1692
| ~ spl0_130
| ~ spl0_1281
| ~ spl0_1691 ),
inference(avatar_split_clause,[],[f13439,f13436,f10228,f3840,f13441]) ).
fof(f13441,plain,
( spl0_1692
<=> ! [X11] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f3840,plain,
( spl0_130
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f10228,plain,
( spl0_1281
<=> ! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f13436,plain,
( spl0_1691
<=> ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f13439,plain,
( ! [X11] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X11 )
| ~ spl0_130
| ~ spl0_1281
| ~ spl0_1691 ),
inference(forward_demodulation,[],[f13437,f10497]) ).
fof(f10497,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_130
| ~ spl0_1281 ),
inference(superposition,[],[f10229,f3842]) ).
fof(f3842,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f3840]) ).
fof(f10229,plain,
( ! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint)
| ~ spl0_1281 ),
inference(avatar_component_clause,[],[f10228]) ).
fof(f13437,plain,
( ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1691 ),
inference(avatar_component_clause,[],[f13436]) ).
fof(f13438,plain,
spl0_1691,
inference(avatar_split_clause,[],[f378,f13436]) ).
fof(f378,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f13434,plain,
spl0_1690,
inference(avatar_split_clause,[],[f371,f13432]) ).
fof(f13432,plain,
( spl0_1690
<=> ! [X1,X10] :
( c_0 = X1
| c_div(c_times(X1,X10,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f371,axiom,
! [X10,X1] :
( c_0 = X1
| c_div(c_times(X1,X10,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f13430,plain,
( spl0_1689
| ~ spl0_1231
| ~ spl0_1374 ),
inference(avatar_split_clause,[],[f11957,f10900,f9680,f13428]) ).
fof(f10900,plain,
( spl0_1374
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f11957,plain,
( ! [X0] : c_0 = c_minus(X0,X0,t_a)
| ~ spl0_1231
| ~ spl0_1374 ),
inference(resolution,[],[f9682,f10901]) ).
fof(f10901,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) )
| ~ spl0_1374 ),
inference(avatar_component_clause,[],[f10900]) ).
fof(f13426,plain,
spl0_1688,
inference(avatar_split_clause,[],[f370,f13424]) ).
fof(f13424,plain,
( spl0_1688
<=> ! [X1,X10] :
( c_0 = X1
| c_div(c_times(X10,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f370,axiom,
! [X10,X1] :
( c_0 = X1
| c_div(c_times(X10,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f13422,plain,
spl0_1687,
inference(avatar_split_clause,[],[f351,f13420]) ).
fof(f13420,plain,
( spl0_1687
<=> ! [X1] : c_IntDiv_OposDivAlg(c_Pair(c_0,X1,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_1687])]) ).
fof(f351,axiom,
! [X1] : c_IntDiv_OposDivAlg(c_Pair(c_0,X1,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(f13418,plain,
spl0_1686,
inference(avatar_split_clause,[],[f336,f13416]) ).
fof(f13416,plain,
( spl0_1686
<=> ! [X1,X3] : c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f336,axiom,
! [X3,X1] : c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f13414,plain,
spl0_1685,
inference(avatar_split_clause,[],[f307,f13412]) ).
fof(f13412,plain,
( spl0_1685
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f307,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f13410,plain,
spl0_1684,
inference(avatar_split_clause,[],[f306,f13408]) ).
fof(f13408,plain,
( spl0_1684
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f306,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f13406,plain,
spl0_1683,
inference(avatar_split_clause,[],[f303,f13404]) ).
fof(f303,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f13402,plain,
spl0_1682,
inference(avatar_split_clause,[],[f302,f13400]) ).
fof(f13400,plain,
( spl0_1682
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f302,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f13398,plain,
spl0_1681,
inference(avatar_split_clause,[],[f300,f13396]) ).
fof(f300,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X33 = X35
| c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f13394,plain,
spl0_1680,
inference(avatar_split_clause,[],[f294,f13392]) ).
fof(f13392,plain,
( spl0_1680
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f294,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f13390,plain,
spl0_1679,
inference(avatar_split_clause,[],[f293,f13388]) ).
fof(f13388,plain,
( spl0_1679
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f293,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f13386,plain,
( spl0_1678
| ~ spl0_1231
| ~ spl0_1373 ),
inference(avatar_split_clause,[],[f11956,f10896,f9680,f13384]) ).
fof(f13384,plain,
( spl0_1678
<=> ! [X0] : c_minus(X0,c_0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f10896,plain,
( spl0_1373
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f11956,plain,
( ! [X0] : c_minus(X0,c_0,t_a) = X0
| ~ spl0_1231
| ~ spl0_1373 ),
inference(resolution,[],[f9682,f10897]) ).
fof(f10897,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 )
| ~ spl0_1373 ),
inference(avatar_component_clause,[],[f10896]) ).
fof(f13382,plain,
spl0_1677,
inference(avatar_split_clause,[],[f292,f13380]) ).
fof(f13380,plain,
( spl0_1677
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f292,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f13378,plain,
spl0_1676,
inference(avatar_split_clause,[],[f291,f13376]) ).
fof(f13376,plain,
( spl0_1676
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f291,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f13374,plain,
spl0_1675,
inference(avatar_split_clause,[],[f255,f13372]) ).
fof(f13372,plain,
( spl0_1675
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| c_in(c_uminus(X3,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f255,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| c_in(c_uminus(X3,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f13370,plain,
spl0_1674,
inference(avatar_split_clause,[],[f250,f13368]) ).
fof(f13368,plain,
( spl0_1674
<=> ! [X10] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X10)) = X10
| ~ c_in(X10,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f250,axiom,
! [X10] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X10)) = X10
| ~ c_in(X10,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(f13366,plain,
spl0_1673,
inference(avatar_split_clause,[],[f236,f13364]) ).
fof(f13364,plain,
( spl0_1673
<=> ! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f236,axiom,
! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f13362,plain,
spl0_1672,
inference(avatar_split_clause,[],[f235,f13360]) ).
fof(f13360,plain,
( spl0_1672
<=> ! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X34,tc_IntDef_Oint)) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f235,axiom,
! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X34,tc_IntDef_Oint)) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f13358,plain,
spl0_1671,
inference(avatar_split_clause,[],[f137,f13356]) ).
fof(f13356,plain,
( spl0_1671
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f137,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f13354,plain,
spl0_1670,
inference(avatar_split_clause,[],[f127,f13352]) ).
fof(f13352,plain,
( spl0_1670
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f127,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f13350,plain,
spl0_1669,
inference(avatar_split_clause,[],[f126,f13348]) ).
fof(f13348,plain,
( spl0_1669
<=> ! [X11,X24] : c_Divides_Oop_Amod(c_plus(X11,X24,tc_nat),X11,tc_nat) = c_Divides_Oop_Amod(X24,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f126,axiom,
! [X11,X24] : c_Divides_Oop_Amod(c_plus(X11,X24,tc_nat),X11,tc_nat) = c_Divides_Oop_Amod(X24,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f13346,plain,
spl0_1668,
inference(avatar_split_clause,[],[f85,f13344]) ).
fof(f13344,plain,
( spl0_1668
<=> ! [X18,X17,X0,X16] :
( X17 = X18
| c_Datatype__Universe_OIn1(X18,X0,X16) != c_Datatype__Universe_OIn1(X17,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f85,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_Datatype__Universe_OIn1(X18,X0,X16) != c_Datatype__Universe_OIn1(X17,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f13342,plain,
( spl0_1667
| ~ spl0_1158
| ~ spl0_1350 ),
inference(avatar_split_clause,[],[f11544,f10743,f9364,f13340]) ).
fof(f13340,plain,
( spl0_1667
<=> ! [X0] : c_LOrder_Omeet(X0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f9364,plain,
( spl0_1158
<=> class_LOrder_Omeet__semilorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f10743,plain,
( spl0_1350
<=> ! [X0,X10] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f11544,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,t_a) = X0
| ~ spl0_1158
| ~ spl0_1350 ),
inference(resolution,[],[f9366,f10744]) ).
fof(f10744,plain,
( ! [X10,X0] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 )
| ~ spl0_1350 ),
inference(avatar_component_clause,[],[f10743]) ).
fof(f9366,plain,
( class_LOrder_Omeet__semilorder(t_a)
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f9364]) ).
fof(f13338,plain,
spl0_1666,
inference(avatar_split_clause,[],[f83,f13336]) ).
fof(f13336,plain,
( spl0_1666
<=> ! [X18,X17,X0,X16] :
( X17 = X18
| c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn0(X18,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f83,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn0(X18,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f13334,plain,
spl0_1665,
inference(avatar_split_clause,[],[f79,f13332]) ).
fof(f13332,plain,
( spl0_1665
<=> ! [X3,X0,X16,X1] :
( X1 = X3
| c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OAtom(X1,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f79,axiom,
! [X3,X0,X1,X16] :
( X1 = X3
| c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OAtom(X1,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f13298,plain,
( spl0_1664
| ~ spl0_1157
| ~ spl0_1349 ),
inference(avatar_split_clause,[],[f11501,f10739,f9359,f13296]) ).
fof(f13296,plain,
( spl0_1664
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f9359,plain,
( spl0_1157
<=> class_LOrder_Ojoin__semilorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f10739,plain,
( spl0_1349
<=> ! [X0,X10] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f11501,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,t_a) = X0
| ~ spl0_1157
| ~ spl0_1349 ),
inference(resolution,[],[f9361,f10740]) ).
fof(f10740,plain,
( ! [X10,X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 )
| ~ spl0_1349 ),
inference(avatar_component_clause,[],[f10739]) ).
fof(f9361,plain,
( class_LOrder_Ojoin__semilorder(t_a)
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9359]) ).
fof(f13266,plain,
( spl0_1663
| ~ spl0_1045
| ~ spl0_1414 ),
inference(avatar_split_clause,[],[f11413,f11102,f8437,f13264]) ).
fof(f13264,plain,
( spl0_1663
<=> ! [X0] : c_SetsAndFunctions_Oelt__set__plus(c_0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f8437,plain,
( spl0_1045
<=> class_OrderedGroup_Ocomm__monoid__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f11102,plain,
( spl0_1414
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f11413,plain,
( ! [X0] : c_SetsAndFunctions_Oelt__set__plus(c_0,X0,t_a) = X0
| ~ spl0_1045
| ~ spl0_1414 ),
inference(resolution,[],[f11103,f8439]) ).
fof(f8439,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ spl0_1045 ),
inference(avatar_component_clause,[],[f8437]) ).
fof(f11103,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 )
| ~ spl0_1414 ),
inference(avatar_component_clause,[],[f11102]) ).
fof(f13156,plain,
( spl0_1662
| ~ spl0_1030
| ~ spl0_1413 ),
inference(avatar_split_clause,[],[f11408,f11098,f8134,f13154]) ).
fof(f13154,plain,
( spl0_1662
<=> ! [X0] : c_SetsAndFunctions_Oelt__set__times(c_1,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f8134,plain,
( spl0_1030
<=> class_OrderedGroup_Ocomm__monoid__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f11098,plain,
( spl0_1413
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f11408,plain,
( ! [X0] : c_SetsAndFunctions_Oelt__set__times(c_1,X0,t_a) = X0
| ~ spl0_1030
| ~ spl0_1413 ),
inference(resolution,[],[f11099,f8136]) ).
fof(f8136,plain,
( class_OrderedGroup_Ocomm__monoid__mult(t_a)
| ~ spl0_1030 ),
inference(avatar_component_clause,[],[f8134]) ).
fof(f11099,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 )
| ~ spl0_1413 ),
inference(avatar_component_clause,[],[f11098]) ).
fof(f13107,plain,
( spl0_1661
| ~ spl0_1055
| ~ spl0_1394 ),
inference(avatar_split_clause,[],[f11343,f11013,f8701,f13105]) ).
fof(f13105,plain,
( spl0_1661
<=> ! [X0] : c_0 = c_times(X0,c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f11013,plain,
( spl0_1394
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f11343,plain,
( ! [X0] : c_0 = c_times(X0,c_0,t_a)
| ~ spl0_1055
| ~ spl0_1394 ),
inference(resolution,[],[f11014,f8703]) ).
fof(f11014,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) )
| ~ spl0_1394 ),
inference(avatar_component_clause,[],[f11013]) ).
fof(f13067,plain,
( spl0_1660
| ~ spl0_1055
| ~ spl0_1392 ),
inference(avatar_split_clause,[],[f11339,f11005,f8701,f13065]) ).
fof(f11005,plain,
( spl0_1392
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f11339,plain,
( ! [X0] : c_0 = c_times(c_0,X0,t_a)
| ~ spl0_1055
| ~ spl0_1392 ),
inference(resolution,[],[f11006,f8703]) ).
fof(f11006,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) )
| ~ spl0_1392 ),
inference(avatar_component_clause,[],[f11005]) ).
fof(f13005,plain,
( spl0_1659
| ~ spl0_1028
| ~ spl0_1391 ),
inference(avatar_split_clause,[],[f11337,f11001,f8104,f13003]) ).
fof(f13003,plain,
( spl0_1659
<=> ! [X0] : c_divide(X0,c_1,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f11001,plain,
( spl0_1391
<=> ! [X0,X10] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_divide(X10,c_1,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f11337,plain,
( ! [X0] : c_divide(X0,c_1,t_a) = X0
| ~ spl0_1028
| ~ spl0_1391 ),
inference(resolution,[],[f11002,f8106]) ).
fof(f11002,plain,
( ! [X10,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_divide(X10,c_1,X0) = X10 )
| ~ spl0_1391 ),
inference(avatar_component_clause,[],[f11001]) ).
fof(f12990,plain,
( spl0_1658
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_1586 ),
inference(avatar_split_clause,[],[f12662,f12659,f11630,f3498,f12988]) ).
fof(f12988,plain,
( spl0_1658
<=> ! [X0] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f12659,plain,
( spl0_1586
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f12662,plain,
( ! [X0] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_1586 ),
inference(forward_demodulation,[],[f12660,f11976]) ).
fof(f12660,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) )
| ~ spl0_1586 ),
inference(avatar_component_clause,[],[f12659]) ).
fof(f12967,plain,
( spl0_1657
| ~ spl0_1063
| ~ spl0_1381 ),
inference(avatar_split_clause,[],[f11306,f10947,f8892,f12965]) ).
fof(f12965,plain,
( spl0_1657
<=> ! [X0] : c_Orderings_Omax(X0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f10947,plain,
( spl0_1381
<=> ! [X16,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f11306,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,t_a) = X0
| ~ spl0_1063
| ~ spl0_1381 ),
inference(resolution,[],[f10948,f8894]) ).
fof(f10948,plain,
( ! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 )
| ~ spl0_1381 ),
inference(avatar_component_clause,[],[f10947]) ).
fof(f12951,plain,
spl0_1656,
inference(avatar_split_clause,[],[f3101,f12949]) ).
fof(f12949,plain,
( spl0_1656
<=> ! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f3101,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X11,tc_nat) ),
inference(forward_demodulation,[],[f2924,f2791]) ).
fof(f2924,plain,
! [X11,X24] :
( c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f990,f1438]) ).
fof(f990,axiom,
! [X11,X24] :
( c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f12947,plain,
spl0_1655,
inference(avatar_split_clause,[],[f3100,f12945]) ).
fof(f12945,plain,
( spl0_1655
<=> ! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f3100,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2923,f2791]) ).
fof(f2923,plain,
! [X11,X24] :
( c_lessequals(c_1,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f989,f1438]) ).
fof(f989,axiom,
! [X11,X24] :
( c_lessequals(c_1,X24,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f12943,plain,
spl0_1654,
inference(avatar_split_clause,[],[f3090,f12941]) ).
fof(f12941,plain,
( spl0_1654
<=> ! [X11,X23] :
( c_lessequals(c_1,c_Nat_Opower(X23,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X23,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f3090,plain,
! [X11,X23] :
( c_lessequals(c_1,c_Nat_Opower(X23,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X23,tc_nat) ),
inference(forward_demodulation,[],[f2908,f2791]) ).
fof(f2908,plain,
! [X11,X23] :
( ~ c_lessequals(c_1,X23,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X23,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1234,f1438]) ).
fof(f1234,axiom,
! [X11,X23] :
( ~ c_lessequals(c_1,X23,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X23,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f12939,plain,
spl0_1653,
inference(avatar_split_clause,[],[f3031,f12937]) ).
fof(f12937,plain,
( spl0_1653
<=> ! [X11,X24] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f3031,plain,
! [X11,X24] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2831,f2827]) ).
fof(f2831,plain,
! [X11,X24] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1659,f1438]) ).
fof(f1659,axiom,
! [X11,X24] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f12935,plain,
spl0_1652,
inference(avatar_split_clause,[],[f3027,f12933]) ).
fof(f12933,plain,
( spl0_1652
<=> ! [X33] : c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f3027,plain,
! [X33] : c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2829,f2806]) ).
fof(f2829,plain,
! [X33] : c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f1025,f1007,f1007]) ).
fof(f1025,axiom,
! [X33] : c_Numeral_Obin__pred(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X33),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f12931,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2830,f12929]) ).
fof(f12929,plain,
( spl0_1651
<=> ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f2830,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f1017,f1023,f1023]) ).
fof(f1017,axiom,
! [X33] : c_Numeral_Obin__minus(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f12923,plain,
( spl0_1650
| ~ spl0_1063
| ~ spl0_1380 ),
inference(avatar_split_clause,[],[f11303,f10943,f8892,f12921]) ).
fof(f12921,plain,
( spl0_1650
<=> ! [X0] : c_Orderings_Omin(X0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f10943,plain,
( spl0_1380
<=> ! [X16,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f11303,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,t_a) = X0
| ~ spl0_1063
| ~ spl0_1380 ),
inference(resolution,[],[f10944,f8894]) ).
fof(f10944,plain,
( ! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 )
| ~ spl0_1380 ),
inference(avatar_component_clause,[],[f10943]) ).
fof(f12919,plain,
( spl0_1649
| ~ spl0_1648 ),
inference(avatar_split_clause,[],[f12915,f12912,f12917]) ).
fof(f12917,plain,
( spl0_1649
<=> ! [X11] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f12912,plain,
( spl0_1648
<=> ! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f12915,plain,
( ! [X11] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1648 ),
inference(forward_demodulation,[],[f12913,f2827]) ).
fof(f12913,plain,
( ! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1648 ),
inference(avatar_component_clause,[],[f12912]) ).
fof(f12914,plain,
spl0_1648,
inference(avatar_split_clause,[],[f2819,f12912]) ).
fof(f2819,plain,
! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f288,f1438]) ).
fof(f288,axiom,
! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f12910,plain,
spl0_1647,
inference(avatar_split_clause,[],[f1609,f12908]) ).
fof(f12908,plain,
( spl0_1647
<=> ! [X0,X19] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ORange(X19,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f1609,axiom,
! [X0,X19] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ORange(X19,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f12906,plain,
spl0_1646,
inference(avatar_split_clause,[],[f1607,f12904]) ).
fof(f12904,plain,
( spl0_1646
<=> ! [X0,X19] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ODomain(X19,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f1607,axiom,
! [X0,X19] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ODomain(X19,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f12902,plain,
spl0_1645,
inference(avatar_split_clause,[],[f1579,f12900]) ).
fof(f12900,plain,
( spl0_1645
<=> ! [X0,X3,X1,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X3,c_insert(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f1579,axiom,
! [X3,X0,X1,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X3,c_insert(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f12898,plain,
spl0_1644,
inference(avatar_split_clause,[],[f1536,f12896]) ).
fof(f12896,plain,
( spl0_1644
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f1536,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f12894,plain,
spl0_1643,
inference(avatar_split_clause,[],[f1535,f12892]) ).
fof(f12892,plain,
( spl0_1643
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f1535,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f12890,plain,
spl0_1642,
inference(avatar_split_clause,[],[f1477,f12888]) ).
fof(f12888,plain,
( spl0_1642
<=> ! [X25,X0,X26] :
( c_in(X25,X26,X0)
| c_in(X25,c_uminus(X26,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f1477,axiom,
! [X0,X26,X25] :
( c_in(X25,X26,X0)
| c_in(X25,c_uminus(X26,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f12886,plain,
spl0_1641,
inference(avatar_split_clause,[],[f1476,f12884]) ).
fof(f12884,plain,
( spl0_1641
<=> ! [X25,X0,X26] :
( ~ c_in(X25,X26,X0)
| ~ c_in(X25,c_uminus(X26,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f1476,axiom,
! [X0,X26,X25] :
( ~ c_in(X25,X26,X0)
| ~ c_in(X25,c_uminus(X26,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f12882,plain,
spl0_1640,
inference(avatar_split_clause,[],[f1439,f12880]) ).
fof(f12880,plain,
( spl0_1640
<=> ! [X36,X72] : c_minus(X36,X72,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f1439,axiom,
! [X72,X36] : c_minus(X36,X72,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f12878,plain,
( spl0_1639
| ~ spl0_1034
| ~ spl0_1376 ),
inference(avatar_split_clause,[],[f11297,f10908,f8194,f12876]) ).
fof(f8194,plain,
( spl0_1034
<=> class_OrderedGroup_Omonoid__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f10908,plain,
( spl0_1376
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f11297,plain,
( ! [X0] : c_times(X0,c_1,t_a) = X0
| ~ spl0_1034
| ~ spl0_1376 ),
inference(resolution,[],[f10909,f8196]) ).
fof(f8196,plain,
( class_OrderedGroup_Omonoid__mult(t_a)
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f8194]) ).
fof(f10909,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 )
| ~ spl0_1376 ),
inference(avatar_component_clause,[],[f10908]) ).
fof(f12874,plain,
spl0_1638,
inference(avatar_split_clause,[],[f1436,f12872]) ).
fof(f12872,plain,
( spl0_1638
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f1436,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,X72,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f12870,plain,
spl0_1637,
inference(avatar_split_clause,[],[f1416,f12868]) ).
fof(f1416,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f12866,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1326,f12864]) ).
fof(f12864,plain,
( spl0_1636
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(X3,c_0,X0) = c_times(X1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f1326,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(X3,c_0,X0) = c_times(X1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
fof(f12862,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1324,f12860]) ).
fof(f12860,plain,
( spl0_1635
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(c_0,X3,X0) = c_times(c_0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f1324,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_times(c_0,X3,X0) = c_times(c_0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
fof(f12858,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1165,f12856]) ).
fof(f12856,plain,
( spl0_1634
<=> ! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f1165,axiom,
! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,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(f12854,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1164,f12852]) ).
fof(f12852,plain,
( spl0_1633
<=> ! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f1164,axiom,
! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,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(f12850,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1146,f12848]) ).
fof(f1146,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_less(c_0,c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f12846,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1139,f12844]) ).
fof(f1139,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f12842,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1138,f12840]) ).
fof(f1138,axiom,
! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f12838,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1134,f12836]) ).
fof(f12836,plain,
( spl0_1629
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X10,c_0,X0)
| c_OrderedGroup_Onprt(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f1134,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X10,c_0,X0)
| c_OrderedGroup_Onprt(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f12834,plain,
( spl0_1628
| ~ spl0_1034
| ~ spl0_1375 ),
inference(avatar_split_clause,[],[f11292,f10904,f8194,f12832]) ).
fof(f10904,plain,
( spl0_1375
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f11292,plain,
( ! [X0] : c_times(c_1,X0,t_a) = X0
| ~ spl0_1034
| ~ spl0_1375 ),
inference(resolution,[],[f10905,f8196]) ).
fof(f10905,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 )
| ~ spl0_1375 ),
inference(avatar_component_clause,[],[f10904]) ).
fof(f12830,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1133,f12828]) ).
fof(f1133,axiom,
! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f12826,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1093,f12824]) ).
fof(f12824,plain,
( spl0_1626
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_0 != c_minus(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f1093,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_0 != c_minus(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f12822,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1077,f12820]) ).
fof(f12820,plain,
( spl0_1625
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_HOL_Oabs(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f1077,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_HOL_Oabs(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f12818,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1075,f12816]) ).
fof(f1075,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f12814,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1073,f12812]) ).
fof(f12812,plain,
( spl0_1623
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| ~ c_lessequals(c_HOL_Oabs(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f1073,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| ~ c_lessequals(c_HOL_Oabs(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f12810,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1072,f12808]) ).
fof(f1072,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f12806,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1041,f12804]) ).
fof(f12804,plain,
( spl0_1621
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f1041,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f12802,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1021,f12800]) ).
fof(f12800,plain,
( spl0_1620
<=> ! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33) = c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f12798,plain,
spl0_1619,
inference(avatar_split_clause,[],[f998,f12796]) ).
fof(f12796,plain,
( spl0_1619
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f998,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f12794,plain,
spl0_1618,
inference(avatar_split_clause,[],[f997,f12792]) ).
fof(f12792,plain,
( spl0_1618
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f997,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f12790,plain,
( spl0_1617
| ~ spl0_1045
| ~ spl0_1372 ),
inference(avatar_split_clause,[],[f11263,f10892,f8437,f12788]) ).
fof(f12788,plain,
( spl0_1617
<=> ! [X0] : c_plus(c_0,X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f10892,plain,
( spl0_1372
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f11263,plain,
( ! [X0] : c_plus(c_0,X0,t_a) = X0
| ~ spl0_1045
| ~ spl0_1372 ),
inference(resolution,[],[f10893,f8439]) ).
fof(f10893,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 )
| ~ spl0_1372 ),
inference(avatar_component_clause,[],[f10892]) ).
fof(f12786,plain,
spl0_1616,
inference(avatar_split_clause,[],[f973,f12784]) ).
fof(f12784,plain,
( spl0_1616
<=> ! [X11,X24] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f973,axiom,
! [X11,X24] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f12782,plain,
spl0_1615,
inference(avatar_split_clause,[],[f972,f12780]) ).
fof(f12780,plain,
( spl0_1615
<=> ! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f972,axiom,
! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f12778,plain,
spl0_1614,
inference(avatar_split_clause,[],[f924,f12776]) ).
fof(f12776,plain,
( spl0_1614
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f924,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f12774,plain,
spl0_1613,
inference(avatar_split_clause,[],[f923,f12772]) ).
fof(f12772,plain,
( spl0_1613
<=> ! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f923,axiom,
! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f12770,plain,
spl0_1612,
inference(avatar_split_clause,[],[f745,f12768]) ).
fof(f12768,plain,
( spl0_1612
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f745,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f12766,plain,
spl0_1611,
inference(avatar_split_clause,[],[f708,f12764]) ).
fof(f12764,plain,
( spl0_1611
<=> ! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f708,axiom,
! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f12762,plain,
spl0_1610,
inference(avatar_split_clause,[],[f655,f12760]) ).
fof(f12760,plain,
( spl0_1610
<=> ! [X0,X12] : c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f655,axiom,
! [X0,X12] : c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).
fof(f12758,plain,
spl0_1609,
inference(avatar_split_clause,[],[f625,f12756]) ).
fof(f12756,plain,
( spl0_1609
<=> ! [X11,X0,X12] : c_List_Oreplicate(X11,X12,X0) = c_List_Orev(c_List_Oreplicate(X11,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f625,axiom,
! [X0,X11,X12] : c_List_Oreplicate(X11,X12,X0) = c_List_Orev(c_List_Oreplicate(X11,X12,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f12754,plain,
spl0_1608,
inference(avatar_split_clause,[],[f606,f12752]) ).
fof(f12752,plain,
( spl0_1608
<=> ! [X10,X40,X14,X12] :
( ~ c_List_Oop_Amem(X12,X40,X14)
| c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f606,axiom,
! [X40,X10,X14,X12] :
( ~ c_List_Oop_Amem(X12,X40,X14)
| c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f12750,plain,
spl0_1607,
inference(avatar_split_clause,[],[f507,f12748]) ).
fof(f12748,plain,
( spl0_1607
<=> ! [X50,X23] : c_Nat_Osize(c_List_Oupt(X23,X50),tc_List_Olist(tc_nat)) = c_minus(X50,X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f507,axiom,
! [X50,X23] : c_Nat_Osize(c_List_Oupt(X23,X50),tc_List_Olist(tc_nat)) = c_minus(X50,X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f12746,plain,
( spl0_1606
| ~ spl0_1045
| ~ spl0_1371 ),
inference(avatar_split_clause,[],[f11258,f10888,f8437,f12744]) ).
fof(f12744,plain,
( spl0_1606
<=> ! [X0] : c_plus(X0,c_0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f10888,plain,
( spl0_1371
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f11258,plain,
( ! [X0] : c_plus(X0,c_0,t_a) = X0
| ~ spl0_1045
| ~ spl0_1371 ),
inference(resolution,[],[f10889,f8439]) ).
fof(f10889,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 )
| ~ spl0_1371 ),
inference(avatar_component_clause,[],[f10888]) ).
fof(f12742,plain,
spl0_1605,
inference(avatar_split_clause,[],[f503,f12740]) ).
fof(f12740,plain,
( spl0_1605
<=> ! [X0,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate1(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f503,axiom,
! [X39,X0] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate1(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f12738,plain,
spl0_1604,
inference(avatar_split_clause,[],[f502,f12736]) ).
fof(f12736,plain,
( spl0_1604
<=> ! [X0,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orev(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f502,axiom,
! [X39,X0] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orev(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f12734,plain,
spl0_1603,
inference(avatar_split_clause,[],[f489,f12732]) ).
fof(f12732,plain,
( spl0_1603
<=> ! [X0,X39,X10] : c_List_Olast(c_append(X39,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f489,axiom,
! [X39,X10,X0] : c_List_Olast(c_append(X39,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f12730,plain,
spl0_1602,
inference(avatar_split_clause,[],[f488,f12728]) ).
fof(f12728,plain,
( spl0_1602
<=> ! [X0,X11,X10] :
( c_0 = X11
| c_List_Olast(c_List_Oreplicate(X11,X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f488,axiom,
! [X10,X0,X11] :
( c_0 = X11
| c_List_Olast(c_List_Oreplicate(X11,X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f12726,plain,
spl0_1601,
inference(avatar_split_clause,[],[f487,f12724]) ).
fof(f12724,plain,
( spl0_1601
<=> ! [X0,X51] :
( c_List_Olist_ONil = X51
| c_in(c_List_Olast(X51,X0),c_List_Oset(X51,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f487,axiom,
! [X51,X0] :
( c_List_Olist_ONil = X51
| c_in(c_List_Olast(X51,X0),c_List_Oset(X51,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f12722,plain,
spl0_1600,
inference(avatar_split_clause,[],[f478,f12720]) ).
fof(f12720,plain,
( spl0_1600
<=> ! [X50,X10] :
( ~ c_less(X10,X50,tc_nat)
| c_List_Ohd(c_List_Oupt(X10,X50),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f478,axiom,
! [X50,X10] :
( ~ c_less(X10,X50,tc_nat)
| c_List_Ohd(c_List_Oupt(X10,X50),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f12718,plain,
spl0_1599,
inference(avatar_split_clause,[],[f477,f12716]) ).
fof(f12716,plain,
( spl0_1599
<=> ! [X0,X11,X10] :
( c_0 = X11
| c_List_Ohd(c_List_Oreplicate(X11,X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f477,axiom,
! [X10,X0,X11] :
( c_0 = X11
| c_List_Ohd(c_List_Oreplicate(X11,X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f12714,plain,
spl0_1598,
inference(avatar_split_clause,[],[f476,f12712]) ).
fof(f12712,plain,
( spl0_1598
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_in(c_List_Ohd(X39,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f476,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_in(c_List_Ohd(X39,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f12710,plain,
spl0_1597,
inference(avatar_split_clause,[],[f433,f12708]) ).
fof(f12708,plain,
( spl0_1597
<=> ! [X0,X12,X10] : c_List_Obutlast(c_append(X10,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f433,axiom,
! [X10,X0,X12] : c_List_Obutlast(c_append(X10,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f12706,plain,
spl0_1596,
inference(avatar_split_clause,[],[f357,f12704]) ).
fof(f12704,plain,
( spl0_1596
<=> ! [X1,X3] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f357,axiom,
! [X3,X1] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f12698,plain,
spl0_1595,
inference(avatar_split_clause,[],[f356,f12696]) ).
fof(f12696,plain,
( spl0_1595
<=> ! [X1,X3] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f356,axiom,
! [X3,X1] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f12694,plain,
spl0_1594,
inference(avatar_split_clause,[],[f349,f12692]) ).
fof(f12692,plain,
( spl0_1594
<=> ! [X1,X3] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f349,axiom,
! [X3,X1] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f12690,plain,
spl0_1593,
inference(avatar_split_clause,[],[f348,f12688]) ).
fof(f12688,plain,
( spl0_1593
<=> ! [X1,X3] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_less(X1,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f348,axiom,
! [X3,X1] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_less(X1,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f12686,plain,
spl0_1592,
inference(avatar_split_clause,[],[f312,f12684]) ).
fof(f312,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f12682,plain,
spl0_1591,
inference(avatar_split_clause,[],[f248,f12680]) ).
fof(f248,axiom,
! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f12678,plain,
spl0_1590,
inference(avatar_split_clause,[],[f247,f12676]) ).
fof(f247,axiom,
! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f12674,plain,
spl0_1589,
inference(avatar_split_clause,[],[f246,f12672]) ).
fof(f246,axiom,
! [X35,X33] :
( ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f12670,plain,
spl0_1588,
inference(avatar_split_clause,[],[f245,f12668]) ).
fof(f245,axiom,
! [X35,X33] :
( c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f12666,plain,
spl0_1587,
inference(avatar_split_clause,[],[f242,f12664]) ).
fof(f12664,plain,
( spl0_1587
<=> ! [X35,X33] : c_plus(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X35,X33,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f242,axiom,
! [X35,X33] : c_plus(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X35,X33,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(f12661,plain,
spl0_1586,
inference(avatar_split_clause,[],[f239,f12659]) ).
fof(f239,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f12656,plain,
spl0_1585,
inference(avatar_split_clause,[],[f204,f12654]) ).
fof(f204,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f12652,plain,
spl0_1584,
inference(avatar_split_clause,[],[f201,f12650]) ).
fof(f12650,plain,
( spl0_1584
<=> ! [X11,X10] : c_GCD_Ogcd(c_Pair(X10,c_times(X10,X11,tc_nat),tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f201,axiom,
! [X10,X11] : c_GCD_Ogcd(c_Pair(X10,c_times(X10,X11,tc_nat),tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f12648,plain,
spl0_1583,
inference(avatar_split_clause,[],[f130,f12646]) ).
fof(f12646,plain,
( spl0_1583
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f130,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f12644,plain,
spl0_1582,
inference(avatar_split_clause,[],[f128,f12642]) ).
fof(f12642,plain,
( spl0_1582
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f128,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f12640,plain,
spl0_1581,
inference(avatar_split_clause,[],[f72,f12638]) ).
fof(f12638,plain,
( spl0_1581
<=> ! [X16,X0,X1,X3] : c_0 = c_Nat_Osize(c_Pair(X3,X1,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f72,axiom,
! [X3,X0,X1,X16] : c_0 = c_Nat_Osize(c_Pair(X3,X1,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f12636,plain,
spl0_1580,
inference(avatar_split_clause,[],[f60,f12634]) ).
fof(f12634,plain,
( spl0_1580
<=> ! [X13,X0,X12] :
( c_Datatype_Ooption_OSome(X12,X0) = X13
| ~ c_in(X12,c_Datatype_Oo2s(X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f60,axiom,
! [X0,X12,X13] :
( c_Datatype_Ooption_OSome(X12,X0) = X13
| ~ c_in(X12,c_Datatype_Oo2s(X13,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f12518,plain,
( spl0_1579
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_1528 ),
inference(avatar_split_clause,[],[f12205,f12202,f11630,f3498,f12516]) ).
fof(f12516,plain,
( spl0_1579
<=> ! [X3] : c_uminus(X3,tc_IntDef_Oint) = c_div(X3,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f12202,plain,
( spl0_1528
<=> ! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f12205,plain,
( ! [X3] : c_uminus(X3,tc_IntDef_Oint) = c_div(X3,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1462
| ~ spl0_1528 ),
inference(forward_demodulation,[],[f12203,f11976]) ).
fof(f12203,plain,
( ! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint)
| ~ spl0_1528 ),
inference(avatar_component_clause,[],[f12202]) ).
fof(f12415,plain,
spl0_1578,
inference(avatar_split_clause,[],[f3149,f12413]) ).
fof(f12413,plain,
( spl0_1578
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_0,X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f3149,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_0,X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(inner_rewriting,[],[f3148]) ).
fof(f3148,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f3147,f1009]) ).
fof(f3147,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2956,f2790]) ).
fof(f2956,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f231,f1023]) ).
fof(f231,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f12411,plain,
spl0_1577,
inference(avatar_split_clause,[],[f3034,f12409]) ).
fof(f12409,plain,
( spl0_1577
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f3034,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2836,f2791]) ).
fof(f2836,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f103,f1438]) ).
fof(f103,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f12407,plain,
spl0_1576,
inference(avatar_split_clause,[],[f3033,f12405]) ).
fof(f12405,plain,
( spl0_1576
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f3033,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2835,f2791]) ).
fof(f2835,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f104,f1438]) ).
fof(f104,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f12403,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2907,f12401]) ).
fof(f12401,plain,
( spl0_1575
<=> ! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f2907,plain,
! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1173,f1438]) ).
fof(f1173,axiom,
! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f12399,plain,
( spl0_1574
| ~ spl0_1253
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f12024,f10280,f9771,f12396]) ).
fof(f9771,plain,
( spl0_1253
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f10280,plain,
( spl0_1293
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f12024,plain,
( c_1 = c_NatArith_Oof__nat(c_1,t_a)
| ~ spl0_1253
| ~ spl0_1293 ),
inference(resolution,[],[f9773,f10281]) ).
fof(f10281,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) )
| ~ spl0_1293 ),
inference(avatar_component_clause,[],[f10280]) ).
fof(f9773,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(t_a)
| ~ spl0_1253 ),
inference(avatar_component_clause,[],[f9771]) ).
fof(f12394,plain,
spl0_1573,
inference(avatar_split_clause,[],[f2897,f12392]) ).
fof(f12392,plain,
( spl0_1573
<=> ! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f2897,plain,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1172,f1438]) ).
fof(f1172,axiom,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f12387,plain,
( spl0_1572
| ~ spl0_1571 ),
inference(avatar_split_clause,[],[f12383,f12380,f12385]) ).
fof(f12385,plain,
( spl0_1572
<=> ! [X11] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f12380,plain,
( spl0_1571
<=> ! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f12383,plain,
( ! [X11] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1571 ),
inference(forward_demodulation,[],[f12381,f2827]) ).
fof(f12381,plain,
( ! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1571 ),
inference(avatar_component_clause,[],[f12380]) ).
fof(f12382,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2818,f12380]) ).
fof(f2818,plain,
! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f282,f1438]) ).
fof(f282,axiom,
! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f12378,plain,
( spl0_1570
| ~ spl0_1263
| ~ spl0_1569 ),
inference(avatar_split_clause,[],[f12374,f12371,f9812,f12376]) ).
fof(f12376,plain,
( spl0_1570
<=> ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f9812,plain,
( spl0_1263
<=> ! [X0,X10] : c_union(c_emptyset,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f12371,plain,
( spl0_1569
<=> ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f12374,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X0)
| ~ spl0_1263
| ~ spl0_1569 ),
inference(forward_demodulation,[],[f12372,f9813]) ).
fof(f9813,plain,
( ! [X10,X0] : c_union(c_emptyset,X10,X0) = X10
| ~ spl0_1263 ),
inference(avatar_component_clause,[],[f9812]) ).
fof(f12372,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0)
| ~ spl0_1569 ),
inference(avatar_component_clause,[],[f12371]) ).
fof(f12373,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2792,f12371]) ).
fof(f2792,plain,
! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1603,f1610]) ).
fof(f1603,axiom,
! [X0] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f12369,plain,
spl0_1568,
inference(avatar_split_clause,[],[f1726,f12367]) ).
fof(f1726,axiom,
! [X3,X0,X1] :
( X1 = X3
| ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f12365,plain,
spl0_1567,
inference(avatar_split_clause,[],[f1724,f12363]) ).
fof(f12363,plain,
( spl0_1567
<=> ! [X0,X30,X26] :
( ~ c_less(X26,X30,tc_set(X0))
| c_lessequals(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f1724,axiom,
! [X0,X26,X30] :
( ~ c_less(X26,X30,tc_set(X0))
| c_lessequals(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f12361,plain,
spl0_1566,
inference(avatar_split_clause,[],[f1723,f12359]) ).
fof(f12359,plain,
( spl0_1566
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| ~ c_less(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f1723,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| ~ c_less(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f12357,plain,
( spl0_1565
| ~ spl0_1231
| ~ spl0_1309 ),
inference(avatar_split_clause,[],[f11955,f10346,f9680,f12354]) ).
fof(f12354,plain,
( spl0_1565
<=> c_0 = c_uminus(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f10346,plain,
( spl0_1309
<=> ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f11955,plain,
( c_0 = c_uminus(c_0,t_a)
| ~ spl0_1231
| ~ spl0_1309 ),
inference(resolution,[],[f9682,f10347]) ).
fof(f10347,plain,
( ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) )
| ~ spl0_1309 ),
inference(avatar_component_clause,[],[f10346]) ).
fof(f12352,plain,
spl0_1564,
inference(avatar_split_clause,[],[f1565,f12350]) ).
fof(f12350,plain,
( spl0_1564
<=> ! [X0,X26] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f1565,axiom,
! [X0,X26] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f12348,plain,
spl0_1563,
inference(avatar_split_clause,[],[f1548,f12346]) ).
fof(f12346,plain,
( spl0_1563
<=> ! [X0,X26] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f1548,axiom,
! [X0,X26] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f12344,plain,
spl0_1562,
inference(avatar_split_clause,[],[f1512,f12342]) ).
fof(f12342,plain,
( spl0_1562
<=> ! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f1512,axiom,
! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f12340,plain,
spl0_1561,
inference(avatar_split_clause,[],[f1509,f12338]) ).
fof(f12338,plain,
( spl0_1561
<=> ! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f1509,axiom,
! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f12336,plain,
spl0_1560,
inference(avatar_split_clause,[],[f1282,f12334]) ).
fof(f12334,plain,
( spl0_1560
<=> ! [X0,X12] : c_in(c_Pair(X12,X12,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f1282,axiom,
! [X0,X12] : c_in(c_Pair(X12,X12,X0,X0),c_Relation_OId,tc_prod(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f12332,plain,
spl0_1559,
inference(avatar_split_clause,[],[f1277,f12330]) ).
fof(f12330,plain,
( spl0_1559
<=> ! [X0,X26] : c_Relation_Odiag(X26,X0) = c_Relation_Oconverse(c_Relation_Odiag(X26,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f1277,axiom,
! [X0,X26] : c_Relation_Odiag(X26,X0) = c_Relation_Oconverse(c_Relation_Odiag(X26,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f12328,plain,
spl0_1558,
inference(avatar_split_clause,[],[f1260,f12326]) ).
fof(f1260,axiom,
! [X3,X10,X0,X16] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f12324,plain,
spl0_1557,
inference(avatar_split_clause,[],[f1258,f12322]) ).
fof(f1258,axiom,
! [X10,X0,X1,X16] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f12320,plain,
spl0_1556,
inference(avatar_split_clause,[],[f1236,f12318]) ).
fof(f12318,plain,
( spl0_1556
<=> ! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(X12,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f1236,axiom,
! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(X12,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f12316,plain,
spl0_1555,
inference(avatar_split_clause,[],[f1235,f12314]) ).
fof(f12314,plain,
( spl0_1555
<=> ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f1235,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f12312,plain,
( spl0_1554
| ~ spl0_1220
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f11929,f10284,f9635,f12309]) ).
fof(f12309,plain,
( spl0_1554
<=> c_0 = c_NatArith_Oof__nat(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f10284,plain,
( spl0_1294
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f11929,plain,
( c_0 = c_NatArith_Oof__nat(c_0,t_a)
| ~ spl0_1220
| ~ spl0_1294 ),
inference(resolution,[],[f9637,f10285]) ).
fof(f10285,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) )
| ~ spl0_1294 ),
inference(avatar_component_clause,[],[f10284]) ).
fof(f9637,plain,
( class_Ring__and__Field_Oordered__semidom(t_a)
| ~ spl0_1220 ),
inference(avatar_component_clause,[],[f9635]) ).
fof(f12307,plain,
spl0_1553,
inference(avatar_split_clause,[],[f1188,f12305]) ).
fof(f12305,plain,
( spl0_1553
<=> ! [X12,X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1188,axiom,
! [X11,X12] :
( c_less(c_0,X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f12303,plain,
spl0_1552,
inference(avatar_split_clause,[],[f1175,f12301]) ).
fof(f12301,plain,
( spl0_1552
<=> ! [X12,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f1175,axiom,
! [X10,X12] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f12299,plain,
spl0_1551,
inference(avatar_split_clause,[],[f1141,f12297]) ).
fof(f1141,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f12295,plain,
spl0_1550,
inference(avatar_split_clause,[],[f1119,f12293]) ).
fof(f1119,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = X3
| c_0 != c_uminus(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f12291,plain,
spl0_1549,
inference(avatar_split_clause,[],[f1107,f12289]) ).
fof(f12289,plain,
( spl0_1549
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f1107,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f12287,plain,
spl0_1548,
inference(avatar_split_clause,[],[f1105,f12285]) ).
fof(f12285,plain,
( spl0_1548
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f1105,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f12283,plain,
spl0_1547,
inference(avatar_split_clause,[],[f1091,f12281]) ).
fof(f1091,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f12279,plain,
spl0_1546,
inference(avatar_split_clause,[],[f1066,f12277]) ).
fof(f1066,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_0 != c_HOL_Oabs(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f12275,plain,
spl0_1545,
inference(avatar_split_clause,[],[f1065,f12273]) ).
fof(f1065,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f12271,plain,
spl0_1544,
inference(avatar_split_clause,[],[f933,f12269]) ).
fof(f12269,plain,
( spl0_1544
<=> ! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_0 = c_minus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f933,axiom,
! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_0 = c_minus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f12267,plain,
( spl0_1543
| ~ spl0_1155
| ~ spl0_1311 ),
inference(avatar_split_clause,[],[f11433,f10356,f9343,f12264]) ).
fof(f12264,plain,
( spl0_1543
<=> c_0 = c_OrderedGroup_Opprt(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f10356,plain,
( spl0_1311
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f11433,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,t_a)
| ~ spl0_1155
| ~ spl0_1311 ),
inference(resolution,[],[f9345,f10357]) ).
fof(f10357,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) )
| ~ spl0_1311 ),
inference(avatar_component_clause,[],[f10356]) ).
fof(f9345,plain,
( class_OrderedGroup_Olordered__ab__group(t_a)
| ~ spl0_1155 ),
inference(avatar_component_clause,[],[f9343]) ).
fof(f12262,plain,
spl0_1542,
inference(avatar_split_clause,[],[f932,f12260]) ).
fof(f12260,plain,
( spl0_1542
<=> ! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| c_0 != c_minus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f932,axiom,
! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| c_0 != c_minus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f12258,plain,
spl0_1541,
inference(avatar_split_clause,[],[f743,f12256]) ).
fof(f12256,plain,
( spl0_1541
<=> ! [X34] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f743,axiom,
! [X34] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f12254,plain,
spl0_1540,
inference(avatar_split_clause,[],[f726,f12252]) ).
fof(f12252,plain,
( spl0_1540
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f726,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f12250,plain,
spl0_1539,
inference(avatar_split_clause,[],[f697,f12248]) ).
fof(f12248,plain,
( spl0_1539
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X11
| c_0 != c_NatArith_Oof__nat(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f697,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X11
| c_0 != c_NatArith_Oof__nat(X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f12246,plain,
spl0_1538,
inference(avatar_split_clause,[],[f653,f12244]) ).
fof(f12244,plain,
( spl0_1538
<=> ! [X0,X11,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate(X11,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f653,axiom,
! [X39,X0,X11] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f12242,plain,
spl0_1537,
inference(avatar_split_clause,[],[f624,f12240]) ).
fof(f12240,plain,
( spl0_1537
<=> ! [X39,X0,X40] :
( X39 = X40
| c_List_Orev(X39,X0) != c_List_Orev(X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f624,axiom,
! [X40,X39,X0] :
( X39 = X40
| c_List_Orev(X39,X0) != c_List_Orev(X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f12238,plain,
spl0_1536,
inference(avatar_split_clause,[],[f497,f12236]) ).
fof(f12236,plain,
( spl0_1536
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_less(c_0,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f497,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_less(c_0,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f12234,plain,
spl0_1535,
inference(avatar_split_clause,[],[f442,f12232]) ).
fof(f12232,plain,
( spl0_1535
<=> ! [X41,X0] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f442,axiom,
! [X41,X0] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f12230,plain,
spl0_1534,
inference(avatar_split_clause,[],[f435,f12228]) ).
fof(f12228,plain,
( spl0_1534
<=> ! [X45,X48,X46,X47] :
( X46 = X48
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f435,axiom,
! [X48,X46,X47,X45] :
( X46 = X48
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f12226,plain,
spl0_1533,
inference(avatar_split_clause,[],[f434,f12224]) ).
fof(f12224,plain,
( spl0_1533
<=> ! [X48,X47,X46,X45] :
( X45 = X47
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f434,axiom,
! [X48,X46,X47,X45] :
( X45 = X47
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f12222,plain,
( spl0_1532
| ~ spl0_1155
| ~ spl0_1310 ),
inference(avatar_split_clause,[],[f11432,f10350,f9343,f12219]) ).
fof(f12219,plain,
( spl0_1532
<=> c_0 = c_OrderedGroup_Onprt(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f10350,plain,
( spl0_1310
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f11432,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,t_a)
| ~ spl0_1155
| ~ spl0_1310 ),
inference(resolution,[],[f9345,f10351]) ).
fof(f10351,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) )
| ~ spl0_1310 ),
inference(avatar_component_clause,[],[f10350]) ).
fof(f12217,plain,
spl0_1531,
inference(avatar_split_clause,[],[f403,f12215]) ).
fof(f12215,plain,
( spl0_1531
<=> ! [X41,X0] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f403,axiom,
! [X41,X0] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f12213,plain,
spl0_1530,
inference(avatar_split_clause,[],[f382,f12211]) ).
fof(f12211,plain,
( spl0_1530
<=> ! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f382,axiom,
! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f12209,plain,
spl0_1529,
inference(avatar_split_clause,[],[f381,f12207]) ).
fof(f12207,plain,
( spl0_1529
<=> ! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f381,axiom,
! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f12204,plain,
spl0_1528,
inference(avatar_split_clause,[],[f361,f12202]) ).
fof(f361,axiom,
! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f12200,plain,
spl0_1527,
inference(avatar_split_clause,[],[f334,f12198]) ).
fof(f12198,plain,
( spl0_1527
<=> ! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f334,axiom,
! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f12196,plain,
spl0_1526,
inference(avatar_split_clause,[],[f333,f12194]) ).
fof(f12194,plain,
( spl0_1526
<=> ! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f333,axiom,
! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f12192,plain,
spl0_1525,
inference(avatar_split_clause,[],[f324,f12190]) ).
fof(f12190,plain,
( spl0_1525
<=> ! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f324,axiom,
! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f12188,plain,
spl0_1524,
inference(avatar_split_clause,[],[f323,f12186]) ).
fof(f12186,plain,
( spl0_1524
<=> ! [X35,X33] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f323,axiom,
! [X35,X33] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f12184,plain,
spl0_1523,
inference(avatar_split_clause,[],[f322,f12182]) ).
fof(f12182,plain,
( spl0_1523
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f322,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f12180,plain,
spl0_1522,
inference(avatar_split_clause,[],[f321,f12178]) ).
fof(f12178,plain,
( spl0_1522
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f321,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f12176,plain,
( spl0_1521
| ~ spl0_1127
| ~ spl0_1308 ),
inference(avatar_split_clause,[],[f11287,f10342,f9203,f12173]) ).
fof(f10342,plain,
( spl0_1308
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f11287,plain,
( c_0 = c_HOL_Oabs(c_0,t_a)
| ~ spl0_1127
| ~ spl0_1308 ),
inference(resolution,[],[f9205,f10343]) ).
fof(f10343,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) )
| ~ spl0_1308 ),
inference(avatar_component_clause,[],[f10342]) ).
fof(f12171,plain,
spl0_1520,
inference(avatar_split_clause,[],[f320,f12169]) ).
fof(f12169,plain,
( spl0_1520
<=> ! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f320,axiom,
! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f12167,plain,
spl0_1519,
inference(avatar_split_clause,[],[f319,f12165]) ).
fof(f12165,plain,
( spl0_1519
<=> ! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f319,axiom,
! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f12163,plain,
spl0_1518,
inference(avatar_split_clause,[],[f301,f12161]) ).
fof(f301,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f12159,plain,
spl0_1517,
inference(avatar_split_clause,[],[f289,f12157]) ).
fof(f12157,plain,
( spl0_1517
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X35
| c_0 != c_IntDef_Oof__int(X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f289,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X35
| c_0 != c_IntDef_Oof__int(X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f12155,plain,
spl0_1516,
inference(avatar_split_clause,[],[f284,f12153]) ).
fof(f12153,plain,
( spl0_1516
<=> ! [X11,X24] :
( c_0 = X24
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f284,axiom,
! [X11,X24] :
( c_0 = X24
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f12151,plain,
spl0_1515,
inference(avatar_split_clause,[],[f283,f12149]) ).
fof(f12149,plain,
( spl0_1515
<=> ! [X11,X24] :
( c_0 = X11
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f283,axiom,
! [X11,X24] :
( c_0 = X11
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f12147,plain,
spl0_1514,
inference(avatar_split_clause,[],[f173,f12145]) ).
fof(f12145,plain,
( spl0_1514
<=> ! [X0,X26] :
( c_0 = c_Finite__Set_Ocard(X26,X0)
| c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f173,axiom,
! [X0,X26] :
( c_0 = c_Finite__Set_Ocard(X26,X0)
| c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f12143,plain,
spl0_1513,
inference(avatar_split_clause,[],[f169,f12141]) ).
fof(f169,axiom,
! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f12139,plain,
spl0_1512,
inference(avatar_split_clause,[],[f159,f12137]) ).
fof(f159,axiom,
! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f12135,plain,
spl0_1511,
inference(avatar_split_clause,[],[f129,f12133]) ).
fof(f12133,plain,
( spl0_1511
<=> ! [X11,X10] :
( ~ c_less(X10,X11,tc_nat)
| c_Divides_Oop_Amod(X10,X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f129,axiom,
! [X10,X11] :
( ~ c_less(X10,X11,tc_nat)
| c_Divides_Oop_Amod(X10,X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f12131,plain,
( spl0_1510
| ~ spl0_1055
| ~ spl0_1314 ),
inference(avatar_split_clause,[],[f10602,f10368,f8701,f12128]) ).
fof(f10368,plain,
( spl0_1314
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f10602,plain,
( c_1 = c_HOL_Oabs(c_1,t_a)
| ~ spl0_1055
| ~ spl0_1314 ),
inference(resolution,[],[f8703,f10369]) ).
fof(f10369,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) )
| ~ spl0_1314 ),
inference(avatar_component_clause,[],[f10368]) ).
fof(f12126,plain,
spl0_1509,
inference(avatar_split_clause,[],[f118,f12124]) ).
fof(f12124,plain,
( spl0_1509
<=> ! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_1 = c_div(X11,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f118,axiom,
! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_1 = c_div(X11,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f12122,plain,
spl0_1508,
inference(avatar_split_clause,[],[f110,f12120]) ).
fof(f12120,plain,
( spl0_1508
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_0 = c_div(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f110,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_0 = c_div(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f12118,plain,
spl0_1507,
inference(avatar_split_clause,[],[f93,f12116]) ).
fof(f12116,plain,
( spl0_1507
<=> ! [X18,X0,X16,X17,X3] : c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OScons(X17,X18,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f93,axiom,
! [X3,X0,X18,X16,X17] : c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OScons(X17,X18,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).
fof(f12114,plain,
spl0_1506,
inference(avatar_split_clause,[],[f90,f12112]) ).
fof(f12112,plain,
( spl0_1506
<=> ! [X18,X0,X9,X17,X16] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f90,axiom,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f12110,plain,
spl0_1505,
inference(avatar_split_clause,[],[f88,f12108]) ).
fof(f12108,plain,
( spl0_1505
<=> ! [X18,X0,X16,X17,X3] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OLeaf(X3,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f88,axiom,
! [X3,X0,X18,X16,X17] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OLeaf(X3,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
fof(f12106,plain,
spl0_1504,
inference(avatar_split_clause,[],[f74,f12104]) ).
fof(f12104,plain,
( spl0_1504
<=> ! [X16,X0,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X1,X16,X0),tc_sum(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f74,axiom,
! [X0,X1,X16] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X1,X16,X0),tc_sum(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f12102,plain,
spl0_1503,
inference(avatar_split_clause,[],[f73,f12100]) ).
fof(f12100,plain,
( spl0_1503
<=> ! [X16,X0,X3] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X3,X0,X16),tc_sum(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f73,axiom,
! [X3,X0,X16] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X3,X0,X16),tc_sum(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f12098,plain,
spl0_1502,
inference(avatar_split_clause,[],[f69,f12096]) ).
fof(f12096,plain,
( spl0_1502
<=> ! [X0,X3,X15] :
( X3 = X15
| c_Datatype_Ooption_OSome(X15,X0) != c_Datatype_Ooption_OSome(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f69,axiom,
! [X3,X0,X15] :
( X3 = X15
| c_Datatype_Ooption_OSome(X15,X0) != c_Datatype_Ooption_OSome(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f12094,plain,
spl0_1501,
inference(avatar_split_clause,[],[f64,f12092]) ).
fof(f12092,plain,
( spl0_1501
<=> ! [X12,X14] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X14),X14) = c_insert(X12,c_emptyset,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f64,axiom,
! [X14,X12] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X14),X14) = c_insert(X12,c_emptyset,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f12090,plain,
spl0_1500,
inference(avatar_split_clause,[],[f63,f12088]) ).
fof(f12088,plain,
( spl0_1500
<=> ! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f63,axiom,
! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f12086,plain,
( spl0_1499
| ~ spl0_1055
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10601,f10240,f8701,f12083]) ).
fof(f12083,plain,
( spl0_1499
<=> c_0 = c_IntDef_Oof__int(c_0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f10240,plain,
( spl0_1284
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f10601,plain,
( c_0 = c_IntDef_Oof__int(c_0,t_a)
| ~ spl0_1055
| ~ spl0_1284 ),
inference(resolution,[],[f8703,f10241]) ).
fof(f10241,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) )
| ~ spl0_1284 ),
inference(avatar_component_clause,[],[f10240]) ).
fof(f12081,plain,
spl0_1498,
inference(avatar_split_clause,[],[f62,f12079]) ).
fof(f12079,plain,
( spl0_1498
<=> ! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f62,axiom,
! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f12054,plain,
( spl0_1497
| ~ spl0_1050
| ~ spl0_1285 ),
inference(avatar_split_clause,[],[f10506,f10244,f8599,f12051]) ).
fof(f10244,plain,
( spl0_1285
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f10506,plain,
( c_1 = c_IntDef_Oof__int(c_1,t_a)
| ~ spl0_1050
| ~ spl0_1285 ),
inference(resolution,[],[f10245,f8601]) ).
fof(f10245,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) )
| ~ spl0_1285 ),
inference(avatar_component_clause,[],[f10244]) ).
fof(f11791,plain,
spl0_1496,
inference(avatar_split_clause,[],[f3102,f11789]) ).
fof(f11789,plain,
( spl0_1496
<=> ! [X35] :
( ~ c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| c_less(c_1,X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f3102,plain,
! [X35] :
( ~ c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| c_less(c_1,X35,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2926,f2791]) ).
fof(f2926,plain,
! [X35] :
( c_less(c_1,X35,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X35),tc_nat) ),
inference(definition_unfolding,[],[f240,f1438]) ).
fof(f240,axiom,
! [X35] :
( c_less(c_1,X35,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f11787,plain,
spl0_1495,
inference(avatar_split_clause,[],[f3091,f11785]) ).
fof(f11785,plain,
( spl0_1495
<=> ! [X35] :
( c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| ~ c_less(c_1,X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f3091,plain,
! [X35] :
( c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| ~ c_less(c_1,X35,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2911,f2791]) ).
fof(f2911,plain,
! [X35] :
( ~ c_less(c_1,X35,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X35),tc_nat) ),
inference(definition_unfolding,[],[f241,f1438]) ).
fof(f241,axiom,
! [X35] :
( ~ c_less(c_1,X35,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f11782,plain,
spl0_1494,
inference(avatar_split_clause,[],[f3087,f11780]) ).
fof(f11780,plain,
( spl0_1494
<=> ! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f3087,plain,
! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X24 ),
inference(forward_demodulation,[],[f2904,f2791]) ).
fof(f2904,plain,
! [X11,X24] :
( c_1 = X24
| c_times(X24,X11,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f956,f1438]) ).
fof(f956,axiom,
! [X11,X24] :
( c_1 = X24
| c_Suc(c_0) != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
fof(f11778,plain,
spl0_1493,
inference(avatar_split_clause,[],[f3085,f11776]) ).
fof(f11776,plain,
( spl0_1493
<=> ! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f3085,plain,
! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X11 ),
inference(forward_demodulation,[],[f2902,f2791]) ).
fof(f2902,plain,
! [X11,X24] :
( c_1 = X11
| c_times(X24,X11,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f987,f1438]) ).
fof(f987,axiom,
! [X11,X24] :
( c_1 = X11
| c_Suc(c_0) != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f11774,plain,
spl0_1492,
inference(avatar_split_clause,[],[f2822,f11772]) ).
fof(f11772,plain,
( spl0_1492
<=> ! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f2822,plain,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f1026,f1007]) ).
fof(f1026,axiom,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f11770,plain,
spl0_1491,
inference(avatar_split_clause,[],[f2811,f11768]) ).
fof(f11768,plain,
( spl0_1491
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(X10,X0),X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2811,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(X10,X0),X10,X0,X0) = X10,
inference(definition_unfolding,[],[f1497,f1267]) ).
fof(f1497,axiom,
! [X10,X0] : c_inter(X10,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f11766,plain,
spl0_1490,
inference(avatar_split_clause,[],[f2810,f11764]) ).
fof(f11764,plain,
( spl0_1490
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X0),X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2810,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X0),X10,X0,X0) = X10,
inference(definition_unfolding,[],[f1495,f1267]) ).
fof(f1495,axiom,
! [X10,X0] : c_inter(c_UNIV,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f11762,plain,
spl0_1489,
inference(avatar_split_clause,[],[f2809,f11760]) ).
fof(f11760,plain,
( spl0_1489
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(X10,X0),c_UNIV,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2809,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(X10,X0),c_UNIV,X0,X0) = X10,
inference(definition_unfolding,[],[f1496,f1267]) ).
fof(f1496,axiom,
! [X10,X0] : c_inter(X10,c_UNIV,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f11758,plain,
spl0_1488,
inference(avatar_split_clause,[],[f2803,f11756]) ).
fof(f11756,plain,
( spl0_1488
<=> ! [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_1488])]) ).
fof(f2803,plain,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f54,f1438]) ).
fof(f54,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(f11754,plain,
spl0_1487,
inference(avatar_split_clause,[],[f1684,f11752]) ).
fof(f11752,plain,
( spl0_1487
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X19,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f1684,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X19,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f11750,plain,
spl0_1486,
inference(avatar_split_clause,[],[f1683,f11748]) ).
fof(f11748,plain,
( spl0_1486
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X19,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f1683,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X19,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f11746,plain,
spl0_1485,
inference(avatar_split_clause,[],[f1656,f11744]) ).
fof(f11744,plain,
( spl0_1485
<=> ! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f1656,axiom,
! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f11737,plain,
spl0_1484,
inference(avatar_split_clause,[],[f1655,f11735]) ).
fof(f11735,plain,
( spl0_1484
<=> ! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f1655,axiom,
! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f11733,plain,
spl0_1483,
inference(avatar_split_clause,[],[f1612,f11731]) ).
fof(f11731,plain,
( spl0_1483
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f1612,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f11729,plain,
spl0_1482,
inference(avatar_split_clause,[],[f1611,f11727]) ).
fof(f11727,plain,
( spl0_1482
<=> ! [X0,X19] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f1611,axiom,
! [X0,X19] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f11725,plain,
spl0_1481,
inference(avatar_split_clause,[],[f1596,f11723]) ).
fof(f11723,plain,
( spl0_1481
<=> ! [X0,X1,X16,X3] : c_Sum__Type_OInl(X3,X0,X16) != c_Sum__Type_OInr(X1,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f1596,axiom,
! [X3,X0,X1,X16] : c_Sum__Type_OInl(X3,X0,X16) != c_Sum__Type_OInr(X1,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).
fof(f11721,plain,
spl0_1480,
inference(avatar_split_clause,[],[f1561,f11719]) ).
fof(f11719,plain,
( spl0_1480
<=> ! [X0,X10] : c_uminus(c_uminus(X10,tc_set(X0)),tc_set(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f1561,axiom,
! [X10,X0] : c_uminus(c_uminus(X10,tc_set(X0)),tc_set(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f11717,plain,
spl0_1479,
inference(avatar_split_clause,[],[f1553,f11715]) ).
fof(f11715,plain,
( spl0_1479
<=> ! [X0,X26] :
( c_emptyset = X26
| c_in(c_Main_Oall__not__in__conv__1(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f1553,axiom,
! [X0,X26] :
( c_emptyset = X26
| c_in(c_Main_Oall__not__in__conv__1(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f11713,plain,
spl0_1478,
inference(avatar_split_clause,[],[f1530,f11711]) ).
fof(f11711,plain,
( spl0_1478
<=> ! [X0,X30,X26] :
( c_emptyset = X30
| c_emptyset != c_union(X26,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f1530,axiom,
! [X0,X26,X30] :
( c_emptyset = X30
| c_emptyset != c_union(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f11709,plain,
spl0_1477,
inference(avatar_split_clause,[],[f1529,f11707]) ).
fof(f11707,plain,
( spl0_1477
<=> ! [X0,X30,X26] :
( c_emptyset = X26
| c_emptyset != c_union(X26,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f1529,axiom,
! [X0,X26,X30] :
( c_emptyset = X26
| c_emptyset != c_union(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f11705,plain,
spl0_1476,
inference(avatar_split_clause,[],[f1520,f11703]) ).
fof(f11703,plain,
( spl0_1476
<=> ! [X0] : c_Pow(c_emptyset,X0) = c_insert(c_emptyset,c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f1520,axiom,
! [X0] : c_Pow(c_emptyset,X0) = c_insert(c_emptyset,c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f11701,plain,
spl0_1475,
inference(avatar_split_clause,[],[f1284,f11699]) ).
fof(f11699,plain,
( spl0_1475
<=> ! [X77,X14] : c_Relation_OId = c_Nat_Opower(X77,c_0,tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f1284,axiom,
! [X14,X77] : c_Relation_OId = c_Nat_Opower(X77,c_0,tc_set(tc_prod(X14,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f11689,plain,
spl0_1474,
inference(avatar_split_clause,[],[f1283,f11687]) ).
fof(f11687,plain,
( spl0_1474
<=> ! [X0,X10] : c_Nat_Opower(X10,c_1,tc_set(tc_prod(X0,X0))) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f1283,axiom,
! [X10,X0] : c_Nat_Opower(X10,c_1,tc_set(tc_prod(X0,X0))) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f11685,plain,
spl0_1473,
inference(avatar_split_clause,[],[f1276,f11683]) ).
fof(f11683,plain,
( spl0_1473
<=> ! [X0,X16,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X10,X0,X16),X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f1276,axiom,
! [X10,X0,X16] : c_Relation_Oconverse(c_Relation_Oconverse(X10,X0,X16),X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f11681,plain,
spl0_1472,
inference(avatar_split_clause,[],[f1192,f11679]) ).
fof(f11679,plain,
( spl0_1472
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f1192,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f11677,plain,
spl0_1471,
inference(avatar_split_clause,[],[f1191,f11675]) ).
fof(f11675,plain,
( spl0_1471
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f1191,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f11673,plain,
spl0_1470,
inference(avatar_split_clause,[],[f1187,f11671]) ).
fof(f11671,plain,
( spl0_1470
<=> ! [X11,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f1187,axiom,
! [X11,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f11669,plain,
spl0_1469,
inference(avatar_split_clause,[],[f1179,f11667]) ).
fof(f11667,plain,
( spl0_1469
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f1179,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f11665,plain,
spl0_1468,
inference(avatar_split_clause,[],[f1178,f11663]) ).
fof(f11663,plain,
( spl0_1468
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f1178,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f11661,plain,
spl0_1467,
inference(avatar_split_clause,[],[f1174,f11659]) ).
fof(f11659,plain,
( spl0_1467
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f1174,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f11657,plain,
spl0_1466,
inference(avatar_split_clause,[],[f1110,f11655]) ).
fof(f1110,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f11653,plain,
spl0_1465,
inference(avatar_split_clause,[],[f1048,f11651]) ).
fof(f11651,plain,
( spl0_1465
<=> ! [X33] : c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f11640,plain,
spl0_1464,
inference(avatar_split_clause,[],[f1044,f11638]) ).
fof(f11638,plain,
( spl0_1464
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1044,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f11636,plain,
spl0_1463,
inference(avatar_split_clause,[],[f1030,f11634]) ).
fof(f11634,plain,
( spl0_1463
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f1030,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f11632,plain,
spl0_1462,
inference(avatar_split_clause,[],[f1012,f11630]) ).
fof(f1012,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f11628,plain,
spl0_1461,
inference(avatar_split_clause,[],[f926,f11626]) ).
fof(f11626,plain,
( spl0_1461
<=> ! [X11,X24] :
( c_0 = X11
| c_0 != c_plus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f926,axiom,
! [X11,X24] :
( c_0 = X11
| c_0 != c_plus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f11624,plain,
spl0_1460,
inference(avatar_split_clause,[],[f925,f11622]) ).
fof(f11622,plain,
( spl0_1460
<=> ! [X11,X24] :
( c_0 = X24
| c_0 != c_plus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f925,axiom,
! [X11,X24] :
( c_0 = X24
| c_0 != c_plus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f11620,plain,
spl0_1459,
inference(avatar_split_clause,[],[f680,f11618]) ).
fof(f11618,plain,
( spl0_1459
<=> ! [X50,X23] :
( ~ c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f680,axiom,
! [X50,X23] :
( ~ c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f11616,plain,
spl0_1458,
inference(avatar_split_clause,[],[f652,f11614]) ).
fof(f11614,plain,
( spl0_1458
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate1(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f652,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate1(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f11612,plain,
spl0_1457,
inference(avatar_split_clause,[],[f651,f11610]) ).
fof(f11610,plain,
( spl0_1457
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orev(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f651,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orev(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f11608,plain,
spl0_1456,
inference(avatar_split_clause,[],[f648,f11606]) ).
fof(f11606,plain,
( spl0_1456
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Oremdups(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f648,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Oremdups(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f11604,plain,
spl0_1455,
inference(avatar_split_clause,[],[f638,f11602]) ).
fof(f11602,plain,
( spl0_1455
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_append(X39,X40,X0) != X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f638,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_append(X39,X40,X0) != X40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f11586,plain,
spl0_1454,
inference(avatar_split_clause,[],[f634,f11584]) ).
fof(f11584,plain,
( spl0_1454
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate(X11,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f634,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate(X11,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f11582,plain,
spl0_1453,
inference(avatar_split_clause,[],[f614,f11580]) ).
fof(f11580,plain,
( spl0_1453
<=> ! [X0,X12,X39] : c_List_Oremove1(X12,c_List_Olist_OCons(X12,X39,X0),X0) = X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f614,axiom,
! [X39,X0,X12] : c_List_Oremove1(X12,c_List_Olist_OCons(X12,X39,X0),X0) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f11578,plain,
spl0_1452,
inference(avatar_split_clause,[],[f586,f11576]) ).
fof(f11576,plain,
( spl0_1452
<=> ! [X0,X39,X10] : c_List_Onth(c_List_Olist_OCons(X10,X39,X0),c_0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f586,axiom,
! [X10,X39,X0] : c_List_Onth(c_List_Olist_OCons(X10,X39,X0),c_0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f11574,plain,
spl0_1451,
inference(avatar_split_clause,[],[f533,f11572]) ).
fof(f11572,plain,
( spl0_1451
<=> ! [X14] : c_List_Olistset(c_List_Olist_ONil,X14) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f11570,plain,
spl0_1450,
inference(avatar_split_clause,[],[f501,f11568]) ).
fof(f11568,plain,
( spl0_1450
<=> ! [X0,X12,X10] : c_Nat_Osize(c_List_Oreplicate(X10,X12,X0),tc_List_Olist(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f501,axiom,
! [X10,X0,X12] : c_Nat_Osize(c_List_Oreplicate(X10,X12,X0),tc_List_Olist(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f11566,plain,
spl0_1449,
inference(avatar_split_clause,[],[f491,f11564]) ).
fof(f11564,plain,
( spl0_1449
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_0 != c_Nat_Osize(X39,tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f491,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_0 != c_Nat_Osize(X39,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f11562,plain,
spl0_1448,
inference(avatar_split_clause,[],[f459,f11560]) ).
fof(f11560,plain,
( spl0_1448
<=> ! [X0,X39,X49] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Osublist(X39,X49,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f459,axiom,
! [X39,X0,X49] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Osublist(X39,X49,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f11558,plain,
spl0_1447,
inference(avatar_split_clause,[],[f458,f11556]) ).
fof(f11556,plain,
( spl0_1447
<=> ! [X0,X11,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f458,axiom,
! [X39,X0,X11] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f11554,plain,
spl0_1446,
inference(avatar_split_clause,[],[f457,f11552]) ).
fof(f11552,plain,
( spl0_1446
<=> ! [X0,X11,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f457,axiom,
! [X39,X0,X11] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f11550,plain,
spl0_1445,
inference(avatar_split_clause,[],[f454,f11548]) ).
fof(f11548,plain,
( spl0_1445
<=> ! [X0,X12,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Oremove1(X12,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f454,axiom,
! [X39,X0,X12] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Oremove1(X12,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f11543,plain,
spl0_1444,
inference(avatar_split_clause,[],[f453,f11541]) ).
fof(f11541,plain,
( spl0_1444
<=> ! [X0,X39,X23] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Odrop(X23,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f453,axiom,
! [X39,X0,X23] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Odrop(X23,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f11539,plain,
spl0_1443,
inference(avatar_split_clause,[],[f450,f11537]) ).
fof(f11537,plain,
( spl0_1443
<=> ! [X39,X0,X40] :
( c_List_Odistinct(X40,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f450,axiom,
! [X40,X39,X0] :
( c_List_Odistinct(X40,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f11535,plain,
spl0_1442,
inference(avatar_split_clause,[],[f449,f11533]) ).
fof(f11533,plain,
( spl0_1442
<=> ! [X40,X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f449,axiom,
! [X40,X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f11531,plain,
spl0_1441,
inference(avatar_split_clause,[],[f447,f11529]) ).
fof(f11529,plain,
( spl0_1441
<=> ! [X12,X39,X14] :
( c_List_Odistinct(X39,X14)
| ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f447,axiom,
! [X39,X14,X12] :
( c_List_Odistinct(X39,X14)
| ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f11527,plain,
spl0_1440,
inference(avatar_split_clause,[],[f427,f11525]) ).
fof(f11525,plain,
( spl0_1440
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_append(X39,X40,X0) != X39 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f427,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_append(X39,X40,X0) != X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f11523,plain,
spl0_1439,
inference(avatar_split_clause,[],[f422,f11521]) ).
fof(f11521,plain,
( spl0_1439
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_List_Olist_ONil != c_append(X39,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f422,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_List_Olist_ONil != c_append(X39,X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f11519,plain,
spl0_1438,
inference(avatar_split_clause,[],[f421,f11517]) ).
fof(f11517,plain,
( spl0_1438
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_append(X39,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f421,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_append(X39,X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f11515,plain,
spl0_1437,
inference(avatar_split_clause,[],[f391,f11513]) ).
fof(f11513,plain,
( spl0_1437
<=> ! [X1,X3] : c_0 = c_Divides_Oop_Amod(c_times(X1,X3,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f391,axiom,
! [X3,X1] : c_0 = c_Divides_Oop_Amod(c_times(X1,X3,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f11511,plain,
spl0_1436,
inference(avatar_split_clause,[],[f390,f11509]) ).
fof(f11509,plain,
( spl0_1436
<=> ! [X1,X3] : c_0 = c_Divides_Oop_Amod(c_times(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f390,axiom,
! [X3,X1] : c_0 = c_Divides_Oop_Amod(c_times(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f11507,plain,
spl0_1435,
inference(avatar_split_clause,[],[f377,f11505]) ).
fof(f11505,plain,
( spl0_1435
<=> ! [X12,X11] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f377,axiom,
! [X11,X12] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f11500,plain,
spl0_1434,
inference(avatar_split_clause,[],[f365,f11498]) ).
fof(f11498,plain,
( spl0_1434
<=> ! [X3] :
( c_0 = X3
| c_1 = c_div(X3,X3,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f365,axiom,
! [X3] :
( c_0 = X3
| c_1 = c_div(X3,X3,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f11496,plain,
spl0_1433,
inference(avatar_split_clause,[],[f335,f11494]) ).
fof(f11494,plain,
( spl0_1433
<=> ! [X1,X3] : c_0 = c_div(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f335,axiom,
! [X3,X1] : c_0 = c_div(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f11492,plain,
spl0_1432,
inference(avatar_split_clause,[],[f317,f11490]) ).
fof(f11490,plain,
( spl0_1432
<=> ! [X35] :
( ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f317,axiom,
! [X35] :
( ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f11488,plain,
spl0_1431,
inference(avatar_split_clause,[],[f316,f11486]) ).
fof(f11486,plain,
( spl0_1431
<=> ! [X35] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f316,axiom,
! [X35] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f11484,plain,
spl0_1430,
inference(avatar_split_clause,[],[f315,f11482]) ).
fof(f11482,plain,
( spl0_1430
<=> ! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f315,axiom,
! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f11480,plain,
spl0_1429,
inference(avatar_split_clause,[],[f314,f11478]) ).
fof(f11478,plain,
( spl0_1429
<=> ! [X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f314,axiom,
! [X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f11476,plain,
spl0_1428,
inference(avatar_split_clause,[],[f274,f11474]) ).
fof(f11474,plain,
( spl0_1428
<=> ! [X35] :
( c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f274,axiom,
! [X35] :
( c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f11472,plain,
spl0_1427,
inference(avatar_split_clause,[],[f273,f11470]) ).
fof(f11470,plain,
( spl0_1427
<=> ! [X35] :
( ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X35)) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f273,axiom,
! [X35] :
( ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X35)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f11468,plain,
spl0_1426,
inference(avatar_split_clause,[],[f243,f11466]) ).
fof(f11466,plain,
( spl0_1426
<=> ! [X35] :
( c_0 = X35
| ~ c_less(c_HOL_Oabs(X35,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f243,axiom,
! [X35] :
( c_0 = X35
| ~ c_less(c_HOL_Oabs(X35,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f11464,plain,
spl0_1425,
inference(avatar_split_clause,[],[f140,f11462]) ).
fof(f11462,plain,
( spl0_1425
<=> ! [X0,X19,X26] :
( c_emptyset = X26
| c_emptyset != c_Equiv__Relations_Oquotient(X26,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f140,axiom,
! [X0,X19,X26] :
( c_emptyset = X26
| c_emptyset != c_Equiv__Relations_Oquotient(X26,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f11456,plain,
spl0_1424,
inference(avatar_split_clause,[],[f136,f11454]) ).
fof(f11454,plain,
( spl0_1424
<=> ! [X11,X24] : c_0 = c_div(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f136,axiom,
! [X11,X24] : c_0 = c_div(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f11452,plain,
spl0_1423,
inference(avatar_split_clause,[],[f134,f11450]) ).
fof(f11450,plain,
( spl0_1423
<=> ! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f134,axiom,
! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f11448,plain,
spl0_1422,
inference(avatar_split_clause,[],[f132,f11446]) ).
fof(f11446,plain,
( spl0_1422
<=> ! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X11,X24,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f132,axiom,
! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X11,X24,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f11444,plain,
spl0_1421,
inference(avatar_split_clause,[],[f87,f11442]) ).
fof(f11442,plain,
( spl0_1421
<=> ! [X9,X16,X0,X3] : c_Datatype__Universe_OLeaf(X3,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f87,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb_0) ).
fof(f11440,plain,
spl0_1420,
inference(avatar_split_clause,[],[f86,f11438]) ).
fof(f11438,plain,
( spl0_1420
<=> ! [X18,X16,X0,X17] : c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn1(X18,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f86,axiom,
! [X0,X18,X16,X17] : c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn1(X18,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0_0) ).
fof(f11155,plain,
spl0_1419,
inference(avatar_split_clause,[],[f3074,f11153]) ).
fof(f11153,plain,
( spl0_1419
<=> ! [X0] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f3074,plain,
! [X0] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f1064,f1050]) ).
fof(f1064,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f11151,plain,
spl0_1418,
inference(avatar_split_clause,[],[f3026,f11149]) ).
fof(f11149,plain,
( spl0_1418
<=> ! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X24,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f3026,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X24,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2826,f2791]) ).
fof(f2826,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X24,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f194,f1438]) ).
fof(f194,axiom,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X24,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f11147,plain,
spl0_1417,
inference(avatar_split_clause,[],[f3025,f11145]) ).
fof(f11145,plain,
( spl0_1417
<=> ! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f3025,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2825,f2791]) ).
fof(f2825,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f193,f1438]) ).
fof(f193,axiom,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f11112,plain,
spl0_1416,
inference(avatar_split_clause,[],[f2797,f11110]) ).
fof(f11110,plain,
( spl0_1416
<=> ! [X11] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f2797,plain,
! [X11] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1688,f1438]) ).
fof(f1688,axiom,
! [X11] : c_less(c_0,c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f11108,plain,
spl0_1415,
inference(avatar_split_clause,[],[f2796,f11106]) ).
fof(f11106,plain,
( spl0_1415
<=> ! [X11] : c_less(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f2796,plain,
! [X11] : c_less(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1686,f1438]) ).
fof(f1686,axiom,
! [X11] : c_less(X11,c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f11104,plain,
spl0_1414,
inference(avatar_split_clause,[],[f2783,f11102]) ).
fof(f2783,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__zero__plus_0) ).
fof(f11100,plain,
spl0_1413,
inference(avatar_split_clause,[],[f2782,f11098]) ).
fof(f2782,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__one__times_0) ).
fof(f11096,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1873,f11094]) ).
fof(f11094,plain,
( spl0_1412
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_sum(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1873,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_sum(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f11092,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1867,f11090]) ).
fof(f11090,plain,
( spl0_1411
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_prod(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1867,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_prod(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f11088,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1817,f11086]) ).
fof(f11086,plain,
( spl0_1410
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1817,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f11084,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1715,f11082]) ).
fof(f11082,plain,
( spl0_1409
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1715,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,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(f11080,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1714,f11078]) ).
fof(f11078,plain,
( spl0_1408
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1714,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f11076,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1713,f11074]) ).
fof(f11074,plain,
( spl0_1407
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1713,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,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(f11069,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1712,f11067]) ).
fof(f11067,plain,
( spl0_1406
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1712,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f11065,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1710,f11063]) ).
fof(f11063,plain,
( spl0_1405
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1710,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,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(f11061,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1709,f11059]) ).
fof(f11059,plain,
( spl0_1404
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1709,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f11057,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1708,f11055]) ).
fof(f11055,plain,
( spl0_1403
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1708,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,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(f11053,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1707,f11051]) ).
fof(f11051,plain,
( spl0_1402
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f1707,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f11049,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1658,f11047]) ).
fof(f11047,plain,
( spl0_1401
<=> ! [X11,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1658,axiom,
! [X11,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f11045,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1593,f11043]) ).
fof(f11043,plain,
( spl0_1400
<=> ! [X0,X26] :
( c_emptyset = X26
| ~ c_lessequals(X26,c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1593,axiom,
! [X0,X26] :
( c_emptyset = X26
| ~ c_lessequals(X26,c_emptyset,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f11041,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1554,f11039]) ).
fof(f1554,axiom,
! [X10,X0] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f11037,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1428,f11034]) ).
fof(f11034,plain,
( spl0_1398
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f1428,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(f11032,plain,
spl0_1397,
inference(avatar_split_clause,[],[f1386,f11030]) ).
fof(f11030,plain,
( spl0_1397
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(X3,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f1386,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(X3,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f11023,plain,
spl0_1396,
inference(avatar_split_clause,[],[f1385,f11021]) ).
fof(f11021,plain,
( spl0_1396
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(c_0,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f1385,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(c_0,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f11019,plain,
spl0_1395,
inference(avatar_split_clause,[],[f1368,f11017]) ).
fof(f11017,plain,
( spl0_1395
<=> ! [X25,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(c_1,X25,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f1368,axiom,
! [X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(c_1,X25,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f11015,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1367,f11013]) ).
fof(f1367,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f11011,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1364,f11009]) ).
fof(f11009,plain,
( spl0_1393
<=> ! [X25,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(X25,c_1,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1364,axiom,
! [X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(X25,c_1,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f11007,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1363,f11005]) ).
fof(f1363,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f11003,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1290,f11001]) ).
fof(f1290,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_divide(X10,c_1,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Odivide__1_0) ).
fof(f10999,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1273,f10997]) ).
fof(f10997,plain,
( spl0_1390
<=> ! [X0,X10] : c_Relation_ORange(c_Relation_Odiag(X10,X0),X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1273,axiom,
! [X10,X0] : c_Relation_ORange(c_Relation_Odiag(X10,X0),X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f10995,plain,
spl0_1389,
inference(avatar_split_clause,[],[f1271,f10993]) ).
fof(f10993,plain,
( spl0_1389
<=> ! [X0,X16,X10] : c_Relation_Orel__comp(X10,c_Relation_OId,X0,X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f1271,axiom,
! [X10,X0,X16] : c_Relation_Orel__comp(X10,c_Relation_OId,X0,X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f10991,plain,
spl0_1388,
inference(avatar_split_clause,[],[f1265,f10989]) ).
fof(f10989,plain,
( spl0_1388
<=> ! [X0,X16,X10] : c_Relation_Orel__comp(c_Relation_OId,X10,X16,X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f1265,axiom,
! [X10,X0,X16] : c_Relation_Orel__comp(c_Relation_OId,X10,X16,X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f10987,plain,
spl0_1387,
inference(avatar_split_clause,[],[f1263,f10985]) ).
fof(f10985,plain,
( spl0_1387
<=> ! [X0,X10] : c_Relation_ODomain(c_Relation_Odiag(X10,X0),X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f1263,axiom,
! [X10,X0] : c_Relation_ODomain(c_Relation_Odiag(X10,X0),X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f10969,plain,
spl0_1386,
inference(avatar_split_clause,[],[f1251,f10967]) ).
fof(f10967,plain,
( spl0_1386
<=> ! [X0,X3] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(X3,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1251,axiom,
! [X3,X0] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(X3,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f10965,plain,
spl0_1385,
inference(avatar_split_clause,[],[f1248,f10963]) ).
fof(f10963,plain,
( spl0_1385
<=> ! [X0,X10] :
( ~ class_Power_Orecpower(X0)
| c_Nat_Opower(X10,c_1,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f1248,axiom,
! [X10,X0] :
( ~ class_Power_Orecpower(X0)
| c_Nat_Opower(X10,c_1,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f10961,plain,
spl0_1384,
inference(avatar_split_clause,[],[f1247,f10959]) ).
fof(f10959,plain,
( spl0_1384
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(c_1,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1247,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(c_1,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f10957,plain,
spl0_1383,
inference(avatar_split_clause,[],[f1186,f10955]) ).
fof(f10955,plain,
( spl0_1383
<=> ! [X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f1186,axiom,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f10953,plain,
spl0_1382,
inference(avatar_split_clause,[],[f1185,f10951]) ).
fof(f10951,plain,
( spl0_1382
<=> ! [X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f1185,axiom,
! [X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f10949,plain,
spl0_1381,
inference(avatar_split_clause,[],[f1161,f10947]) ).
fof(f1161,axiom,
! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f10945,plain,
spl0_1380,
inference(avatar_split_clause,[],[f1156,f10943]) ).
fof(f1156,axiom,
! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f10941,plain,
spl0_1379,
inference(avatar_split_clause,[],[f1145,f10939]) ).
fof(f1145,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f10937,plain,
spl0_1378,
inference(avatar_split_clause,[],[f1144,f10935]) ).
fof(f10935,plain,
( spl0_1378
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f1144,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f10933,plain,
spl0_1377,
inference(avatar_split_clause,[],[f1135,f10931]) ).
fof(f10931,plain,
( spl0_1377
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f1135,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f10910,plain,
spl0_1376,
inference(avatar_split_clause,[],[f1112,f10908]) ).
fof(f1112,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f10906,plain,
spl0_1375,
inference(avatar_split_clause,[],[f1111,f10904]) ).
fof(f1111,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f10902,plain,
spl0_1374,
inference(avatar_split_clause,[],[f1099,f10900]) ).
fof(f1099,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f10898,plain,
spl0_1373,
inference(avatar_split_clause,[],[f1092,f10896]) ).
fof(f1092,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f10894,plain,
spl0_1372,
inference(avatar_split_clause,[],[f1090,f10892]) ).
fof(f1090,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f10890,plain,
spl0_1371,
inference(avatar_split_clause,[],[f1079,f10888]) ).
fof(f1079,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f10886,plain,
spl0_1370,
inference(avatar_split_clause,[],[f1076,f10884]) ).
fof(f1076,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f10882,plain,
spl0_1369,
inference(avatar_split_clause,[],[f1074,f10880]) ).
fof(f1074,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f10878,plain,
spl0_1368,
inference(avatar_split_clause,[],[f1071,f10876]) ).
fof(f1071,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f10874,plain,
spl0_1367,
inference(avatar_split_clause,[],[f1047,f10872]) ).
fof(f10872,plain,
( spl0_1367
<=> ! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f1047,axiom,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f10846,plain,
spl0_1366,
inference(avatar_split_clause,[],[f759,f10844]) ).
fof(f10844,plain,
( spl0_1366
<=> ! [X33] : c_IntDef_Onat(c_Numeral_Onumber__of(X33,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X33,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f759,axiom,
! [X33] : c_IntDef_Onat(c_Numeral_Onumber__of(X33,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X33,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f10842,plain,
spl0_1365,
inference(avatar_split_clause,[],[f712,f10840]) ).
fof(f10840,plain,
( spl0_1365
<=> ! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f712,axiom,
! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f10838,plain,
spl0_1364,
inference(avatar_split_clause,[],[f709,f10836]) ).
fof(f10836,plain,
( spl0_1364
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_NatArith_Oof__nat(c_0,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f709,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_NatArith_Oof__nat(c_0,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f10834,plain,
spl0_1363,
inference(avatar_split_clause,[],[f699,f10832]) ).
fof(f10832,plain,
( spl0_1363
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f699,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f10830,plain,
spl0_1362,
inference(avatar_split_clause,[],[f673,f10828]) ).
fof(f10828,plain,
( spl0_1362
<=> ! [X12,X14,X10] : c_List_Otl(c_List_Olist_OCons(X12,X10,X14),X14) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f673,axiom,
! [X10,X14,X12] : c_List_Otl(c_List_Olist_OCons(X12,X10,X14),X14) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f10826,plain,
spl0_1361,
inference(avatar_split_clause,[],[f646,f10824]) ).
fof(f10824,plain,
( spl0_1361
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_emptyset != c_List_Oset(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f646,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_emptyset != c_List_Oset(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
fof(f10822,plain,
spl0_1360,
inference(avatar_split_clause,[],[f629,f10820]) ).
fof(f10820,plain,
( spl0_1360
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate1(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f629,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate1(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f10818,plain,
spl0_1359,
inference(avatar_split_clause,[],[f611,f10816]) ).
fof(f10816,plain,
( spl0_1359
<=> ! [X0,X12] :
( c_List_Olist_ONil = X12
| c_List_Olist_ONil != c_List_Oremdups(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f611,axiom,
! [X0,X12] :
( c_List_Olist_ONil = X12
| c_List_Olist_ONil != c_List_Oremdups(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f10814,plain,
spl0_1358,
inference(avatar_split_clause,[],[f482,f10812]) ).
fof(f10812,plain,
( spl0_1358
<=> ! [X0,X12] : c_List_Olast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f482,axiom,
! [X0,X12] : c_List_Olast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f10810,plain,
spl0_1357,
inference(avatar_split_clause,[],[f473,f10808]) ).
fof(f10808,plain,
( spl0_1357
<=> ! [X0,X39,X10] : c_List_Ohd(c_List_Olist_OCons(X10,X39,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f473,axiom,
! [X10,X39,X0] : c_List_Ohd(c_List_Olist_OCons(X10,X39,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f10769,plain,
spl0_1356,
inference(avatar_split_clause,[],[f456,f10767]) ).
fof(f10767,plain,
( spl0_1356
<=> ! [X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orev(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f456,axiom,
! [X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orev(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f10765,plain,
spl0_1355,
inference(avatar_split_clause,[],[f455,f10763]) ).
fof(f10763,plain,
( spl0_1355
<=> ! [X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orev(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f455,axiom,
! [X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orev(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f10761,plain,
spl0_1354,
inference(avatar_split_clause,[],[f444,f10759]) ).
fof(f10759,plain,
( spl0_1354
<=> ! [X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f444,axiom,
! [X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f10757,plain,
spl0_1353,
inference(avatar_split_clause,[],[f443,f10755]) ).
fof(f10755,plain,
( spl0_1353
<=> ! [X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f443,axiom,
! [X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f10753,plain,
spl0_1352,
inference(avatar_split_clause,[],[f431,f10751]) ).
fof(f10751,plain,
( spl0_1352
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f431,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f10749,plain,
spl0_1351,
inference(avatar_split_clause,[],[f407,f10747]) ).
fof(f10747,plain,
( spl0_1351
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orev(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f407,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orev(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f10745,plain,
spl0_1350,
inference(avatar_split_clause,[],[f393,f10743]) ).
fof(f393,axiom,
! [X10,X0] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f10741,plain,
spl0_1349,
inference(avatar_split_clause,[],[f392,f10739]) ).
fof(f392,axiom,
! [X10,X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f10737,plain,
spl0_1348,
inference(avatar_split_clause,[],[f384,f10735]) ).
fof(f10735,plain,
( spl0_1348
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f384,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,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(f10733,plain,
spl0_1347,
inference(avatar_split_clause,[],[f313,f10731]) ).
fof(f10731,plain,
( spl0_1347
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_NatArith_Oof__nat(X11,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f313,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_NatArith_Oof__nat(X11,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f10713,plain,
spl0_1346,
inference(avatar_split_clause,[],[f286,f10711]) ).
fof(f10711,plain,
( spl0_1346
<=> ! [X11,X24] : ~ c_less(c_IntDef_Oint(X11),c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f286,axiom,
! [X11,X24] : ~ c_less(c_IntDef_Oint(X11),c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f10709,plain,
spl0_1345,
inference(avatar_split_clause,[],[f279,f10707]) ).
fof(f279,axiom,
! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f10705,plain,
spl0_1344,
inference(avatar_split_clause,[],[f270,f10703]) ).
fof(f10703,plain,
( spl0_1344
<=> ! [X11] :
( c_0 = X11
| ~ c_lessequals(c_IntDef_Oint(X11),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f270,axiom,
! [X11] :
( c_0 = X11
| ~ c_lessequals(c_IntDef_Oint(X11),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f10701,plain,
spl0_1343,
inference(avatar_split_clause,[],[f269,f10699]) ).
fof(f10699,plain,
( spl0_1343
<=> ! [X11,X24] :
( X11 = X24
| c_IntDef_Oint(X24) != c_IntDef_Oint(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f269,axiom,
! [X11,X24] :
( X11 = X24
| c_IntDef_Oint(X24) != c_IntDef_Oint(X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f10697,plain,
spl0_1342,
inference(avatar_split_clause,[],[f202,f10695]) ).
fof(f10695,plain,
( spl0_1342
<=> ! [X10] : c_GCD_Ogcd(c_Pair(X10,X10,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f202,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(X10,X10,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f10693,plain,
spl0_1341,
inference(avatar_split_clause,[],[f192,f10691]) ).
fof(f10691,plain,
( spl0_1341
<=> ! [X10] : c_GCD_Ogcd(c_Pair(c_0,X10,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f192,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(c_0,X10,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f10689,plain,
spl0_1340,
inference(avatar_split_clause,[],[f191,f10687]) ).
fof(f10687,plain,
( spl0_1340
<=> ! [X10] : c_GCD_Ogcd(c_Pair(X10,c_0,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f191,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(X10,c_0,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f10685,plain,
spl0_1339,
inference(avatar_split_clause,[],[f71,f10683]) ).
fof(f10683,plain,
( spl0_1339
<=> ! [X0,X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X3,X0),tc_Datatype_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f71,axiom,
! [X3,X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X3,X0),tc_Datatype_Ooption(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f10681,plain,
spl0_1338,
inference(avatar_split_clause,[],[f65,f10679]) ).
fof(f10679,plain,
( spl0_1338
<=> ! [X13,X0] :
( c_Datatype_Ooption_ONone = X13
| c_Datatype_Oo2s(X13,X0) != c_emptyset ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f65,axiom,
! [X0,X13] :
( c_Datatype_Ooption_ONone = X13
| c_Datatype_Oo2s(X13,X0) != c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f10676,plain,
spl0_1337,
inference(avatar_split_clause,[],[f61,f10674]) ).
fof(f10674,plain,
( spl0_1337
<=> ! [X0,X12] : c_in(X12,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f61,axiom,
! [X0,X12] : c_in(X12,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f10490,plain,
spl0_1336,
inference(avatar_split_clause,[],[f3099,f10488]) ).
fof(f10488,plain,
( spl0_1336
<=> ! [X24] :
( ~ c_Divides_Oop_Advd(X24,c_1,tc_nat)
| c_1 = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f3099,plain,
! [X24] :
( ~ c_Divides_Oop_Advd(X24,c_1,tc_nat)
| c_1 = X24 ),
inference(forward_demodulation,[],[f3098,f2791]) ).
fof(f3098,plain,
! [X24] :
( c_1 = X24
| ~ c_Divides_Oop_Advd(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2922,f2791]) ).
fof(f2922,plain,
! [X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X24
| ~ c_Divides_Oop_Advd(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f121,f1438,f1438]) ).
fof(f121,axiom,
! [X24] :
( c_Suc(c_0) = X24
| ~ c_Divides_Oop_Advd(X24,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f10486,plain,
spl0_1335,
inference(avatar_split_clause,[],[f3013,f10484]) ).
fof(f10484,plain,
( spl0_1335
<=> ! [X0,X30] : c_emptyset = c_Relation_OImage(c_emptyset,X30,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f3013,plain,
! [X0,X30] : c_emptyset = c_Relation_OImage(c_emptyset,X30,X0,X0),
inference(forward_demodulation,[],[f2802,f1280]) ).
fof(f1280,axiom,
! [X0] : c_emptyset = c_Relation_Odiag(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2802,plain,
! [X0,X30] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X0),X30,X0,X0),
inference(definition_unfolding,[],[f1498,f1267]) ).
fof(f1498,axiom,
! [X0,X30] : c_emptyset = c_inter(c_emptyset,X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f10482,plain,
spl0_1334,
inference(avatar_split_clause,[],[f2806,f10480]) ).
fof(f10478,plain,
spl0_1333,
inference(avatar_split_clause,[],[f2804,f10475]) ).
fof(f10475,plain,
( spl0_1333
<=> 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_1333])]) ).
fof(f2804,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f1027,f1007]) ).
fof(f1027,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(f10473,plain,
spl0_1332,
inference(avatar_split_clause,[],[f2791,f10470]) ).
fof(f10470,plain,
( spl0_1332
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f10468,plain,
spl0_1331,
inference(avatar_split_clause,[],[f2787,f10466]) ).
fof(f10466,plain,
( spl0_1331
<=> ! [X24] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f2787,plain,
! [X24] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),
inference(definition_unfolding,[],[f919,f1438]) ).
fof(f919,axiom,
! [X24] : c_0 != c_Suc(X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
fof(f10435,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1716,f10433]) ).
fof(f10433,plain,
( spl0_1330
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1716,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(f10431,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1711,f10429]) ).
fof(f10429,plain,
( spl0_1329
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f1711,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(f10427,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1682,f10425]) ).
fof(f10425,plain,
( spl0_1328
<=> ! [X0,X26] : c_in(c_List_Olist_ONil,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f1682,axiom,
! [X0,X26] : c_in(c_List_Olist_ONil,c_List_Olists(X26,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f10423,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1666,f10421]) ).
fof(f10421,plain,
( spl0_1327
<=> ! [X0,X39] : c_in(c_List_Oset(X39,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f1666,axiom,
! [X39,X0] : c_in(c_List_Oset(X39,X0),c_Finite__Set_OFinites,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f10419,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1663,f10417]) ).
fof(f10417,plain,
( spl0_1326
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1663,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f10415,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1662,f10413]) ).
fof(f10413,plain,
( spl0_1325
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1662,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f10411,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1647,f10409]) ).
fof(f10409,plain,
( spl0_1324
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f1647,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f10407,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1646,f10405]) ).
fof(f10405,plain,
( spl0_1323
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1646,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f10403,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1599,f10401]) ).
fof(f10401,plain,
( spl0_1322
<=> ! [X16,X0] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f1599,axiom,
! [X0,X16] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f10399,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1578,f10397]) ).
fof(f1578,axiom,
! [X0,X26,X12] : c_in(X12,c_insert(X12,X26,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f10394,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1562,f10392]) ).
fof(f10392,plain,
( spl0_1320
<=> ! [X0,X26] : c_emptyset = c_minus(c_emptyset,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1562,axiom,
! [X0,X26] : c_emptyset = c_minus(c_emptyset,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f10390,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1542,f10388]) ).
fof(f10388,plain,
( spl0_1319
<=> ! [X0,X10] : c_Union(c_Pow(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1542,axiom,
! [X10,X0] : c_Union(c_Pow(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f10386,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1484,f10384]) ).
fof(f10384,plain,
( spl0_1318
<=> ! [X0,X10] : c_minus(X10,c_emptyset,tc_set(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1484,axiom,
! [X10,X0] : c_minus(X10,c_emptyset,tc_set(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f10382,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1482,f10380]) ).
fof(f10380,plain,
( spl0_1317
<=> ! [X0,X26] : c_emptyset = c_minus(X26,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1482,axiom,
! [X0,X26] : c_emptyset = c_minus(X26,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f10378,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1481,f10376]) ).
fof(f10376,plain,
( spl0_1316
<=> ! [X0,X26] : c_emptyset = c_minus(X26,c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f1481,axiom,
! [X0,X26] : c_emptyset = c_minus(X26,c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f10374,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1443,f10372]) ).
fof(f10372,plain,
( spl0_1315
<=> ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X10,tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f1443,axiom,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X10,tc_nat),tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f10370,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1288,f10368]) ).
fof(f1288,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f10366,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1268,f10364]) ).
fof(f10364,plain,
( spl0_1313
<=> ! [X77,X0,X16] : c_emptyset = c_Relation_OImage(X77,c_emptyset,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1268,axiom,
! [X0,X16,X77] : c_emptyset = c_Relation_OImage(X77,c_emptyset,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f10362,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1266,f10360]) ).
fof(f10360,plain,
( spl0_1312
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_OId,X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1266,axiom,
! [X10,X0] : c_Relation_OImage(c_Relation_OId,X10,X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f10358,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1137,f10356]) ).
fof(f1137,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f10352,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1132,f10350]) ).
fof(f1132,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f10348,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1120,f10346]) ).
fof(f1120,axiom,
! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f10344,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1070,f10342]) ).
fof(f1070,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f10340,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1063,f10338]) ).
fof(f10338,plain,
( spl0_1307
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1063,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f10336,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1056,f10334]) ).
fof(f10334,plain,
( spl0_1306
<=> ! [X0,X28,X10] : c_Numeral_Obit_Obit__rec(X28,X10,c_Numeral_Obit_OB1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1056,axiom,
! [X28,X10,X0] : c_Numeral_Obit_Obit__rec(X28,X10,c_Numeral_Obit_OB1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f10332,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1055,f10330]) ).
fof(f10330,plain,
( spl0_1305
<=> ! [X0,X27,X10] : c_Numeral_Obit_Obit__rec(X10,X27,c_Numeral_Obit_OB0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1055,axiom,
! [X10,X0,X27] : c_Numeral_Obit_Obit__rec(X10,X27,c_Numeral_Obit_OB0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f10328,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1052,f10326]) ).
fof(f10326,plain,
( spl0_1304
<=> ! [X0,X28,X10] : c_Numeral_Obit_Obit__case(X28,X10,c_Numeral_Obit_OB1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1052,axiom,
! [X28,X10,X0] : c_Numeral_Obit_Obit__case(X28,X10,c_Numeral_Obit_OB1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f10324,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1051,f10322]) ).
fof(f10322,plain,
( spl0_1303
<=> ! [X0,X27,X10] : c_Numeral_Obit_Obit__case(X10,X27,c_Numeral_Obit_OB0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1051,axiom,
! [X10,X0,X27] : c_Numeral_Obit_Obit__case(X10,X27,c_Numeral_Obit_OB0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f10320,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1038,f10318]) ).
fof(f10318,plain,
( spl0_1302
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1038,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f10316,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1037,f10314]) ).
fof(f10314,plain,
( spl0_1301
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1037,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f10310,plain,
spl0_1300,
inference(avatar_split_clause,[],[f983,f10308]) ).
fof(f10308,plain,
( spl0_1300
<=> ! [X11] :
( c_0 = X11
| c_less(c_0,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f983,axiom,
! [X11] :
( c_0 = X11
| c_less(c_0,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f10306,plain,
spl0_1299,
inference(avatar_split_clause,[],[f982,f10304]) ).
fof(f10304,plain,
( spl0_1299
<=> ! [X50,X23] : ~ c_less(c_plus(X50,X23,tc_nat),X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f982,axiom,
! [X50,X23] : ~ c_less(c_plus(X50,X23,tc_nat),X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f10302,plain,
spl0_1298,
inference(avatar_split_clause,[],[f981,f10300]) ).
fof(f10300,plain,
( spl0_1298
<=> ! [X50,X23] : ~ c_less(c_plus(X23,X50,tc_nat),X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f981,axiom,
! [X50,X23] : ~ c_less(c_plus(X23,X50,tc_nat),X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f10298,plain,
spl0_1297,
inference(avatar_split_clause,[],[f942,f10296]) ).
fof(f10296,plain,
( spl0_1297
<=> ! [X11] :
( c_0 = X11
| ~ c_less(X11,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f942,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(X11,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f10294,plain,
spl0_1296,
inference(avatar_split_clause,[],[f936,f10292]) ).
fof(f10292,plain,
( spl0_1296
<=> ! [X23] :
( c_0 = X23
| ~ c_lessequals(X23,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f936,axiom,
! [X23] :
( c_0 = X23
| ~ c_lessequals(X23,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f10290,plain,
spl0_1295,
inference(avatar_split_clause,[],[f934,f10288]) ).
fof(f10288,plain,
( spl0_1295
<=> ! [X11,X24] : c_lessequals(c_minus(X24,X11,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f934,axiom,
! [X11,X24] : c_lessequals(c_minus(X24,X11,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f10286,plain,
spl0_1294,
inference(avatar_split_clause,[],[f706,f10284]) ).
fof(f706,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f10282,plain,
spl0_1293,
inference(avatar_split_clause,[],[f702,f10280]) ).
fof(f702,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f10278,plain,
spl0_1292,
inference(avatar_split_clause,[],[f684,f10276]) ).
fof(f10276,plain,
( spl0_1292
<=> ! [X16,X0,X40] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X40,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f684,axiom,
! [X40,X0,X16] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X40,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f10274,plain,
spl0_1291,
inference(avatar_split_clause,[],[f682,f10272]) ).
fof(f10272,plain,
( spl0_1291
<=> ! [X39,X14,X74] : c_List_Olist_ONil = c_List_Ozip(X39,c_List_Olist_ONil,X14,X74) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f682,axiom,
! [X39,X14,X74] : c_List_Olist_ONil = c_List_Ozip(X39,c_List_Olist_ONil,X14,X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f10266,plain,
spl0_1290,
inference(avatar_split_clause,[],[f626,f10264]) ).
fof(f10264,plain,
( spl0_1290
<=> ! [X0,X10] : c_List_Orev(c_List_Orev(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f626,axiom,
! [X10,X0] : c_List_Orev(c_List_Orev(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f10262,plain,
spl0_1289,
inference(avatar_split_clause,[],[f605,f10260]) ).
fof(f10260,plain,
( spl0_1289
<=> ! [X0,X12,X40] : c_List_Oop_Amem(X12,c_List_Olist_OCons(X12,X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f605,axiom,
! [X40,X0,X12] : c_List_Oop_Amem(X12,c_List_Olist_OCons(X12,X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f10258,plain,
spl0_1288,
inference(avatar_split_clause,[],[f525,f10256]) ).
fof(f10256,plain,
( spl0_1288
<=> ! [X34,X23,X14] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X23,X34,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f525,axiom,
! [X14,X34,X23] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X23,X34,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f10254,plain,
spl0_1287,
inference(avatar_split_clause,[],[f436,f10252]) ).
fof(f10252,plain,
( spl0_1287
<=> ! [X45,X46] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X45,X46),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f436,axiom,
! [X46,X45] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X45,X46),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f10250,plain,
spl0_1286,
inference(avatar_split_clause,[],[f372,f10248]) ).
fof(f10248,plain,
( spl0_1286
<=> ! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f372,axiom,
! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f10246,plain,
spl0_1285,
inference(avatar_split_clause,[],[f295,f10244]) ).
fof(f295,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f10242,plain,
spl0_1284,
inference(avatar_split_clause,[],[f290,f10240]) ).
fof(f290,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f10238,plain,
spl0_1283,
inference(avatar_split_clause,[],[f281,f10236]) ).
fof(f10236,plain,
( spl0_1283
<=> ! [X11] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f281,axiom,
! [X11] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f10234,plain,
spl0_1282,
inference(avatar_split_clause,[],[f267,f10232]) ).
fof(f10232,plain,
( spl0_1282
<=> ! [X11] :
( c_0 = X11
| c_0 != c_IntDef_Oint(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f267,axiom,
! [X11] :
( c_0 = X11
| c_0 != c_IntDef_Oint(X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f10230,plain,
spl0_1281,
inference(avatar_split_clause,[],[f261,f10228]) ).
fof(f261,axiom,
! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f10222,plain,
spl0_1280,
inference(avatar_split_clause,[],[f147,f10220]) ).
fof(f10220,plain,
( spl0_1280
<=> ! [X0,X28,X10] : c_Extraction_Osumbool_Osumbool__rec(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f147,axiom,
! [X28,X10,X0] : c_Extraction_Osumbool_Osumbool__rec(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f10218,plain,
spl0_1279,
inference(avatar_split_clause,[],[f146,f10216]) ).
fof(f10216,plain,
( spl0_1279
<=> ! [X0,X27,X10] : c_Extraction_Osumbool_Osumbool__rec(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f146,axiom,
! [X10,X0,X27] : c_Extraction_Osumbool_Osumbool__rec(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f10214,plain,
spl0_1278,
inference(avatar_split_clause,[],[f143,f10212]) ).
fof(f10212,plain,
( spl0_1278
<=> ! [X0,X28,X10] : c_Extraction_Osumbool_Osumbool__case(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f143,axiom,
! [X28,X10,X0] : c_Extraction_Osumbool_Osumbool__case(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f10210,plain,
spl0_1277,
inference(avatar_split_clause,[],[f142,f10208]) ).
fof(f10208,plain,
( spl0_1277
<=> ! [X0,X27,X10] : c_Extraction_Osumbool_Osumbool__case(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f142,axiom,
! [X10,X0,X27] : c_Extraction_Osumbool_Osumbool__case(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f10206,plain,
spl0_1276,
inference(avatar_split_clause,[],[f119,f10204]) ).
fof(f10204,plain,
( spl0_1276
<=> ! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f119,axiom,
! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f10202,plain,
spl0_1275,
inference(avatar_split_clause,[],[f109,f10200]) ).
fof(f10200,plain,
( spl0_1275
<=> ! [X11,X24] : c_lessequals(c_div(X24,X11,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f109,axiom,
! [X11,X24] : c_lessequals(c_div(X24,X11,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f10198,plain,
spl0_1274,
inference(avatar_split_clause,[],[f96,f10196]) ).
fof(f10196,plain,
( spl0_1274
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X17,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f96,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X17,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f10194,plain,
spl0_1273,
inference(avatar_split_clause,[],[f75,f10192]) ).
fof(f10192,plain,
( spl0_1273
<=> ! [X0,X10] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f75,axiom,
! [X10,X0] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f9855,plain,
spl0_1272,
inference(avatar_split_clause,[],[f3023,f9853]) ).
fof(f9853,plain,
( spl0_1272
<=> ! [X10] : c_div(X10,c_1,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f3023,plain,
! [X10] : c_div(X10,c_1,tc_nat) = X10,
inference(forward_demodulation,[],[f2817,f2791]) ).
fof(f2817,plain,
! [X10] : c_div(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X10,
inference(definition_unfolding,[],[f108,f1438]) ).
fof(f108,axiom,
! [X10] : c_div(X10,c_Suc(c_0),tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f9851,plain,
spl0_1271,
inference(avatar_split_clause,[],[f3021,f9848]) ).
fof(f9848,plain,
( spl0_1271
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f3021,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2814,f2791]) ).
fof(f2814,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,[],[f988,f1438]) ).
fof(f988,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(f9846,plain,
spl0_1270,
inference(avatar_split_clause,[],[f3019,f9844]) ).
fof(f9844,plain,
( spl0_1270
<=> ! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f3019,plain,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_1,tc_nat),
inference(forward_demodulation,[],[f2813,f2791]) ).
fof(f2813,plain,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f125,f1438]) ).
fof(f125,axiom,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f9842,plain,
spl0_1269,
inference(avatar_split_clause,[],[f3018,f9839]) ).
fof(f9839,plain,
( spl0_1269
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f3018,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f761,f1050]) ).
fof(f761,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(f9837,plain,
spl0_1268,
inference(avatar_split_clause,[],[f3016,f9835]) ).
fof(f9835,plain,
( spl0_1268
<=> ! [X14,X10] : c_append(c_List_Olist_ONil,X10,X14) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f3016,plain,
! [X10,X14] : c_append(c_List_Olist_ONil,X10,X14) = X10,
inference(forward_demodulation,[],[f2808,f623]) ).
fof(f623,axiom,
! [X0] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2808,plain,
! [X10,X14] : c_append(c_List_Orev(c_List_Olist_ONil,X14),X10,X14) = X10,
inference(definition_unfolding,[],[f480,f479]) ).
fof(f480,axiom,
! [X10,X14] : c_List_Oitrev(c_List_Olist_ONil,X10,X14) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f9833,plain,
spl0_1267,
inference(avatar_split_clause,[],[f3014,f9830]) ).
fof(f9830,plain,
( spl0_1267
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f3014,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2805,f1050]) ).
fof(f2805,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f1019,f1023]) ).
fof(f1019,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(f9828,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1689,f9826]) ).
fof(f9826,plain,
( spl0_1266
<=> ! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1689,axiom,
! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f9824,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1581,f9822]) ).
fof(f1581,axiom,
! [X3,X0,X26] : c_emptyset != c_insert(X3,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f9820,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1533,f9818]) ).
fof(f9818,plain,
( spl0_1264
<=> ! [X0,X10] : c_union(X10,c_emptyset,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f1533,axiom,
! [X10,X0] : c_union(X10,c_emptyset,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f9814,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1532,f9812]) ).
fof(f1532,axiom,
! [X10,X0] : c_union(c_emptyset,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f9810,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1528,f9808]) ).
fof(f9808,plain,
( spl0_1262
<=> ! [X0,X10] : c_union(X10,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1528,axiom,
! [X10,X0] : c_union(X10,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f9806,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1527,f9804]) ).
fof(f9804,plain,
( spl0_1261
<=> ! [X0,X26] : c_UNIV = c_union(X26,c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1527,axiom,
! [X0,X26] : c_UNIV = c_union(X26,c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f9802,plain,
spl0_1260,
inference(avatar_split_clause,[],[f1526,f9800]) ).
fof(f9800,plain,
( spl0_1260
<=> ! [X0,X30] : c_UNIV = c_union(c_UNIV,X30,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f1526,axiom,
! [X0,X30] : c_UNIV = c_union(c_UNIV,X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f9798,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1474,f9796]) ).
fof(f9796,plain,
( spl0_1259
<=> ! [X0] : c_UNIV = c_uminus(c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f1474,axiom,
! [X0] : c_UNIV = c_uminus(c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f9794,plain,
spl0_1258,
inference(avatar_split_clause,[],[f1470,f9792]) ).
fof(f9792,plain,
( spl0_1258
<=> ! [X0] : c_emptyset = c_uminus(c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f1470,axiom,
! [X0] : c_emptyset = c_uminus(c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f9790,plain,
spl0_1257,
inference(avatar_split_clause,[],[f1405,f9788]) ).
fof(f9788,plain,
( spl0_1257
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f1405,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f9786,plain,
spl0_1256,
inference(avatar_split_clause,[],[f1393,f9784]) ).
fof(f9784,plain,
( spl0_1256
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f1393,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f9782,plain,
spl0_1255,
inference(avatar_split_clause,[],[f1388,f9780]) ).
fof(f9780,plain,
( spl0_1255
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f1388,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f9778,plain,
spl0_1254,
inference(avatar_split_clause,[],[f1387,f9776]) ).
fof(f9776,plain,
( spl0_1254
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f1387,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f9774,plain,
( spl0_1253
| ~ spl0_1
| ~ spl0_682 ),
inference(avatar_split_clause,[],[f8176,f6052,f3203,f9771]) ).
fof(f3203,plain,
( spl0_1
<=> class_Ring__and__Field_Oordered__field(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f6052,plain,
( spl0_682
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f8176,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(t_a)
| ~ spl0_1
| ~ spl0_682 ),
inference(resolution,[],[f6053,f3205]) ).
fof(f3205,plain,
( class_Ring__and__Field_Oordered__field(t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f3203]) ).
fof(f6053,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) )
| ~ spl0_682 ),
inference(avatar_component_clause,[],[f6052]) ).
fof(f9769,plain,
spl0_1252,
inference(avatar_split_clause,[],[f1275,f9767]) ).
fof(f9767,plain,
( spl0_1252
<=> ! [X0] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f1275,axiom,
! [X0] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f9765,plain,
spl0_1251,
inference(avatar_split_clause,[],[f1274,f9763]) ).
fof(f9763,plain,
( spl0_1251
<=> ! [X0,X16] : c_emptyset = c_Relation_ORange(c_emptyset,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f1274,axiom,
! [X0,X16] : c_emptyset = c_Relation_ORange(c_emptyset,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f9761,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1272,f9759]) ).
fof(f9759,plain,
( spl0_1250
<=> ! [X0] : c_UNIV = c_Relation_ORange(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f1272,axiom,
! [X0] : c_UNIV = c_Relation_ORange(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f9757,plain,
spl0_1249,
inference(avatar_split_clause,[],[f1264,f9755]) ).
fof(f9755,plain,
( spl0_1249
<=> ! [X16,X0] : c_emptyset = c_Relation_ODomain(c_emptyset,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f1264,axiom,
! [X0,X16] : c_emptyset = c_Relation_ODomain(c_emptyset,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f9753,plain,
spl0_1248,
inference(avatar_split_clause,[],[f1262,f9751]) ).
fof(f9751,plain,
( spl0_1248
<=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f1262,axiom,
! [X0] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f9749,plain,
spl0_1247,
inference(avatar_split_clause,[],[f1238,f9747]) ).
fof(f9747,plain,
( spl0_1247
<=> ! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f1238,axiom,
! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f9745,plain,
spl0_1246,
inference(avatar_split_clause,[],[f1163,f9743]) ).
fof(f9743,plain,
( spl0_1246
<=> ! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f1163,axiom,
! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f9741,plain,
spl0_1245,
inference(avatar_split_clause,[],[f1050,f9738]) ).
fof(f9736,plain,
spl0_1244,
inference(avatar_split_clause,[],[f996,f9734]) ).
fof(f9734,plain,
( spl0_1244
<=> ! [X10] : c_minus(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f996,axiom,
! [X10] : c_minus(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f9732,plain,
spl0_1243,
inference(avatar_split_clause,[],[f994,f9730]) ).
fof(f994,axiom,
! [X10] : c_plus(c_0,X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f9728,plain,
( spl0_1242
| ~ spl0_1
| ~ spl0_681 ),
inference(avatar_split_clause,[],[f8175,f6048,f3203,f9725]) ).
fof(f9725,plain,
( spl0_1242
<=> class_HOL_Ominus(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f6048,plain,
( spl0_681
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f8175,plain,
( class_HOL_Ominus(t_a)
| ~ spl0_1
| ~ spl0_681 ),
inference(resolution,[],[f6049,f3205]) ).
fof(f6049,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ominus(X87) )
| ~ spl0_681 ),
inference(avatar_component_clause,[],[f6048]) ).
fof(f9723,plain,
spl0_1241,
inference(avatar_split_clause,[],[f992,f9721]) ).
fof(f9721,plain,
( spl0_1241
<=> ! [X11] : c_0 = c_times(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f992,axiom,
! [X11] : c_0 = c_times(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f9719,plain,
spl0_1240,
inference(avatar_split_clause,[],[f950,f9717]) ).
fof(f9717,plain,
( spl0_1240
<=> ! [X24] : c_0 = c_times(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f950,axiom,
! [X24] : c_0 = c_times(X24,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f9715,plain,
spl0_1239,
inference(avatar_split_clause,[],[f948,f9713]) ).
fof(f9713,plain,
( spl0_1239
<=> ! [X11] : c_0 = c_Orderings_Omin(X11,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f948,axiom,
! [X11] : c_0 = c_Orderings_Omin(X11,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f9711,plain,
spl0_1238,
inference(avatar_split_clause,[],[f947,f9709]) ).
fof(f9709,plain,
( spl0_1238
<=> ! [X11] : c_0 = c_Orderings_Omin(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f947,axiom,
! [X11] : c_0 = c_Orderings_Omin(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f9707,plain,
spl0_1237,
inference(avatar_split_clause,[],[f945,f9705]) ).
fof(f9705,plain,
( spl0_1237
<=> ! [X10] : c_Orderings_Omax(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f945,axiom,
! [X10] : c_Orderings_Omax(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f9703,plain,
spl0_1236,
inference(avatar_split_clause,[],[f944,f9701]) ).
fof(f9701,plain,
( spl0_1236
<=> ! [X10] : c_Orderings_Omax(c_0,X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f944,axiom,
! [X10] : c_Orderings_Omax(c_0,X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f9699,plain,
spl0_1235,
inference(avatar_split_clause,[],[f935,f9697]) ).
fof(f9697,plain,
( spl0_1235
<=> ! [X24] : c_0 = c_minus(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f935,axiom,
! [X24] : c_0 = c_minus(X24,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f9695,plain,
spl0_1234,
inference(avatar_split_clause,[],[f928,f9693]) ).
fof(f9693,plain,
( spl0_1234
<=> ! [X11] : c_0 = c_minus(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f928,axiom,
! [X11] : c_0 = c_minus(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f9691,plain,
spl0_1233,
inference(avatar_split_clause,[],[f920,f9689]) ).
fof(f920,axiom,
! [X10] : c_plus(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f9687,plain,
spl0_1232,
inference(avatar_split_clause,[],[f657,f9685]) ).
fof(f9685,plain,
( spl0_1232
<=> ! [X0,X26] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f657,axiom,
! [X0,X26] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f9683,plain,
( spl0_1231
| ~ spl0_1
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f8174,f6044,f3203,f9680]) ).
fof(f6044,plain,
( spl0_680
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f8174,plain,
( class_OrderedGroup_Oab__group__add(t_a)
| ~ spl0_1
| ~ spl0_680 ),
inference(resolution,[],[f6045,f3205]) ).
fof(f6045,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__group__add(X87) )
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f6044]) ).
fof(f9678,plain,
spl0_1230,
inference(avatar_split_clause,[],[f656,f9676]) ).
fof(f9676,plain,
( spl0_1230
<=> ! [X0,X39] : c_List_Olist_ONil = c_List_Osublist(X39,c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f656,axiom,
! [X39,X0] : c_List_Olist_ONil = c_List_Osublist(X39,c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f9674,plain,
spl0_1229,
inference(avatar_split_clause,[],[f635,f9672]) ).
fof(f9672,plain,
( spl0_1229
<=> ! [X0,X11] : c_List_Olist_ONil = c_List_Orotate(X11,c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f635,axiom,
! [X0,X11] : c_List_Olist_ONil = c_List_Orotate(X11,c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f9670,plain,
spl0_1228,
inference(avatar_split_clause,[],[f616,f9668]) ).
fof(f616,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f9666,plain,
spl0_1227,
inference(avatar_split_clause,[],[f613,f9664]) ).
fof(f9664,plain,
( spl0_1227
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Oremove1(X12,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f613,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Oremove1(X12,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f9662,plain,
spl0_1226,
inference(avatar_split_clause,[],[f601,f9660]) ).
fof(f9660,plain,
( spl0_1226
<=> ! [X12,X39,X14] : ~ c_List_Onull(c_List_Olist_OCons(X12,X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f601,axiom,
! [X39,X14,X12] : ~ c_List_Onull(c_List_Olist_OCons(X12,X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f9658,plain,
spl0_1225,
inference(avatar_split_clause,[],[f583,f9656]) ).
fof(f9656,plain,
( spl0_1225
<=> ! [X0,X12,X39] : c_List_Olist_OCons(X12,X39,X0) != X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f583,axiom,
! [X39,X0,X12] : c_List_Olist_OCons(X12,X39,X0) != X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
fof(f9654,plain,
spl0_1224,
inference(avatar_split_clause,[],[f522,f9652]) ).
fof(f9652,plain,
( spl0_1224
<=> ! [X56,X14] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X56,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f522,axiom,
! [X56,X14] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X56,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f9650,plain,
spl0_1223,
inference(avatar_split_clause,[],[f518,f9648]) ).
fof(f9648,plain,
( spl0_1223
<=> ! [X54,X0,X15] : c_List_Olist_ONil != c_List_Olist_OCons(X15,X54,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f518,axiom,
! [X0,X54,X15] : c_List_Olist_ONil != c_List_Olist_OCons(X15,X54,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f9646,plain,
spl0_1222,
inference(avatar_split_clause,[],[f509,f9644]) ).
fof(f9644,plain,
( spl0_1222
<=> ! [X19,X14] : c_emptyset = c_List_Olexn(X19,c_0,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f509,axiom,
! [X19,X14] : c_emptyset = c_List_Olexn(X19,c_0,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f9642,plain,
spl0_1221,
inference(avatar_split_clause,[],[f492,f9640]) ).
fof(f9640,plain,
( spl0_1221
<=> ! [X0] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f492,axiom,
! [X0] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f9638,plain,
( spl0_1220
| ~ spl0_1
| ~ spl0_679 ),
inference(avatar_split_clause,[],[f8173,f6040,f3203,f9635]) ).
fof(f6040,plain,
( spl0_679
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f8173,plain,
( class_Ring__and__Field_Oordered__semidom(t_a)
| ~ spl0_1
| ~ spl0_679 ),
inference(resolution,[],[f6041,f3205]) ).
fof(f6041,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semidom(X87) )
| ~ spl0_679 ),
inference(avatar_component_clause,[],[f6040]) ).
fof(f9633,plain,
spl0_1219,
inference(avatar_split_clause,[],[f463,f9631]) ).
fof(f9631,plain,
( spl0_1219
<=> ! [X0,X10] : c_List_Odrop(c_0,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f463,axiom,
! [X10,X0] : c_List_Odrop(c_0,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f9629,plain,
spl0_1218,
inference(avatar_split_clause,[],[f462,f9627]) ).
fof(f9627,plain,
( spl0_1218
<=> ! [X11,X14] : c_List_Olist_ONil = c_List_Odrop(X11,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f462,axiom,
! [X11,X14] : c_List_Olist_ONil = c_List_Odrop(X11,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f9625,plain,
spl0_1217,
inference(avatar_split_clause,[],[f428,f9623]) ).
fof(f9623,plain,
( spl0_1217
<=> ! [X0,X39] : c_append(X39,c_List_Olist_ONil,X0) = X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f428,axiom,
! [X39,X0] : c_append(X39,c_List_Olist_ONil,X0) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
fof(f9621,plain,
spl0_1216,
inference(avatar_split_clause,[],[f388,f9619]) ).
fof(f9619,plain,
( spl0_1216
<=> ! [X1] : c_0 = c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f388,axiom,
! [X1] : c_0 = c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f9617,plain,
spl0_1215,
inference(avatar_split_clause,[],[f385,f9615]) ).
fof(f9615,plain,
( spl0_1215
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f385,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f9613,plain,
spl0_1214,
inference(avatar_split_clause,[],[f383,f9611]) ).
fof(f9611,plain,
( spl0_1214
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f383,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f9609,plain,
spl0_1213,
inference(avatar_split_clause,[],[f368,f9607]) ).
fof(f9607,plain,
( spl0_1213
<=> ! [X1] : c_0 = c_div(c_0,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f368,axiom,
! [X1] : c_0 = c_div(c_0,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f9605,plain,
spl0_1212,
inference(avatar_split_clause,[],[f360,f9603]) ).
fof(f9603,plain,
( spl0_1212
<=> ! [X10] : c_div(X10,c_1,tc_IntDef_Oint) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f360,axiom,
! [X10] : c_div(X10,c_1,tc_IntDef_Oint) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f9601,plain,
spl0_1211,
inference(avatar_split_clause,[],[f358,f9599]) ).
fof(f9599,plain,
( spl0_1211
<=> ! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f358,axiom,
! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f9597,plain,
spl0_1210,
inference(avatar_split_clause,[],[f326,f9595]) ).
fof(f9595,plain,
( spl0_1210
<=> ! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_IntDef_Oint) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f326,axiom,
! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_IntDef_Oint) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f9593,plain,
( spl0_1209
| ~ spl0_1
| ~ spl0_678 ),
inference(avatar_split_clause,[],[f8172,f6036,f3203,f9590]) ).
fof(f9590,plain,
( spl0_1209
<=> class_Ring__and__Field_Oring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f6036,plain,
( spl0_678
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f8172,plain,
( class_Ring__and__Field_Oring(t_a)
| ~ spl0_1
| ~ spl0_678 ),
inference(resolution,[],[f6037,f3205]) ).
fof(f6037,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring(X87) )
| ~ spl0_678 ),
inference(avatar_component_clause,[],[f6036]) ).
fof(f9588,plain,
spl0_1208,
inference(avatar_split_clause,[],[f258,f9586]) ).
fof(f9586,plain,
( spl0_1208
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_1,c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f258,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_1,c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f9584,plain,
spl0_1207,
inference(avatar_split_clause,[],[f257,f9582]) ).
fof(f9582,plain,
( spl0_1207
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_0,c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f257,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_0,c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f9580,plain,
spl0_1206,
inference(avatar_split_clause,[],[f252,f9578]) ).
fof(f9578,plain,
( spl0_1206
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_1,c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f252,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_1,c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f9576,plain,
spl0_1205,
inference(avatar_split_clause,[],[f251,f9574]) ).
fof(f9574,plain,
( spl0_1205
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_0,c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f251,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_0,c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f9572,plain,
spl0_1204,
inference(avatar_split_clause,[],[f244,f9569]) ).
fof(f9569,plain,
( spl0_1204
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f244,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(f9567,plain,
spl0_1203,
inference(avatar_split_clause,[],[f139,f9565]) ).
fof(f9565,plain,
( spl0_1203
<=> ! [X0,X19] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X19,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f139,axiom,
! [X0,X19] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X19,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f9563,plain,
spl0_1202,
inference(avatar_split_clause,[],[f135,f9561]) ).
fof(f9561,plain,
( spl0_1202
<=> ! [X11] : c_0 = c_Divides_Oop_Amod(X11,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f135,axiom,
! [X11] : c_0 = c_Divides_Oop_Amod(X11,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f9559,plain,
spl0_1201,
inference(avatar_split_clause,[],[f124,f9557]) ).
fof(f9557,plain,
( spl0_1201
<=> ! [X24] : c_0 = c_Divides_Oop_Amod(c_0,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f124,axiom,
! [X24] : c_0 = c_Divides_Oop_Amod(c_0,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f9555,plain,
spl0_1200,
inference(avatar_split_clause,[],[f107,f9553]) ).
fof(f9553,plain,
( spl0_1200
<=> ! [X24] : c_0 = c_div(c_0,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f107,axiom,
! [X24] : c_0 = c_div(c_0,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f9551,plain,
spl0_1199,
inference(avatar_split_clause,[],[f106,f9549]) ).
fof(f9549,plain,
( spl0_1199
<=> ! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f106,axiom,
! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f9547,plain,
( spl0_1198
| ~ spl0_1
| ~ spl0_677 ),
inference(avatar_split_clause,[],[f8171,f6032,f3203,f9544]) ).
fof(f6032,plain,
( spl0_677
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f8171,plain,
( class_Orderings_Oord(t_a)
| ~ spl0_1
| ~ spl0_677 ),
inference(resolution,[],[f6033,f3205]) ).
fof(f6033,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oord(X87) )
| ~ spl0_677 ),
inference(avatar_component_clause,[],[f6032]) ).
fof(f9542,plain,
spl0_1197,
inference(avatar_split_clause,[],[f105,f9540]) ).
fof(f9540,plain,
( spl0_1197
<=> ! [X3] : c_0 = c_div(X3,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f105,axiom,
! [X3] : c_0 = c_div(X3,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f9538,plain,
spl0_1196,
inference(avatar_split_clause,[],[f77,f9536]) ).
fof(f9536,plain,
( spl0_1196
<=> ! [X0,X10] : c_Datatype_Ounit_Ounit__rec(X10,c_Product__Type_OUnity,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f77,axiom,
! [X10,X0] : c_Datatype_Ounit_Ounit__rec(X10,c_Product__Type_OUnity,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f9534,plain,
spl0_1195,
inference(avatar_split_clause,[],[f76,f9532]) ).
fof(f9532,plain,
( spl0_1195
<=> ! [X0,X10] : c_Datatype_Ounit_Ounit__case(X10,c_Product__Type_OUnity,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f76,axiom,
! [X10,X0] : c_Datatype_Ounit_Ounit__case(X10,c_Product__Type_OUnity,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f9530,plain,
spl0_1194,
inference(avatar_split_clause,[],[f70,f9528]) ).
fof(f9528,plain,
( spl0_1194
<=> ! [X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f70,axiom,
! [X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f9526,plain,
spl0_1193,
inference(avatar_split_clause,[],[f42,f9524]) ).
fof(f9524,plain,
( spl0_1193
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f42,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_9) ).
fof(f9522,plain,
spl0_1192,
inference(avatar_split_clause,[],[f41,f9520]) ).
fof(f9520,plain,
( spl0_1192
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f41,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_8) ).
fof(f9518,plain,
spl0_1191,
inference(avatar_split_clause,[],[f40,f9516]) ).
fof(f9516,plain,
( spl0_1191
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f40,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_7) ).
fof(f9514,plain,
spl0_1190,
inference(avatar_split_clause,[],[f39,f9512]) ).
fof(f9512,plain,
( spl0_1190
<=> ! [X8,X7] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f39,axiom,
! [X8,X7] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_6) ).
fof(f9510,plain,
spl0_1189,
inference(avatar_split_clause,[],[f38,f9508]) ).
fof(f9508,plain,
( spl0_1189
<=> ! [X8,X7] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f38,axiom,
! [X8,X7] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_5) ).
fof(f9506,plain,
spl0_1188,
inference(avatar_split_clause,[],[f37,f9504]) ).
fof(f9504,plain,
( spl0_1188
<=> ! [X8,X7] :
( ~ class_HOL_Ominus(X8)
| class_HOL_Ominus(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f37,axiom,
! [X8,X7] :
( ~ class_HOL_Ominus(X8)
| class_HOL_Ominus(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_4) ).
fof(f9502,plain,
( spl0_1187
| ~ spl0_1
| ~ spl0_676 ),
inference(avatar_split_clause,[],[f8170,f6028,f3203,f9499]) ).
fof(f6028,plain,
( spl0_676
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f8170,plain,
( class_Orderings_Oorder(t_a)
| ~ spl0_1
| ~ spl0_676 ),
inference(resolution,[],[f6029,f3205]) ).
fof(f6029,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oorder(X87) )
| ~ spl0_676 ),
inference(avatar_component_clause,[],[f6028]) ).
fof(f9497,plain,
spl0_1186,
inference(avatar_split_clause,[],[f36,f9495]) ).
fof(f9495,plain,
( spl0_1186
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f36,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_31) ).
fof(f9493,plain,
spl0_1185,
inference(avatar_split_clause,[],[f35,f9491]) ).
fof(f9491,plain,
( spl0_1185
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f35,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_30) ).
fof(f9489,plain,
spl0_1184,
inference(avatar_split_clause,[],[f34,f9487]) ).
fof(f9487,plain,
( spl0_1184
<=> ! [X8,X7] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f34,axiom,
! [X8,X7] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_3) ).
fof(f9485,plain,
spl0_1183,
inference(avatar_split_clause,[],[f33,f9483]) ).
fof(f9483,plain,
( spl0_1183
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f33,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_29) ).
fof(f9481,plain,
spl0_1182,
inference(avatar_split_clause,[],[f32,f9479]) ).
fof(f9479,plain,
( spl0_1182
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f32,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_28) ).
fof(f9477,plain,
spl0_1181,
inference(avatar_split_clause,[],[f31,f9475]) ).
fof(f9475,plain,
( spl0_1181
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f31,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_27) ).
fof(f9473,plain,
spl0_1180,
inference(avatar_split_clause,[],[f30,f9471]) ).
fof(f9471,plain,
( spl0_1180
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f30,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_26) ).
fof(f9469,plain,
spl0_1179,
inference(avatar_split_clause,[],[f29,f9467]) ).
fof(f9467,plain,
( spl0_1179
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f29,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_25) ).
fof(f9465,plain,
spl0_1178,
inference(avatar_split_clause,[],[f28,f9463]) ).
fof(f9463,plain,
( spl0_1178
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f28,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_24) ).
fof(f9461,plain,
spl0_1177,
inference(avatar_split_clause,[],[f27,f9459]) ).
fof(f9459,plain,
( spl0_1177
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f27,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_23) ).
fof(f9457,plain,
( spl0_1176
| ~ spl0_1
| ~ spl0_675 ),
inference(avatar_split_clause,[],[f8169,f6024,f3203,f9454]) ).
fof(f9454,plain,
( spl0_1176
<=> class_OrderedGroup_Opordered__ab__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f6024,plain,
( spl0_675
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f8169,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_675 ),
inference(resolution,[],[f6025,f3205]) ).
fof(f6025,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) )
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f6024]) ).
fof(f9452,plain,
spl0_1175,
inference(avatar_split_clause,[],[f26,f9450]) ).
fof(f9450,plain,
( spl0_1175
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f26,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_22) ).
fof(f9448,plain,
spl0_1174,
inference(avatar_split_clause,[],[f25,f9446]) ).
fof(f9446,plain,
( spl0_1174
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f25,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_21) ).
fof(f9444,plain,
spl0_1173,
inference(avatar_split_clause,[],[f24,f9442]) ).
fof(f9442,plain,
( spl0_1173
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f24,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_20) ).
fof(f9440,plain,
spl0_1172,
inference(avatar_split_clause,[],[f23,f9438]) ).
fof(f9438,plain,
( spl0_1172
<=> ! [X8,X7] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f23,axiom,
! [X8,X7] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_2) ).
fof(f9436,plain,
spl0_1171,
inference(avatar_split_clause,[],[f22,f9434]) ).
fof(f9434,plain,
( spl0_1171
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f22,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_19) ).
fof(f9432,plain,
spl0_1170,
inference(avatar_split_clause,[],[f21,f9430]) ).
fof(f9430,plain,
( spl0_1170
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f21,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_18) ).
fof(f9428,plain,
spl0_1169,
inference(avatar_split_clause,[],[f20,f9426]) ).
fof(f9426,plain,
( spl0_1169
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f20,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_17) ).
fof(f9424,plain,
spl0_1168,
inference(avatar_split_clause,[],[f19,f9422]) ).
fof(f9422,plain,
( spl0_1168
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f19,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_16) ).
fof(f9420,plain,
spl0_1167,
inference(avatar_split_clause,[],[f18,f9418]) ).
fof(f9418,plain,
( spl0_1167
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f18,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_15) ).
fof(f9416,plain,
spl0_1166,
inference(avatar_split_clause,[],[f17,f9414]) ).
fof(f9414,plain,
( spl0_1166
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f17,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_14) ).
fof(f9412,plain,
( spl0_1165
| ~ spl0_1
| ~ spl0_674 ),
inference(avatar_split_clause,[],[f8168,f6020,f3203,f9409]) ).
fof(f9409,plain,
( spl0_1165
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f6020,plain,
( spl0_674
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f8168,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_674 ),
inference(resolution,[],[f6021,f3205]) ).
fof(f6021,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f6020]) ).
fof(f9407,plain,
spl0_1164,
inference(avatar_split_clause,[],[f16,f9405]) ).
fof(f9405,plain,
( spl0_1164
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f16,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_13) ).
fof(f9403,plain,
spl0_1163,
inference(avatar_split_clause,[],[f15,f9401]) ).
fof(f9401,plain,
( spl0_1163
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Oab__group__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f15,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Oab__group__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_12) ).
fof(f9399,plain,
spl0_1162,
inference(avatar_split_clause,[],[f14,f9397]) ).
fof(f9397,plain,
( spl0_1162
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f14,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_11) ).
fof(f9395,plain,
spl0_1161,
inference(avatar_split_clause,[],[f13,f9393]) ).
fof(f9393,plain,
( spl0_1161
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f13,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_10) ).
fof(f9378,plain,
( spl0_1160
| ~ spl0_1
| ~ spl0_673 ),
inference(avatar_split_clause,[],[f8162,f6016,f3203,f9375]) ).
fof(f9375,plain,
( spl0_1160
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f6016,plain,
( spl0_673
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f8162,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_a)
| ~ spl0_1
| ~ spl0_673 ),
inference(resolution,[],[f6017,f3205]) ).
fof(f6017,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) )
| ~ spl0_673 ),
inference(avatar_component_clause,[],[f6016]) ).
fof(f9373,plain,
( spl0_1159
| ~ spl0_1
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f8161,f6012,f3203,f9370]) ).
fof(f6012,plain,
( spl0_672
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f8161,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_a)
| ~ spl0_1
| ~ spl0_672 ),
inference(resolution,[],[f6013,f3205]) ).
fof(f6013,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) )
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f6012]) ).
fof(f9367,plain,
( spl0_1158
| ~ spl0_1
| ~ spl0_671 ),
inference(avatar_split_clause,[],[f8160,f6008,f3203,f9364]) ).
fof(f6008,plain,
( spl0_671
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f8160,plain,
( class_LOrder_Omeet__semilorder(t_a)
| ~ spl0_1
| ~ spl0_671 ),
inference(resolution,[],[f6009,f3205]) ).
fof(f6009,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Omeet__semilorder(X87) )
| ~ spl0_671 ),
inference(avatar_component_clause,[],[f6008]) ).
fof(f9362,plain,
( spl0_1157
| ~ spl0_1
| ~ spl0_670 ),
inference(avatar_split_clause,[],[f8159,f6004,f3203,f9359]) ).
fof(f6004,plain,
( spl0_670
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f8159,plain,
( class_LOrder_Ojoin__semilorder(t_a)
| ~ spl0_1
| ~ spl0_670 ),
inference(resolution,[],[f6005,f3205]) ).
fof(f6005,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Ojoin__semilorder(X87) )
| ~ spl0_670 ),
inference(avatar_component_clause,[],[f6004]) ).
fof(f9357,plain,
( spl0_1156
| ~ spl0_1
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f8158,f6000,f3203,f9354]) ).
fof(f9354,plain,
( spl0_1156
<=> class_LOrder_Olorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f6000,plain,
( spl0_669
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f8158,plain,
( class_LOrder_Olorder(t_a)
| ~ spl0_1
| ~ spl0_669 ),
inference(resolution,[],[f6001,f3205]) ).
fof(f6001,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Olorder(X87) )
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f6000]) ).
fof(f9346,plain,
( spl0_1155
| ~ spl0_1
| ~ spl0_668 ),
inference(avatar_split_clause,[],[f8157,f5996,f3203,f9343]) ).
fof(f5996,plain,
( spl0_668
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f8157,plain,
( class_OrderedGroup_Olordered__ab__group(t_a)
| ~ spl0_1
| ~ spl0_668 ),
inference(resolution,[],[f5997,f3205]) ).
fof(f5997,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group(X87) )
| ~ spl0_668 ),
inference(avatar_component_clause,[],[f5996]) ).
fof(f9340,plain,
( spl0_1154
| ~ spl0_1
| ~ spl0_667 ),
inference(avatar_split_clause,[],[f8156,f5992,f3203,f9337]) ).
fof(f9337,plain,
( spl0_1154
<=> class_Ring__and__Field_Oring__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f5992,plain,
( spl0_667
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f8156,plain,
( class_Ring__and__Field_Oring__1(t_a)
| ~ spl0_1
| ~ spl0_667 ),
inference(resolution,[],[f5993,f3205]) ).
fof(f5993,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring__1(X87) )
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f5992]) ).
fof(f9318,plain,
spl0_1153,
inference(avatar_split_clause,[],[f3020,f9315]) ).
fof(f9315,plain,
( spl0_1153
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f3020,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f285,f268]) ).
fof(f268,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f285,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(f9313,plain,
spl0_1152,
inference(avatar_split_clause,[],[f3015,f9311]) ).
fof(f9311,plain,
( spl0_1152
<=> ! [X10] : c_Binomial_Obinomial(X10,c_1) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f3015,plain,
! [X10] : c_Binomial_Obinomial(X10,c_1) = X10,
inference(forward_demodulation,[],[f2807,f2791]) ).
fof(f2807,plain,
! [X10] : c_Binomial_Obinomial(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X10,
inference(definition_unfolding,[],[f55,f1438]) ).
fof(f55,axiom,
! [X10] : c_Binomial_Obinomial(X10,c_Suc(c_0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f9309,plain,
spl0_1151,
inference(avatar_split_clause,[],[f2790,f9306]) ).
fof(f9304,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1871,f9302]) ).
fof(f9302,plain,
( spl0_1150
<=> ! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1871,axiom,
! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f9300,plain,
( spl0_1149
| ~ spl0_1
| ~ spl0_666 ),
inference(avatar_split_clause,[],[f8155,f5988,f3203,f9297]) ).
fof(f9297,plain,
( spl0_1149
<=> class_OrderedGroup_Olordered__ab__group__join(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f5988,plain,
( spl0_666
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f8155,plain,
( class_OrderedGroup_Olordered__ab__group__join(t_a)
| ~ spl0_1
| ~ spl0_666 ),
inference(resolution,[],[f5989,f3205]) ).
fof(f5989,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) )
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f5988]) ).
fof(f9295,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1749,f9293]) ).
fof(f9293,plain,
( spl0_1148
<=> ! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1749,axiom,
! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f9291,plain,
spl0_1147,
inference(avatar_split_clause,[],[f1733,f9289]) ).
fof(f9289,plain,
( spl0_1147
<=> ! [X0,X26] : c_lessequals(X26,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1733,axiom,
! [X0,X26] : c_lessequals(X26,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f9287,plain,
spl0_1146,
inference(avatar_split_clause,[],[f1722,f9285]) ).
fof(f9285,plain,
( spl0_1146
<=> ! [X0,X26] : c_lessequals(c_emptyset,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f1722,axiom,
! [X0,X26] : c_lessequals(c_emptyset,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f9283,plain,
spl0_1145,
inference(avatar_split_clause,[],[f1665,f9281]) ).
fof(f9281,plain,
( spl0_1145
<=> ! [X0,X39] : c_List_Odistinct(c_List_Oremdups(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f1665,axiom,
! [X39,X0] : c_List_Odistinct(c_List_Oremdups(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f9279,plain,
spl0_1144,
inference(avatar_split_clause,[],[f1649,f9277]) ).
fof(f9277,plain,
( spl0_1144
<=> ! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f1649,axiom,
! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f9275,plain,
spl0_1143,
inference(avatar_split_clause,[],[f1608,f9273]) ).
fof(f9273,plain,
( spl0_1143
<=> ! [X0] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f1608,axiom,
! [X0] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f9271,plain,
spl0_1142,
inference(avatar_split_clause,[],[f1592,f9269]) ).
fof(f9269,plain,
( spl0_1142
<=> ! [X0,X26] : c_lessequals(X26,c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f1592,axiom,
! [X0,X26] : c_lessequals(X26,c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f9267,plain,
spl0_1141,
inference(avatar_split_clause,[],[f1585,f9265]) ).
fof(f9265,plain,
( spl0_1141
<=> ! [X0,X26] : ~ c_less(X26,c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f1585,axiom,
! [X0,X26] : ~ c_less(X26,c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f9263,plain,
spl0_1140,
inference(avatar_split_clause,[],[f1545,f9261]) ).
fof(f9261,plain,
( spl0_1140
<=> ! [X0] : c_emptyset = c_Union(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f1545,axiom,
! [X0] : c_emptyset = c_Union(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f9259,plain,
spl0_1139,
inference(avatar_split_clause,[],[f1543,f9257]) ).
fof(f9257,plain,
( spl0_1139
<=> ! [X0] : c_UNIV = c_Union(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f1543,axiom,
! [X0] : c_UNIV = c_Union(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f9255,plain,
( spl0_1138
| ~ spl0_1
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f8154,f5984,f3203,f9252]) ).
fof(f9252,plain,
( spl0_1138
<=> class_OrderedGroup_Olordered__ab__group__meet(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f5984,plain,
( spl0_665
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f8154,plain,
( class_OrderedGroup_Olordered__ab__group__meet(t_a)
| ~ spl0_1
| ~ spl0_665 ),
inference(resolution,[],[f5985,f3205]) ).
fof(f5985,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) )
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f5984]) ).
fof(f9250,plain,
spl0_1137,
inference(avatar_split_clause,[],[f1519,f9248]) ).
fof(f9248,plain,
( spl0_1137
<=> ! [X0] : c_UNIV = c_Pow(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f1519,axiom,
! [X0] : c_UNIV = c_Pow(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f9246,plain,
spl0_1136,
inference(avatar_split_clause,[],[f1513,f9244]) ).
fof(f9244,plain,
( spl0_1136
<=> ! [X0] : c_UNIV = c_Inter(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f1513,axiom,
! [X0] : c_UNIV = c_Inter(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f9242,plain,
spl0_1135,
inference(avatar_split_clause,[],[f1506,f9240]) ).
fof(f9240,plain,
( spl0_1135
<=> ! [X0] : c_emptyset = c_Inter(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f1506,axiom,
! [X0] : c_emptyset = c_Inter(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f9238,plain,
spl0_1134,
inference(avatar_split_clause,[],[f1461,f9235]) ).
fof(f9235,plain,
( spl0_1134
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f1461,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f9233,plain,
spl0_1133,
inference(avatar_split_clause,[],[f1422,f9230]) ).
fof(f9230,plain,
( spl0_1133
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f1422,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f9228,plain,
spl0_1132,
inference(avatar_split_clause,[],[f1280,f9226]) ).
fof(f9226,plain,
( spl0_1132
<=> ! [X0] : c_emptyset = c_Relation_Odiag(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f9224,plain,
spl0_1131,
inference(avatar_split_clause,[],[f1058,f9221]) ).
fof(f9221,plain,
( spl0_1131
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f1058,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(f9219,plain,
spl0_1130,
inference(avatar_split_clause,[],[f1057,f9216]) ).
fof(f9216,plain,
( spl0_1130
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f1057,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(f9214,plain,
spl0_1129,
inference(avatar_split_clause,[],[f1046,f9212]) ).
fof(f9212,plain,
( spl0_1129
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f1046,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f9210,plain,
spl0_1128,
inference(avatar_split_clause,[],[f1045,f9208]) ).
fof(f9208,plain,
( spl0_1128
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f1045,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f9206,plain,
( spl0_1127
| ~ spl0_1
| ~ spl0_664 ),
inference(avatar_split_clause,[],[f8153,f5980,f3203,f9203]) ).
fof(f5980,plain,
( spl0_664
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f8153,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ spl0_1
| ~ spl0_664 ),
inference(resolution,[],[f5981,f3205]) ).
fof(f5981,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) )
| ~ spl0_664 ),
inference(avatar_component_clause,[],[f5980]) ).
fof(f9201,plain,
spl0_1126,
inference(avatar_split_clause,[],[f1029,f9199]) ).
fof(f9199,plain,
( spl0_1126
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_IntDef_Oiszero(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1029,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_IntDef_Oiszero(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f9197,plain,
spl0_1125,
inference(avatar_split_clause,[],[f1024,f9195]) ).
fof(f9195,plain,
( spl0_1125
<=> ! [X33] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1024,axiom,
! [X33] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f9193,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1009,f9191]) ).
fof(f9191,plain,
( spl0_1124
<=> ! [X10] : c_Numeral_Obin__add(X10,c_Numeral_OPls) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f9189,plain,
spl0_1123,
inference(avatar_split_clause,[],[f1008,f9187]) ).
fof(f9185,plain,
spl0_1122,
inference(avatar_split_clause,[],[f1000,f9182]) ).
fof(f9182,plain,
( spl0_1122
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f1000,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(f9180,plain,
spl0_1121,
inference(avatar_split_clause,[],[f999,f9177]) ).
fof(f999,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(f9175,plain,
spl0_1120,
inference(avatar_split_clause,[],[f760,f9172]) ).
fof(f760,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(f9170,plain,
spl0_1119,
inference(avatar_split_clause,[],[f679,f9168]) ).
fof(f9168,plain,
( spl0_1119
<=> ! [X23] : c_List_Olist_ONil = c_List_Oupt(X23,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f679,axiom,
! [X23] : c_List_Olist_ONil = c_List_Oupt(X23,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f9166,plain,
spl0_1118,
inference(avatar_split_clause,[],[f672,f9164]) ).
fof(f9164,plain,
( spl0_1118
<=> ! [X14] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f672,axiom,
! [X14] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f9162,plain,
spl0_1117,
inference(avatar_split_clause,[],[f647,f9160]) ).
fof(f9160,plain,
( spl0_1117
<=> ! [X0] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f647,axiom,
! [X0] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f9142,plain,
spl0_1116,
inference(avatar_split_clause,[],[f630,f9140]) ).
fof(f9140,plain,
( spl0_1116
<=> ! [X0] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f630,axiom,
! [X0] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f9138,plain,
spl0_1115,
inference(avatar_split_clause,[],[f623,f9136]) ).
fof(f9136,plain,
( spl0_1115
<=> ! [X0] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f9134,plain,
spl0_1114,
inference(avatar_split_clause,[],[f612,f9132]) ).
fof(f9132,plain,
( spl0_1114
<=> ! [X0] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f612,axiom,
! [X0] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
fof(f9130,plain,
spl0_1113,
inference(avatar_split_clause,[],[f582,f9127]) ).
fof(f9127,plain,
( spl0_1113
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f582,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(f9125,plain,
spl0_1112,
inference(avatar_split_clause,[],[f581,f9122]) ).
fof(f9122,plain,
( spl0_1112
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f581,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(f9120,plain,
spl0_1111,
inference(avatar_split_clause,[],[f580,f9117]) ).
fof(f9117,plain,
( spl0_1111
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f580,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(f9115,plain,
spl0_1110,
inference(avatar_split_clause,[],[f579,f9112]) ).
fof(f9112,plain,
( spl0_1110
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f579,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(f9110,plain,
spl0_1109,
inference(avatar_split_clause,[],[f578,f9107]) ).
fof(f9107,plain,
( spl0_1109
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f578,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(f9105,plain,
spl0_1108,
inference(avatar_split_clause,[],[f577,f9102]) ).
fof(f9102,plain,
( spl0_1108
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f577,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(f9100,plain,
spl0_1107,
inference(avatar_split_clause,[],[f576,f9097]) ).
fof(f9097,plain,
( spl0_1107
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f576,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(f9095,plain,
( spl0_1106
| ~ spl0_1
| ~ spl0_663 ),
inference(avatar_split_clause,[],[f8147,f5976,f3203,f9092]) ).
fof(f9092,plain,
( spl0_1106
<=> class_Ring__and__Field_Opordered__semiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f5976,plain,
( spl0_663
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f8147,plain,
( class_Ring__and__Field_Opordered__semiring(t_a)
| ~ spl0_1
| ~ spl0_663 ),
inference(resolution,[],[f5977,f3205]) ).
fof(f5977,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__semiring(X87) )
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f5976]) ).
fof(f9090,plain,
spl0_1105,
inference(avatar_split_clause,[],[f575,f9087]) ).
fof(f9087,plain,
( spl0_1105
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f575,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(f9085,plain,
spl0_1104,
inference(avatar_split_clause,[],[f574,f9082]) ).
fof(f9082,plain,
( spl0_1104
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f574,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(f9080,plain,
spl0_1103,
inference(avatar_split_clause,[],[f573,f9077]) ).
fof(f9077,plain,
( spl0_1103
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f573,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(f9075,plain,
spl0_1102,
inference(avatar_split_clause,[],[f572,f9072]) ).
fof(f9072,plain,
( spl0_1102
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f572,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(f9070,plain,
spl0_1101,
inference(avatar_split_clause,[],[f571,f9067]) ).
fof(f9067,plain,
( spl0_1101
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f571,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(f9065,plain,
spl0_1100,
inference(avatar_split_clause,[],[f570,f9062]) ).
fof(f9062,plain,
( spl0_1100
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f570,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(f9060,plain,
spl0_1099,
inference(avatar_split_clause,[],[f569,f9057]) ).
fof(f9057,plain,
( spl0_1099
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f569,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(f9055,plain,
spl0_1098,
inference(avatar_split_clause,[],[f568,f9052]) ).
fof(f9052,plain,
( spl0_1098
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f568,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(f9050,plain,
spl0_1097,
inference(avatar_split_clause,[],[f567,f9047]) ).
fof(f9047,plain,
( spl0_1097
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f567,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(f9045,plain,
spl0_1096,
inference(avatar_split_clause,[],[f532,f9043]) ).
fof(f9043,plain,
( spl0_1096
<=> ! [X0] : c_UNIV = c_List_Olists(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f532,axiom,
! [X0] : c_UNIV = c_List_Olists(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f9041,plain,
( spl0_1095
| ~ spl0_1
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f8146,f5972,f3203,f9038]) ).
fof(f9038,plain,
( spl0_1095
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f5972,plain,
( spl0_662
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f8146,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ spl0_1
| ~ spl0_662 ),
inference(resolution,[],[f5973,f3205]) ).
fof(f5973,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) )
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f5972]) ).
fof(f9036,plain,
spl0_1094,
inference(avatar_split_clause,[],[f461,f9034]) ).
fof(f9034,plain,
( spl0_1094
<=> ! [X50,X23] : c_List_Odistinct(c_List_Oupt(X23,X50),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f461,axiom,
! [X50,X23] : c_List_Odistinct(c_List_Oupt(X23,X50),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f9032,plain,
spl0_1093,
inference(avatar_split_clause,[],[f437,f9030]) ).
fof(f9030,plain,
( spl0_1093
<=> ! [X14] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f437,axiom,
! [X14] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f9028,plain,
spl0_1092,
inference(avatar_split_clause,[],[f430,f9026]) ).
fof(f9026,plain,
( spl0_1092
<=> ! [X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f430,axiom,
! [X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f9024,plain,
spl0_1091,
inference(avatar_split_clause,[],[f318,f9022]) ).
fof(f9022,plain,
( spl0_1091
<=> ! [X11] : c_lessequals(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f318,axiom,
! [X11] : c_lessequals(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f9020,plain,
spl0_1090,
inference(avatar_split_clause,[],[f278,f9018]) ).
fof(f278,axiom,
! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f9016,plain,
spl0_1089,
inference(avatar_split_clause,[],[f272,f9014]) ).
fof(f9014,plain,
( spl0_1089
<=> ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f272,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(f9012,plain,
~ spl0_1088,
inference(avatar_split_clause,[],[f203,f9009]) ).
fof(f9009,plain,
( spl0_1088
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f203,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(f9007,plain,
spl0_1087,
inference(avatar_split_clause,[],[f190,f9005]) ).
fof(f9005,plain,
( spl0_1087
<=> ! [X0,X10] : c_Fun_Oid(X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f190,axiom,
! [X10,X0] : c_Fun_Oid(X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f9003,plain,
spl0_1086,
inference(avatar_split_clause,[],[f189,f9001]) ).
fof(f9001,plain,
( spl0_1086
<=> ! [X10] : c_NatArith_Oof__nat(X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f189,axiom,
! [X10] : c_NatArith_Oof__nat(X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f8999,plain,
spl0_1085,
inference(avatar_split_clause,[],[f172,f8997]) ).
fof(f8997,plain,
( spl0_1085
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f172,axiom,
! [X0] : c_0 = c_Finite__Set_Ocard(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f8995,plain,
( spl0_1084
| ~ spl0_1
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f8145,f5968,f3203,f8992]) ).
fof(f8992,plain,
( spl0_1084
<=> class_Ring__and__Field_Opordered__ring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f5968,plain,
( spl0_661
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f8145,plain,
( class_Ring__and__Field_Opordered__ring(t_a)
| ~ spl0_1
| ~ spl0_661 ),
inference(resolution,[],[f5969,f3205]) ).
fof(f5969,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__ring(X87) )
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f5968]) ).
fof(f8990,plain,
spl0_1083,
inference(avatar_split_clause,[],[f149,f8987]) ).
fof(f8987,plain,
( spl0_1083
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f149,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(f8985,plain,
spl0_1082,
inference(avatar_split_clause,[],[f148,f8982]) ).
fof(f8982,plain,
( spl0_1082
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f148,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(f8980,plain,
spl0_1081,
inference(avatar_split_clause,[],[f78,f8977]) ).
fof(f8977,plain,
( spl0_1081
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f78,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(f8975,plain,
spl0_1080,
inference(avatar_split_clause,[],[f67,f8973]) ).
fof(f8973,plain,
( spl0_1080
<=> ! [X0,X15] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X15,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f67,axiom,
! [X0,X15] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X15,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f8971,plain,
spl0_1079,
inference(avatar_split_clause,[],[f66,f8969]) ).
fof(f8969,plain,
( spl0_1079
<=> ! [X0] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f66,axiom,
! [X0] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f8967,plain,
spl0_1078,
inference(avatar_split_clause,[],[f59,f8965]) ).
fof(f8965,plain,
( spl0_1078
<=> ! [X11] : c_1 = c_Binomial_Obinomial(X11,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f59,axiom,
! [X11] : c_1 = c_Binomial_Obinomial(X11,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f8963,plain,
spl0_1077,
inference(avatar_split_clause,[],[f58,f8961]) ).
fof(f8961,plain,
( spl0_1077
<=> ! [X11] : c_Binomial_Obinomial(X11,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f58,axiom,
! [X11] : c_Binomial_Obinomial(X11,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f8959,plain,
spl0_1076,
inference(avatar_split_clause,[],[f53,f8957]) ).
fof(f8957,plain,
( spl0_1076
<=> ! [X8] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f53,axiom,
! [X8] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_9) ).
fof(f8955,plain,
spl0_1075,
inference(avatar_split_clause,[],[f52,f8953]) ).
fof(f8953,plain,
( spl0_1075
<=> ! [X8] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f52,axiom,
! [X8] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_8) ).
fof(f8951,plain,
spl0_1074,
inference(avatar_split_clause,[],[f51,f8949]) ).
fof(f8949,plain,
( spl0_1074
<=> ! [X8] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f51,axiom,
! [X8] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_7) ).
fof(f8947,plain,
( spl0_1073
| ~ spl0_1
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f8144,f5964,f3203,f8944]) ).
fof(f8944,plain,
( spl0_1073
<=> class_Ring__and__Field_Olordered__ring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f5964,plain,
( spl0_660
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f8144,plain,
( class_Ring__and__Field_Olordered__ring(t_a)
| ~ spl0_1
| ~ spl0_660 ),
inference(resolution,[],[f5965,f3205]) ).
fof(f5965,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Olordered__ring(X87) )
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f5964]) ).
fof(f8942,plain,
spl0_1072,
inference(avatar_split_clause,[],[f50,f8940]) ).
fof(f8940,plain,
( spl0_1072
<=> ! [X8] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f50,axiom,
! [X8] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_6) ).
fof(f8938,plain,
spl0_1071,
inference(avatar_split_clause,[],[f49,f8936]) ).
fof(f8936,plain,
( spl0_1071
<=> ! [X8] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f49,axiom,
! [X8] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_5) ).
fof(f8934,plain,
spl0_1070,
inference(avatar_split_clause,[],[f48,f8932]) ).
fof(f8932,plain,
( spl0_1070
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f48,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_15) ).
fof(f8930,plain,
spl0_1069,
inference(avatar_split_clause,[],[f47,f8928]) ).
fof(f8928,plain,
( spl0_1069
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f47,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_14) ).
fof(f8926,plain,
spl0_1068,
inference(avatar_split_clause,[],[f46,f8924]) ).
fof(f8924,plain,
( spl0_1068
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f46,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_13) ).
fof(f8922,plain,
spl0_1067,
inference(avatar_split_clause,[],[f45,f8920]) ).
fof(f8920,plain,
( spl0_1067
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f45,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_12) ).
fof(f8918,plain,
spl0_1066,
inference(avatar_split_clause,[],[f44,f8916]) ).
fof(f8916,plain,
( spl0_1066
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f44,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_11) ).
fof(f8914,plain,
spl0_1065,
inference(avatar_split_clause,[],[f43,f8912]) ).
fof(f8912,plain,
( spl0_1065
<=> ! [X8] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f43,axiom,
! [X8] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_10) ).
fof(f8910,plain,
( spl0_1064
| ~ spl0_1
| ~ spl0_659 ),
inference(avatar_split_clause,[],[f8143,f5960,f3203,f8907]) ).
fof(f8907,plain,
( spl0_1064
<=> class_Ring__and__Field_Oaxclass__abs__if(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f5960,plain,
( spl0_659
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f8143,plain,
( class_Ring__and__Field_Oaxclass__abs__if(t_a)
| ~ spl0_1
| ~ spl0_659 ),
inference(resolution,[],[f5961,f3205]) ).
fof(f5961,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) )
| ~ spl0_659 ),
inference(avatar_component_clause,[],[f5960]) ).
fof(f8895,plain,
( spl0_1063
| ~ spl0_1
| ~ spl0_658 ),
inference(avatar_split_clause,[],[f8142,f5956,f3203,f8892]) ).
fof(f5956,plain,
( spl0_658
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f8142,plain,
( class_Orderings_Olinorder(t_a)
| ~ spl0_1
| ~ spl0_658 ),
inference(resolution,[],[f5957,f3205]) ).
fof(f5957,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Olinorder(X87) )
| ~ spl0_658 ),
inference(avatar_component_clause,[],[f5956]) ).
fof(f8870,plain,
( spl0_1062
| ~ spl0_1
| ~ spl0_657 ),
inference(avatar_split_clause,[],[f8141,f5952,f3203,f8867]) ).
fof(f8867,plain,
( spl0_1062
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f5952,plain,
( spl0_657
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f8141,plain,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_657 ),
inference(resolution,[],[f5953,f3205]) ).
fof(f5953,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_657 ),
inference(avatar_component_clause,[],[f5952]) ).
fof(f8845,plain,
( spl0_1061
| ~ spl0_1
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f8140,f5948,f3203,f8842]) ).
fof(f8842,plain,
( spl0_1061
<=> class_Ring__and__Field_Ocomm__ring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f5948,plain,
( spl0_656
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f8140,plain,
( class_Ring__and__Field_Ocomm__ring(t_a)
| ~ spl0_1
| ~ spl0_656 ),
inference(resolution,[],[f5949,f3205]) ).
fof(f5949,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring(X87) )
| ~ spl0_656 ),
inference(avatar_component_clause,[],[f5948]) ).
fof(f8820,plain,
( spl0_1060
| ~ spl0_1
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f8139,f5944,f3203,f8817]) ).
fof(f8817,plain,
( spl0_1060
<=> class_Ring__and__Field_Oordered__semiring__strict(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f5944,plain,
( spl0_655
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f8139,plain,
( class_Ring__and__Field_Oordered__semiring__strict(t_a)
| ~ spl0_1
| ~ spl0_655 ),
inference(resolution,[],[f5945,f3205]) ).
fof(f5945,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) )
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f5944]) ).
fof(f8795,plain,
( spl0_1059
| ~ spl0_1
| ~ spl0_654 ),
inference(avatar_split_clause,[],[f8138,f5940,f3203,f8792]) ).
fof(f8792,plain,
( spl0_1059
<=> class_Ring__and__Field_Oordered__ring__strict(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f5940,plain,
( spl0_654
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f8138,plain,
( class_Ring__and__Field_Oordered__ring__strict(t_a)
| ~ spl0_1
| ~ spl0_654 ),
inference(resolution,[],[f5941,f3205]) ).
fof(f5941,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) )
| ~ spl0_654 ),
inference(avatar_component_clause,[],[f5940]) ).
fof(f8755,plain,
( spl0_1058
| ~ spl0_1
| ~ spl0_653 ),
inference(avatar_split_clause,[],[f8132,f5936,f3203,f8752]) ).
fof(f8752,plain,
( spl0_1058
<=> class_Ring__and__Field_Opordered__comm__semiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f5936,plain,
( spl0_653
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f8132,plain,
( class_Ring__and__Field_Opordered__comm__semiring(t_a)
| ~ spl0_1
| ~ spl0_653 ),
inference(resolution,[],[f5937,f3205]) ).
fof(f5937,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) )
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f5936]) ).
fof(f8740,plain,
( spl0_1057
| ~ spl0_1
| ~ spl0_652 ),
inference(avatar_split_clause,[],[f8131,f5932,f3203,f8737]) ).
fof(f8737,plain,
( spl0_1057
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f5932,plain,
( spl0_652
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f8131,plain,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(t_a)
| ~ spl0_1
| ~ spl0_652 ),
inference(resolution,[],[f5933,f3205]) ).
fof(f5933,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) )
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f5932]) ).
fof(f8725,plain,
( spl0_1056
| ~ spl0_1
| ~ spl0_651 ),
inference(avatar_split_clause,[],[f8130,f5928,f3203,f8722]) ).
fof(f8722,plain,
( spl0_1056
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f5928,plain,
( spl0_651
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f8130,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(t_a)
| ~ spl0_1
| ~ spl0_651 ),
inference(resolution,[],[f5929,f3205]) ).
fof(f5929,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) )
| ~ spl0_651 ),
inference(avatar_component_clause,[],[f5928]) ).
fof(f8704,plain,
( spl0_1055
| ~ spl0_1
| ~ spl0_650 ),
inference(avatar_split_clause,[],[f8129,f5924,f3203,f8701]) ).
fof(f5924,plain,
( spl0_650
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__idom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f8129,plain,
( class_Ring__and__Field_Oordered__idom(t_a)
| ~ spl0_1
| ~ spl0_650 ),
inference(resolution,[],[f5925,f3205]) ).
fof(f5925,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__idom(X87) )
| ~ spl0_650 ),
inference(avatar_component_clause,[],[f5924]) ).
fof(f8683,plain,
( spl0_1054
| ~ spl0_1
| ~ spl0_649 ),
inference(avatar_split_clause,[],[f8128,f5920,f3203,f8680]) ).
fof(f8680,plain,
( spl0_1054
<=> class_HOL_Otimes(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f5920,plain,
( spl0_649
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f8128,plain,
( class_HOL_Otimes(t_a)
| ~ spl0_1
| ~ spl0_649 ),
inference(resolution,[],[f5921,f3205]) ).
fof(f5921,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Otimes(X87) )
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f5920]) ).
fof(f8668,plain,
( spl0_1053
| ~ spl0_1
| ~ spl0_648 ),
inference(avatar_split_clause,[],[f8127,f5916,f3203,f8665]) ).
fof(f8665,plain,
( spl0_1053
<=> class_HOL_Ozero(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f5916,plain,
( spl0_648
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f8127,plain,
( class_HOL_Ozero(t_a)
| ~ spl0_1
| ~ spl0_648 ),
inference(resolution,[],[f5917,f3205]) ).
fof(f5917,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ozero(X87) )
| ~ spl0_648 ),
inference(avatar_component_clause,[],[f5916]) ).
fof(f8652,plain,
( spl0_1052
| ~ spl0_1
| ~ spl0_647 ),
inference(avatar_split_clause,[],[f8126,f5912,f3203,f8649]) ).
fof(f8649,plain,
( spl0_1052
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f5912,plain,
( spl0_647
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f8126,plain,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(t_a)
| ~ spl0_1
| ~ spl0_647 ),
inference(resolution,[],[f5913,f3205]) ).
fof(f5913,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) )
| ~ spl0_647 ),
inference(avatar_component_clause,[],[f5912]) ).
fof(f8627,plain,
( spl0_1051
| ~ spl0_1
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f8125,f5908,f3203,f8624]) ).
fof(f8624,plain,
( spl0_1051
<=> class_HOL_Oplus(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f5908,plain,
( spl0_646
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f8125,plain,
( class_HOL_Oplus(t_a)
| ~ spl0_1
| ~ spl0_646 ),
inference(resolution,[],[f5909,f3205]) ).
fof(f5909,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f5908]) ).
fof(f8602,plain,
( spl0_1050
| ~ spl0_1
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f8124,f5904,f3203,f8599]) ).
fof(f5904,plain,
( spl0_645
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f8124,plain,
( class_Ring__and__Field_Ocomm__ring__1(t_a)
| ~ spl0_1
| ~ spl0_645 ),
inference(resolution,[],[f5905,f3205]) ).
fof(f5905,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) )
| ~ spl0_645 ),
inference(avatar_component_clause,[],[f5904]) ).
fof(f8577,plain,
( spl0_1049
| ~ spl0_1
| ~ spl0_644 ),
inference(avatar_split_clause,[],[f8123,f5900,f3203,f8574]) ).
fof(f8574,plain,
( spl0_1049
<=> class_OrderedGroup_Osemigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f5900,plain,
( spl0_644
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f8123,plain,
( class_OrderedGroup_Osemigroup__add(t_a)
| ~ spl0_1
| ~ spl0_644 ),
inference(resolution,[],[f5901,f3205]) ).
fof(f5901,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__add(X87) )
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5900]) ).
fof(f8515,plain,
( spl0_1048
| ~ spl0_1
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f8117,f5896,f3203,f8512]) ).
fof(f8512,plain,
( spl0_1048
<=> class_OrderedGroup_Ocancel__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f5896,plain,
( spl0_643
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f8117,plain,
( class_OrderedGroup_Ocancel__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_643 ),
inference(resolution,[],[f5897,f3205]) ).
fof(f5897,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) )
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f5896]) ).
fof(f8490,plain,
( spl0_1047
| ~ spl0_1
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f8116,f5892,f3203,f8487]) ).
fof(f8487,plain,
( spl0_1047
<=> class_OrderedGroup_Oab__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f5892,plain,
( spl0_642
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f8116,plain,
( class_OrderedGroup_Oab__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_642 ),
inference(resolution,[],[f5893,f3205]) ).
fof(f5893,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f5892]) ).
fof(f8465,plain,
( spl0_1046
| ~ spl0_1
| ~ spl0_641 ),
inference(avatar_split_clause,[],[f8115,f5888,f3203,f8462]) ).
fof(f8462,plain,
( spl0_1046
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f5888,plain,
( spl0_641
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f8115,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(t_a)
| ~ spl0_1
| ~ spl0_641 ),
inference(resolution,[],[f5889,f3205]) ).
fof(f5889,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) )
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5888]) ).
fof(f8440,plain,
( spl0_1045
| ~ spl0_1
| ~ spl0_640 ),
inference(avatar_split_clause,[],[f8114,f5884,f3203,f8437]) ).
fof(f5884,plain,
( spl0_640
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f8114,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ spl0_1
| ~ spl0_640 ),
inference(resolution,[],[f5885,f3205]) ).
fof(f5885,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) )
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f5884]) ).
fof(f8415,plain,
( spl0_1044
| ~ spl0_1
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f8113,f5880,f3203,f8412]) ).
fof(f8412,plain,
( spl0_1044
<=> class_OrderedGroup_Osemigroup__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f5880,plain,
( spl0_639
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f8113,plain,
( class_OrderedGroup_Osemigroup__mult(t_a)
| ~ spl0_1
| ~ spl0_639 ),
inference(resolution,[],[f5881,f3205]) ).
fof(f5881,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__mult(X87) )
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f5880]) ).
fof(f8390,plain,
( spl0_1043
| ~ spl0_1
| ~ spl0_638 ),
inference(avatar_split_clause,[],[f8112,f5876,f3203,f8387]) ).
fof(f8387,plain,
( spl0_1043
<=> class_Ring__and__Field_Osemiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f5876,plain,
( spl0_638
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f8112,plain,
( class_Ring__and__Field_Osemiring(t_a)
| ~ spl0_1
| ~ spl0_638 ),
inference(resolution,[],[f5877,f3205]) ).
fof(f5877,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring(X87) )
| ~ spl0_638 ),
inference(avatar_component_clause,[],[f5876]) ).
fof(f8365,plain,
( spl0_1042
| ~ spl0_1
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f8111,f5872,f3203,f8362]) ).
fof(f8362,plain,
( spl0_1042
<=> class_Ring__and__Field_Osemiring__0(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f5872,plain,
( spl0_637
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f8111,plain,
( class_Ring__and__Field_Osemiring__0(t_a)
| ~ spl0_1
| ~ spl0_637 ),
inference(resolution,[],[f5873,f3205]) ).
fof(f5873,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0(X87) )
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f5872]) ).
fof(f8344,plain,
( spl0_1041
| ~ spl0_1
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f8110,f5868,f3203,f8341]) ).
fof(f8341,plain,
( spl0_1041
<=> class_Ring__and__Field_Osemiring__0__cancel(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f5868,plain,
( spl0_636
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f8110,plain,
( class_Ring__and__Field_Osemiring__0__cancel(t_a)
| ~ spl0_1
| ~ spl0_636 ),
inference(resolution,[],[f5869,f3205]) ).
fof(f5869,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f5868]) ).
fof(f8329,plain,
( spl0_1040
| ~ spl0_1
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f8109,f5864,f3203,f8326]) ).
fof(f8326,plain,
( spl0_1040
<=> class_OrderedGroup_Oab__semigroup__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f5864,plain,
( spl0_635
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f8109,plain,
( class_OrderedGroup_Oab__semigroup__mult(t_a)
| ~ spl0_1
| ~ spl0_635 ),
inference(resolution,[],[f5865,f3205]) ).
fof(f5865,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) )
| ~ spl0_635 ),
inference(avatar_component_clause,[],[f5864]) ).
fof(f8314,plain,
( spl0_1039
| ~ spl0_1
| ~ spl0_634 ),
inference(avatar_split_clause,[],[f8108,f5860,f3203,f8311]) ).
fof(f8311,plain,
( spl0_1039
<=> class_Ring__and__Field_Oidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f5860,plain,
( spl0_634
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f8108,plain,
( class_Ring__and__Field_Oidom(t_a)
| ~ spl0_1
| ~ spl0_634 ),
inference(resolution,[],[f5861,f3205]) ).
fof(f5861,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oidom(X87) )
| ~ spl0_634 ),
inference(avatar_component_clause,[],[f5860]) ).
fof(f8257,plain,
( spl0_1038
| ~ spl0_1
| ~ spl0_633 ),
inference(avatar_split_clause,[],[f8102,f5856,f3203,f8254]) ).
fof(f8254,plain,
( spl0_1038
<=> class_Ring__and__Field_Ocomm__semiring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f5856,plain,
( spl0_633
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f8102,plain,
( class_Ring__and__Field_Ocomm__semiring(t_a)
| ~ spl0_1
| ~ spl0_633 ),
inference(resolution,[],[f5857,f3205]) ).
fof(f5857,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) )
| ~ spl0_633 ),
inference(avatar_component_clause,[],[f5856]) ).
fof(f8242,plain,
( spl0_1037
| ~ spl0_1
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f8101,f5852,f3203,f8239]) ).
fof(f8239,plain,
( spl0_1037
<=> class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f5852,plain,
( spl0_632
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f8101,plain,
( class_Ring__and__Field_Ocomm__semiring__0(t_a)
| ~ spl0_1
| ~ spl0_632 ),
inference(resolution,[],[f5853,f3205]) ).
fof(f5853,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) )
| ~ spl0_632 ),
inference(avatar_component_clause,[],[f5852]) ).
fof(f8227,plain,
( spl0_1036
| ~ spl0_1
| ~ spl0_631 ),
inference(avatar_split_clause,[],[f8100,f5848,f3203,f8224]) ).
fof(f8224,plain,
( spl0_1036
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f5848,plain,
( spl0_631
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f8100,plain,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(t_a)
| ~ spl0_1
| ~ spl0_631 ),
inference(resolution,[],[f5849,f3205]) ).
fof(f5849,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) )
| ~ spl0_631 ),
inference(avatar_component_clause,[],[f5848]) ).
fof(f8212,plain,
( spl0_1035
| ~ spl0_1
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f8099,f5844,f3203,f8209]) ).
fof(f8209,plain,
( spl0_1035
<=> class_HOL_Oone(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f5844,plain,
( spl0_630
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f8099,plain,
( class_HOL_Oone(t_a)
| ~ spl0_1
| ~ spl0_630 ),
inference(resolution,[],[f5845,f3205]) ).
fof(f5845,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oone(X87) )
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f5844]) ).
fof(f8197,plain,
( spl0_1034
| ~ spl0_1
| ~ spl0_629 ),
inference(avatar_split_clause,[],[f8098,f5840,f3203,f8194]) ).
fof(f5840,plain,
( spl0_629
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f8098,plain,
( class_OrderedGroup_Omonoid__mult(t_a)
| ~ spl0_1
| ~ spl0_629 ),
inference(resolution,[],[f5841,f3205]) ).
fof(f5841,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Omonoid__mult(X87) )
| ~ spl0_629 ),
inference(avatar_component_clause,[],[f5840]) ).
fof(f8182,plain,
( spl0_1033
| ~ spl0_1
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f8097,f5836,f3203,f8179]) ).
fof(f8179,plain,
( spl0_1033
<=> class_Ring__and__Field_Oaxclass__0__neq__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f5836,plain,
( spl0_628
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f8097,plain,
( class_Ring__and__Field_Oaxclass__0__neq__1(t_a)
| ~ spl0_1
| ~ spl0_628 ),
inference(resolution,[],[f5837,f3205]) ).
fof(f5837,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f5836]) ).
fof(f8167,plain,
( spl0_1032
| ~ spl0_1
| ~ spl0_627 ),
inference(avatar_split_clause,[],[f8096,f5832,f3203,f8164]) ).
fof(f8164,plain,
( spl0_1032
<=> class_Ring__and__Field_Osemiring__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f5832,plain,
( spl0_627
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f8096,plain,
( class_Ring__and__Field_Osemiring__1(t_a)
| ~ spl0_1
| ~ spl0_627 ),
inference(resolution,[],[f5833,f3205]) ).
fof(f5833,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1(X87) )
| ~ spl0_627 ),
inference(avatar_component_clause,[],[f5832]) ).
fof(f8152,plain,
( spl0_1031
| ~ spl0_1
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f8095,f5828,f3203,f8149]) ).
fof(f8149,plain,
( spl0_1031
<=> class_Ring__and__Field_Osemiring__1__cancel(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f5828,plain,
( spl0_626
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f8095,plain,
( class_Ring__and__Field_Osemiring__1__cancel(t_a)
| ~ spl0_1
| ~ spl0_626 ),
inference(resolution,[],[f5829,f3205]) ).
fof(f5829,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) )
| ~ spl0_626 ),
inference(avatar_component_clause,[],[f5828]) ).
fof(f8137,plain,
( spl0_1030
| ~ spl0_1
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f8094,f5824,f3203,f8134]) ).
fof(f5824,plain,
( spl0_625
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f8094,plain,
( class_OrderedGroup_Ocomm__monoid__mult(t_a)
| ~ spl0_1
| ~ spl0_625 ),
inference(resolution,[],[f5825,f3205]) ).
fof(f5825,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) )
| ~ spl0_625 ),
inference(avatar_component_clause,[],[f5824]) ).
fof(f8122,plain,
( spl0_1029
| ~ spl0_1
| ~ spl0_624 ),
inference(avatar_split_clause,[],[f8093,f5820,f3203,f8119]) ).
fof(f8119,plain,
( spl0_1029
<=> class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f5820,plain,
( spl0_624
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f8093,plain,
( class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ spl0_1
| ~ spl0_624 ),
inference(resolution,[],[f5821,f3205]) ).
fof(f5821,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) )
| ~ spl0_624 ),
inference(avatar_component_clause,[],[f5820]) ).
fof(f8107,plain,
( spl0_1028
| ~ spl0_1
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f8092,f5816,f3203,f8104]) ).
fof(f5816,plain,
( spl0_623
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ofield(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f8092,plain,
( class_Ring__and__Field_Ofield(t_a)
| ~ spl0_1
| ~ spl0_623 ),
inference(resolution,[],[f5817,f3205]) ).
fof(f5817,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ofield(X87) )
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f5816]) ).
fof(f7457,plain,
( ~ spl0_1027
| ~ spl0_130
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f7431,f3850,f3840,f7454]) ).
fof(f7454,plain,
( spl0_1027
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f3850,plain,
( spl0_132
<=> ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f7431,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_130
| ~ spl0_132 ),
inference(superposition,[],[f3851,f3842]) ).
fof(f3851,plain,
( ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f3850]) ).
fof(f7436,plain,
( ~ spl0_1026
| ~ spl0_129
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f7430,f3850,f3835,f7433]) ).
fof(f7433,plain,
( spl0_1026
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f7430,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_129
| ~ spl0_132 ),
inference(superposition,[],[f3851,f3837]) ).
fof(f7429,plain,
spl0_1025,
inference(avatar_split_clause,[],[f3030,f7426]) ).
fof(f7426,plain,
( spl0_1025
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f3030,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f380,f358]) ).
fof(f380,axiom,
! [X12] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,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(f7424,plain,
spl0_1024,
inference(avatar_split_clause,[],[f3011,f7421]) ).
fof(f7421,plain,
( spl0_1024
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3011,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f271,f268]) ).
fof(f271,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(f7419,plain,
spl0_1023,
inference(avatar_split_clause,[],[f3010,f7417]) ).
fof(f7417,plain,
( spl0_1023
<=> ! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f3010,plain,
! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat),
inference(forward_demodulation,[],[f2795,f2791]) ).
fof(f2795,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,[],[f1645,f1438]) ).
fof(f1645,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(f7415,plain,
spl0_1022,
inference(avatar_split_clause,[],[f3008,f7412]) ).
fof(f7412,plain,
( spl0_1022
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f3008,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2793,f2791]) ).
fof(f2793,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f238,f1438]) ).
fof(f238,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f7410,plain,
spl0_1021,
inference(avatar_split_clause,[],[f2780,f7408]) ).
fof(f7408,plain,
( spl0_1021
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f2780,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f7406,plain,
spl0_1020,
inference(avatar_split_clause,[],[f2779,f7404]) ).
fof(f7404,plain,
( spl0_1020
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f2779,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f7402,plain,
spl0_1019,
inference(avatar_split_clause,[],[f2778,f7400]) ).
fof(f7400,plain,
( spl0_1019
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f2778,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f7398,plain,
spl0_1018,
inference(avatar_split_clause,[],[f2777,f7396]) ).
fof(f7396,plain,
( spl0_1018
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f2777,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f7394,plain,
spl0_1017,
inference(avatar_split_clause,[],[f2776,f7392]) ).
fof(f7392,plain,
( spl0_1017
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f2776,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f7390,plain,
spl0_1016,
inference(avatar_split_clause,[],[f2775,f7388]) ).
fof(f7388,plain,
( spl0_1016
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f2775,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f7386,plain,
spl0_1015,
inference(avatar_split_clause,[],[f2774,f7384]) ).
fof(f7384,plain,
( spl0_1015
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f2774,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f7382,plain,
spl0_1014,
inference(avatar_split_clause,[],[f2773,f7380]) ).
fof(f7380,plain,
( spl0_1014
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f2773,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
fof(f7378,plain,
spl0_1013,
inference(avatar_split_clause,[],[f2772,f7376]) ).
fof(f7376,plain,
( spl0_1013
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2772,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
fof(f7374,plain,
spl0_1012,
inference(avatar_split_clause,[],[f2771,f7372]) ).
fof(f7372,plain,
( spl0_1012
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f2771,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
fof(f7370,plain,
spl0_1011,
inference(avatar_split_clause,[],[f2770,f7368]) ).
fof(f7368,plain,
( spl0_1011
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f2770,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
fof(f7366,plain,
spl0_1010,
inference(avatar_split_clause,[],[f2769,f7364]) ).
fof(f7364,plain,
( spl0_1010
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f2769,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f7362,plain,
spl0_1009,
inference(avatar_split_clause,[],[f2768,f7360]) ).
fof(f7360,plain,
( spl0_1009
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f2768,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f7358,plain,
spl0_1008,
inference(avatar_split_clause,[],[f2767,f7356]) ).
fof(f7356,plain,
( spl0_1008
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f2767,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f7354,plain,
spl0_1007,
inference(avatar_split_clause,[],[f2766,f7352]) ).
fof(f7352,plain,
( spl0_1007
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f2766,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f7350,plain,
spl0_1006,
inference(avatar_split_clause,[],[f2765,f7348]) ).
fof(f7348,plain,
( spl0_1006
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2765,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f7346,plain,
spl0_1005,
inference(avatar_split_clause,[],[f2764,f7344]) ).
fof(f7344,plain,
( spl0_1005
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2764,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f7342,plain,
spl0_1004,
inference(avatar_split_clause,[],[f2763,f7340]) ).
fof(f7340,plain,
( spl0_1004
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f2763,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
fof(f7338,plain,
spl0_1003,
inference(avatar_split_clause,[],[f2762,f7336]) ).
fof(f7336,plain,
( spl0_1003
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f2762,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
fof(f7334,plain,
spl0_1002,
inference(avatar_split_clause,[],[f2761,f7332]) ).
fof(f7332,plain,
( spl0_1002
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f2761,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f7330,plain,
spl0_1001,
inference(avatar_split_clause,[],[f2760,f7328]) ).
fof(f7328,plain,
( spl0_1001
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f2760,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f7326,plain,
spl0_1000,
inference(avatar_split_clause,[],[f2759,f7324]) ).
fof(f7324,plain,
( spl0_1000
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f2759,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f7322,plain,
spl0_999,
inference(avatar_split_clause,[],[f2758,f7320]) ).
fof(f7320,plain,
( spl0_999
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f2758,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
fof(f7318,plain,
spl0_998,
inference(avatar_split_clause,[],[f2757,f7316]) ).
fof(f7316,plain,
( spl0_998
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f2757,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
fof(f7314,plain,
spl0_997,
inference(avatar_split_clause,[],[f2756,f7312]) ).
fof(f7312,plain,
( spl0_997
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f2756,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f7310,plain,
spl0_996,
inference(avatar_split_clause,[],[f2755,f7308]) ).
fof(f7308,plain,
( spl0_996
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f2755,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
fof(f7306,plain,
spl0_995,
inference(avatar_split_clause,[],[f2754,f7304]) ).
fof(f7304,plain,
( spl0_995
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f2754,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
fof(f7302,plain,
spl0_994,
inference(avatar_split_clause,[],[f2753,f7300]) ).
fof(f7300,plain,
( spl0_994
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f2753,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f7298,plain,
spl0_993,
inference(avatar_split_clause,[],[f2752,f7296]) ).
fof(f7296,plain,
( spl0_993
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f2752,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f7294,plain,
spl0_992,
inference(avatar_split_clause,[],[f2751,f7292]) ).
fof(f7292,plain,
( spl0_992
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2751,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f7290,plain,
spl0_991,
inference(avatar_split_clause,[],[f2750,f7288]) ).
fof(f7288,plain,
( spl0_991
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f2750,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f7286,plain,
spl0_990,
inference(avatar_split_clause,[],[f2749,f7284]) ).
fof(f7284,plain,
( spl0_990
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f2749,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
fof(f7282,plain,
spl0_989,
inference(avatar_split_clause,[],[f2748,f7280]) ).
fof(f7280,plain,
( spl0_989
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f2748,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
fof(f7278,plain,
spl0_988,
inference(avatar_split_clause,[],[f2747,f7276]) ).
fof(f7276,plain,
( spl0_988
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2747,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f7274,plain,
spl0_987,
inference(avatar_split_clause,[],[f2746,f7272]) ).
fof(f7272,plain,
( spl0_987
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f2746,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f7270,plain,
spl0_986,
inference(avatar_split_clause,[],[f2745,f7268]) ).
fof(f7268,plain,
( spl0_986
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f2745,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
fof(f7266,plain,
spl0_985,
inference(avatar_split_clause,[],[f2744,f7264]) ).
fof(f7264,plain,
( spl0_985
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f2744,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
fof(f7262,plain,
spl0_984,
inference(avatar_split_clause,[],[f2743,f7260]) ).
fof(f7260,plain,
( spl0_984
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f2743,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
fof(f7258,plain,
spl0_983,
inference(avatar_split_clause,[],[f2742,f7256]) ).
fof(f7256,plain,
( spl0_983
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f2742,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
fof(f7254,plain,
spl0_982,
inference(avatar_split_clause,[],[f2741,f7252]) ).
fof(f7252,plain,
( spl0_982
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f2741,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f7250,plain,
spl0_981,
inference(avatar_split_clause,[],[f2740,f7248]) ).
fof(f7248,plain,
( spl0_981
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f2740,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
fof(f7246,plain,
spl0_980,
inference(avatar_split_clause,[],[f2739,f7244]) ).
fof(f7244,plain,
( spl0_980
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f2739,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
fof(f7242,plain,
spl0_979,
inference(avatar_split_clause,[],[f2738,f7240]) ).
fof(f7240,plain,
( spl0_979
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f2738,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f7238,plain,
spl0_978,
inference(avatar_split_clause,[],[f2737,f7236]) ).
fof(f7236,plain,
( spl0_978
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f2737,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f7234,plain,
spl0_977,
inference(avatar_split_clause,[],[f2736,f7232]) ).
fof(f7232,plain,
( spl0_977
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f2736,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f7230,plain,
spl0_976,
inference(avatar_split_clause,[],[f2735,f7228]) ).
fof(f7228,plain,
( spl0_976
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2735,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
fof(f7226,plain,
spl0_975,
inference(avatar_split_clause,[],[f2734,f7224]) ).
fof(f7224,plain,
( spl0_975
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2734,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f7222,plain,
spl0_974,
inference(avatar_split_clause,[],[f2733,f7220]) ).
fof(f7220,plain,
( spl0_974
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2733,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
fof(f7218,plain,
spl0_973,
inference(avatar_split_clause,[],[f2732,f7216]) ).
fof(f7216,plain,
( spl0_973
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2732,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
fof(f7214,plain,
spl0_972,
inference(avatar_split_clause,[],[f2731,f7212]) ).
fof(f7212,plain,
( spl0_972
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f2731,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
fof(f7210,plain,
spl0_971,
inference(avatar_split_clause,[],[f2730,f7208]) ).
fof(f7208,plain,
( spl0_971
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2730,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
fof(f7206,plain,
spl0_970,
inference(avatar_split_clause,[],[f2729,f7204]) ).
fof(f7204,plain,
( spl0_970
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2729,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
fof(f7202,plain,
spl0_969,
inference(avatar_split_clause,[],[f2728,f7200]) ).
fof(f7200,plain,
( spl0_969
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2728,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f7198,plain,
spl0_968,
inference(avatar_split_clause,[],[f2727,f7196]) ).
fof(f7196,plain,
( spl0_968
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f2727,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
fof(f7194,plain,
spl0_967,
inference(avatar_split_clause,[],[f2726,f7192]) ).
fof(f7192,plain,
( spl0_967
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f2726,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
fof(f7190,plain,
spl0_966,
inference(avatar_split_clause,[],[f2725,f7188]) ).
fof(f7188,plain,
( spl0_966
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2725,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
fof(f7186,plain,
spl0_965,
inference(avatar_split_clause,[],[f2724,f7184]) ).
fof(f7184,plain,
( spl0_965
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2724,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
fof(f7182,plain,
spl0_964,
inference(avatar_split_clause,[],[f2723,f7180]) ).
fof(f7180,plain,
( spl0_964
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2723,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
fof(f7178,plain,
spl0_963,
inference(avatar_split_clause,[],[f2722,f7176]) ).
fof(f7176,plain,
( spl0_963
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2722,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
fof(f7174,plain,
spl0_962,
inference(avatar_split_clause,[],[f2721,f7172]) ).
fof(f7172,plain,
( spl0_962
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2721,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
fof(f7170,plain,
spl0_961,
inference(avatar_split_clause,[],[f2720,f7168]) ).
fof(f7168,plain,
( spl0_961
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2720,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f7166,plain,
spl0_960,
inference(avatar_split_clause,[],[f2719,f7164]) ).
fof(f7164,plain,
( spl0_960
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2719,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f7162,plain,
spl0_959,
inference(avatar_split_clause,[],[f2718,f7160]) ).
fof(f7160,plain,
( spl0_959
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2718,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f7158,plain,
spl0_958,
inference(avatar_split_clause,[],[f2717,f7156]) ).
fof(f7156,plain,
( spl0_958
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2717,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f7154,plain,
spl0_957,
inference(avatar_split_clause,[],[f2716,f7152]) ).
fof(f7152,plain,
( spl0_957
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2716,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f7150,plain,
spl0_956,
inference(avatar_split_clause,[],[f2715,f7148]) ).
fof(f7148,plain,
( spl0_956
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2715,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
fof(f7146,plain,
spl0_955,
inference(avatar_split_clause,[],[f2714,f7144]) ).
fof(f7144,plain,
( spl0_955
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2714,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f7142,plain,
spl0_954,
inference(avatar_split_clause,[],[f2713,f7140]) ).
fof(f7140,plain,
( spl0_954
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2713,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f7138,plain,
spl0_953,
inference(avatar_split_clause,[],[f2712,f7136]) ).
fof(f7136,plain,
( spl0_953
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2712,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f7134,plain,
spl0_952,
inference(avatar_split_clause,[],[f2711,f7132]) ).
fof(f7132,plain,
( spl0_952
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2711,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f7130,plain,
spl0_951,
inference(avatar_split_clause,[],[f2710,f7128]) ).
fof(f7128,plain,
( spl0_951
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f2710,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f7126,plain,
spl0_950,
inference(avatar_split_clause,[],[f2709,f7124]) ).
fof(f7124,plain,
( spl0_950
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2709,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
fof(f7122,plain,
spl0_949,
inference(avatar_split_clause,[],[f2708,f7120]) ).
fof(f7120,plain,
( spl0_949
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2708,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
fof(f7118,plain,
spl0_948,
inference(avatar_split_clause,[],[f2707,f7116]) ).
fof(f7116,plain,
( spl0_948
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2707,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
fof(f7114,plain,
spl0_947,
inference(avatar_split_clause,[],[f2706,f7112]) ).
fof(f7112,plain,
( spl0_947
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2706,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
fof(f7110,plain,
spl0_946,
inference(avatar_split_clause,[],[f2705,f7108]) ).
fof(f7108,plain,
( spl0_946
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f2705,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f7106,plain,
spl0_945,
inference(avatar_split_clause,[],[f2704,f7104]) ).
fof(f7104,plain,
( spl0_945
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2704,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f7102,plain,
spl0_944,
inference(avatar_split_clause,[],[f2703,f7100]) ).
fof(f7100,plain,
( spl0_944
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f2703,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f7098,plain,
spl0_943,
inference(avatar_split_clause,[],[f2702,f7096]) ).
fof(f7096,plain,
( spl0_943
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f2702,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
fof(f7094,plain,
spl0_942,
inference(avatar_split_clause,[],[f2701,f7092]) ).
fof(f7092,plain,
( spl0_942
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f2701,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f7090,plain,
spl0_941,
inference(avatar_split_clause,[],[f2700,f7088]) ).
fof(f7088,plain,
( spl0_941
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f2700,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
fof(f7086,plain,
spl0_940,
inference(avatar_split_clause,[],[f2699,f7084]) ).
fof(f7084,plain,
( spl0_940
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f2699,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f7082,plain,
spl0_939,
inference(avatar_split_clause,[],[f2698,f7080]) ).
fof(f7080,plain,
( spl0_939
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f2698,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
fof(f7078,plain,
spl0_938,
inference(avatar_split_clause,[],[f2697,f7076]) ).
fof(f7076,plain,
( spl0_938
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f2697,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
fof(f7074,plain,
spl0_937,
inference(avatar_split_clause,[],[f2696,f7072]) ).
fof(f7072,plain,
( spl0_937
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f2696,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
fof(f7070,plain,
spl0_936,
inference(avatar_split_clause,[],[f2695,f7068]) ).
fof(f7068,plain,
( spl0_936
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2695,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
fof(f7066,plain,
spl0_935,
inference(avatar_split_clause,[],[f2694,f7064]) ).
fof(f7064,plain,
( spl0_935
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f2694,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f7062,plain,
spl0_934,
inference(avatar_split_clause,[],[f2693,f7060]) ).
fof(f7060,plain,
( spl0_934
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f2693,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f7058,plain,
spl0_933,
inference(avatar_split_clause,[],[f2692,f7056]) ).
fof(f7056,plain,
( spl0_933
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f2692,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f7054,plain,
spl0_932,
inference(avatar_split_clause,[],[f2691,f7052]) ).
fof(f7052,plain,
( spl0_932
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f2691,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f7050,plain,
spl0_931,
inference(avatar_split_clause,[],[f2690,f7048]) ).
fof(f7048,plain,
( spl0_931
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f2690,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
fof(f7046,plain,
spl0_930,
inference(avatar_split_clause,[],[f2689,f7044]) ).
fof(f7044,plain,
( spl0_930
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f2689,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f7042,plain,
spl0_929,
inference(avatar_split_clause,[],[f2688,f7040]) ).
fof(f7040,plain,
( spl0_929
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f2688,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f7038,plain,
spl0_928,
inference(avatar_split_clause,[],[f2687,f7036]) ).
fof(f7036,plain,
( spl0_928
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f2687,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
fof(f7034,plain,
spl0_927,
inference(avatar_split_clause,[],[f2686,f7032]) ).
fof(f7032,plain,
( spl0_927
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2686,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
fof(f7030,plain,
spl0_926,
inference(avatar_split_clause,[],[f2685,f7028]) ).
fof(f7028,plain,
( spl0_926
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2685,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
fof(f7026,plain,
spl0_925,
inference(avatar_split_clause,[],[f2684,f7024]) ).
fof(f7024,plain,
( spl0_925
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2684,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
fof(f7022,plain,
spl0_924,
inference(avatar_split_clause,[],[f2683,f7020]) ).
fof(f7020,plain,
( spl0_924
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2683,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f7018,plain,
spl0_923,
inference(avatar_split_clause,[],[f2682,f7016]) ).
fof(f7016,plain,
( spl0_923
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2682,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
fof(f7014,plain,
spl0_922,
inference(avatar_split_clause,[],[f2681,f7012]) ).
fof(f7012,plain,
( spl0_922
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f2681,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
fof(f7010,plain,
spl0_921,
inference(avatar_split_clause,[],[f2680,f7008]) ).
fof(f7008,plain,
( spl0_921
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2680,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f7006,plain,
spl0_920,
inference(avatar_split_clause,[],[f2679,f7004]) ).
fof(f7004,plain,
( spl0_920
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f2679,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f7002,plain,
spl0_919,
inference(avatar_split_clause,[],[f2678,f7000]) ).
fof(f7000,plain,
( spl0_919
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2678,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f6998,plain,
spl0_918,
inference(avatar_split_clause,[],[f2677,f6996]) ).
fof(f6996,plain,
( spl0_918
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2677,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f6994,plain,
spl0_917,
inference(avatar_split_clause,[],[f2676,f6992]) ).
fof(f6992,plain,
( spl0_917
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f2676,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
fof(f6990,plain,
spl0_916,
inference(avatar_split_clause,[],[f2675,f6988]) ).
fof(f6988,plain,
( spl0_916
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2675,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
fof(f6986,plain,
spl0_915,
inference(avatar_split_clause,[],[f2674,f6984]) ).
fof(f6984,plain,
( spl0_915
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f2674,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f6982,plain,
spl0_914,
inference(avatar_split_clause,[],[f2673,f6980]) ).
fof(f6980,plain,
( spl0_914
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2673,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f6978,plain,
spl0_913,
inference(avatar_split_clause,[],[f2672,f6976]) ).
fof(f6976,plain,
( spl0_913
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f2672,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f6974,plain,
spl0_912,
inference(avatar_split_clause,[],[f2671,f6972]) ).
fof(f6972,plain,
( spl0_912
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f2671,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f6970,plain,
spl0_911,
inference(avatar_split_clause,[],[f2670,f6968]) ).
fof(f6968,plain,
( spl0_911
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f2670,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f6966,plain,
spl0_910,
inference(avatar_split_clause,[],[f2669,f6964]) ).
fof(f6964,plain,
( spl0_910
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2669,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f6962,plain,
spl0_909,
inference(avatar_split_clause,[],[f2668,f6960]) ).
fof(f6960,plain,
( spl0_909
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2668,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f6958,plain,
spl0_908,
inference(avatar_split_clause,[],[f2667,f6956]) ).
fof(f6956,plain,
( spl0_908
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f2667,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f6954,plain,
spl0_907,
inference(avatar_split_clause,[],[f2666,f6952]) ).
fof(f6952,plain,
( spl0_907
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f2666,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
fof(f6950,plain,
spl0_906,
inference(avatar_split_clause,[],[f2665,f6948]) ).
fof(f6948,plain,
( spl0_906
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2665,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f6946,plain,
spl0_905,
inference(avatar_split_clause,[],[f2664,f6944]) ).
fof(f6944,plain,
( spl0_905
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2664,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f6942,plain,
spl0_904,
inference(avatar_split_clause,[],[f2663,f6940]) ).
fof(f6940,plain,
( spl0_904
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2663,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f6938,plain,
spl0_903,
inference(avatar_split_clause,[],[f2662,f6936]) ).
fof(f6936,plain,
( spl0_903
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2662,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f6934,plain,
spl0_902,
inference(avatar_split_clause,[],[f2661,f6932]) ).
fof(f6932,plain,
( spl0_902
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2661,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f6930,plain,
spl0_901,
inference(avatar_split_clause,[],[f2660,f6928]) ).
fof(f6928,plain,
( spl0_901
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2660,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
fof(f6926,plain,
spl0_900,
inference(avatar_split_clause,[],[f2659,f6924]) ).
fof(f6924,plain,
( spl0_900
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2659,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
fof(f6922,plain,
spl0_899,
inference(avatar_split_clause,[],[f2658,f6920]) ).
fof(f6920,plain,
( spl0_899
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2658,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
fof(f6918,plain,
spl0_898,
inference(avatar_split_clause,[],[f2657,f6916]) ).
fof(f6916,plain,
( spl0_898
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2657,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
fof(f6914,plain,
spl0_897,
inference(avatar_split_clause,[],[f2656,f6912]) ).
fof(f6912,plain,
( spl0_897
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2656,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f6910,plain,
spl0_896,
inference(avatar_split_clause,[],[f2655,f6908]) ).
fof(f6908,plain,
( spl0_896
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2655,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f6906,plain,
spl0_895,
inference(avatar_split_clause,[],[f2654,f6904]) ).
fof(f6904,plain,
( spl0_895
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2654,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f6902,plain,
spl0_894,
inference(avatar_split_clause,[],[f2653,f6900]) ).
fof(f6900,plain,
( spl0_894
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2653,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
fof(f6898,plain,
spl0_893,
inference(avatar_split_clause,[],[f2652,f6896]) ).
fof(f6896,plain,
( spl0_893
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2652,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
fof(f6894,plain,
spl0_892,
inference(avatar_split_clause,[],[f2651,f6892]) ).
fof(f6892,plain,
( spl0_892
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2651,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f6890,plain,
spl0_891,
inference(avatar_split_clause,[],[f2650,f6888]) ).
fof(f6888,plain,
( spl0_891
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2650,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
fof(f6886,plain,
spl0_890,
inference(avatar_split_clause,[],[f2649,f6884]) ).
fof(f6884,plain,
( spl0_890
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2649,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
fof(f6882,plain,
spl0_889,
inference(avatar_split_clause,[],[f2648,f6880]) ).
fof(f6880,plain,
( spl0_889
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f2648,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f6878,plain,
spl0_888,
inference(avatar_split_clause,[],[f2647,f6876]) ).
fof(f6876,plain,
( spl0_888
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2647,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f6874,plain,
spl0_887,
inference(avatar_split_clause,[],[f2646,f6872]) ).
fof(f6872,plain,
( spl0_887
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2646,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
fof(f6870,plain,
spl0_886,
inference(avatar_split_clause,[],[f2645,f6868]) ).
fof(f6868,plain,
( spl0_886
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2645,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f6866,plain,
spl0_885,
inference(avatar_split_clause,[],[f2644,f6864]) ).
fof(f6864,plain,
( spl0_885
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2644,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f6862,plain,
spl0_884,
inference(avatar_split_clause,[],[f2643,f6860]) ).
fof(f6860,plain,
( spl0_884
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2643,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f6858,plain,
spl0_883,
inference(avatar_split_clause,[],[f2642,f6856]) ).
fof(f6856,plain,
( spl0_883
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2642,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f6854,plain,
spl0_882,
inference(avatar_split_clause,[],[f2641,f6852]) ).
fof(f6852,plain,
( spl0_882
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2641,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
fof(f6850,plain,
spl0_881,
inference(avatar_split_clause,[],[f2640,f6848]) ).
fof(f6848,plain,
( spl0_881
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2640,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
fof(f6846,plain,
spl0_880,
inference(avatar_split_clause,[],[f2639,f6844]) ).
fof(f6844,plain,
( spl0_880
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2639,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f6842,plain,
spl0_879,
inference(avatar_split_clause,[],[f2638,f6840]) ).
fof(f6840,plain,
( spl0_879
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2638,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f6838,plain,
spl0_878,
inference(avatar_split_clause,[],[f2612,f6836]) ).
fof(f6836,plain,
( spl0_878
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2612,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
fof(f6834,plain,
spl0_877,
inference(avatar_split_clause,[],[f2611,f6832]) ).
fof(f6832,plain,
( spl0_877
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2611,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
fof(f6830,plain,
spl0_876,
inference(avatar_split_clause,[],[f2610,f6828]) ).
fof(f6828,plain,
( spl0_876
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2610,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f6826,plain,
spl0_875,
inference(avatar_split_clause,[],[f2609,f6824]) ).
fof(f6824,plain,
( spl0_875
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2609,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
fof(f6822,plain,
spl0_874,
inference(avatar_split_clause,[],[f2608,f6820]) ).
fof(f6820,plain,
( spl0_874
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2608,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f6818,plain,
spl0_873,
inference(avatar_split_clause,[],[f2607,f6816]) ).
fof(f6816,plain,
( spl0_873
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2607,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
fof(f6814,plain,
spl0_872,
inference(avatar_split_clause,[],[f2606,f6812]) ).
fof(f6812,plain,
( spl0_872
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2606,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
fof(f6810,plain,
spl0_871,
inference(avatar_split_clause,[],[f2605,f6808]) ).
fof(f6808,plain,
( spl0_871
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2605,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f6806,plain,
spl0_870,
inference(avatar_split_clause,[],[f2604,f6804]) ).
fof(f6804,plain,
( spl0_870
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2604,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f6802,plain,
spl0_869,
inference(avatar_split_clause,[],[f2603,f6800]) ).
fof(f6800,plain,
( spl0_869
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2603,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f6798,plain,
spl0_868,
inference(avatar_split_clause,[],[f2602,f6796]) ).
fof(f6796,plain,
( spl0_868
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2602,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f6794,plain,
spl0_867,
inference(avatar_split_clause,[],[f2601,f6792]) ).
fof(f6792,plain,
( spl0_867
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2601,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f6790,plain,
spl0_866,
inference(avatar_split_clause,[],[f2600,f6788]) ).
fof(f6788,plain,
( spl0_866
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2600,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f6786,plain,
spl0_865,
inference(avatar_split_clause,[],[f2599,f6784]) ).
fof(f6784,plain,
( spl0_865
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2599,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
fof(f6782,plain,
spl0_864,
inference(avatar_split_clause,[],[f2598,f6780]) ).
fof(f6780,plain,
( spl0_864
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2598,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f6778,plain,
spl0_863,
inference(avatar_split_clause,[],[f2597,f6776]) ).
fof(f6776,plain,
( spl0_863
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2597,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f6774,plain,
spl0_862,
inference(avatar_split_clause,[],[f2596,f6772]) ).
fof(f6772,plain,
( spl0_862
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2596,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
fof(f6770,plain,
spl0_861,
inference(avatar_split_clause,[],[f2595,f6768]) ).
fof(f6768,plain,
( spl0_861
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2595,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f6766,plain,
spl0_860,
inference(avatar_split_clause,[],[f2594,f6764]) ).
fof(f6764,plain,
( spl0_860
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2594,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
fof(f6762,plain,
spl0_859,
inference(avatar_split_clause,[],[f2593,f6760]) ).
fof(f6760,plain,
( spl0_859
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2593,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
fof(f6758,plain,
spl0_858,
inference(avatar_split_clause,[],[f2592,f6756]) ).
fof(f6756,plain,
( spl0_858
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2592,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f6754,plain,
spl0_857,
inference(avatar_split_clause,[],[f2591,f6752]) ).
fof(f6752,plain,
( spl0_857
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2591,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f6750,plain,
spl0_856,
inference(avatar_split_clause,[],[f2590,f6748]) ).
fof(f6748,plain,
( spl0_856
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2590,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
fof(f6746,plain,
spl0_855,
inference(avatar_split_clause,[],[f2589,f6744]) ).
fof(f6744,plain,
( spl0_855
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2589,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f6742,plain,
spl0_854,
inference(avatar_split_clause,[],[f2588,f6740]) ).
fof(f6740,plain,
( spl0_854
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2588,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f6738,plain,
spl0_853,
inference(avatar_split_clause,[],[f2587,f6736]) ).
fof(f6736,plain,
( spl0_853
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2587,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f6734,plain,
spl0_852,
inference(avatar_split_clause,[],[f2586,f6732]) ).
fof(f6732,plain,
( spl0_852
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f2586,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f6730,plain,
spl0_851,
inference(avatar_split_clause,[],[f2585,f6728]) ).
fof(f6728,plain,
( spl0_851
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f2585,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f6726,plain,
spl0_850,
inference(avatar_split_clause,[],[f2584,f6724]) ).
fof(f6724,plain,
( spl0_850
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f2584,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f6722,plain,
spl0_849,
inference(avatar_split_clause,[],[f2583,f6720]) ).
fof(f6720,plain,
( spl0_849
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f2583,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f6718,plain,
spl0_848,
inference(avatar_split_clause,[],[f2582,f6716]) ).
fof(f6716,plain,
( spl0_848
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f2582,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f6714,plain,
spl0_847,
inference(avatar_split_clause,[],[f2581,f6712]) ).
fof(f6712,plain,
( spl0_847
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f2581,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
fof(f6710,plain,
spl0_846,
inference(avatar_split_clause,[],[f2580,f6708]) ).
fof(f6708,plain,
( spl0_846
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f2580,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
fof(f6706,plain,
spl0_845,
inference(avatar_split_clause,[],[f2579,f6704]) ).
fof(f6704,plain,
( spl0_845
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f2579,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
fof(f6702,plain,
spl0_844,
inference(avatar_split_clause,[],[f2578,f6700]) ).
fof(f6700,plain,
( spl0_844
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2578,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f6698,plain,
spl0_843,
inference(avatar_split_clause,[],[f2577,f6696]) ).
fof(f6696,plain,
( spl0_843
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f2577,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f6694,plain,
spl0_842,
inference(avatar_split_clause,[],[f2576,f6692]) ).
fof(f6692,plain,
( spl0_842
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2576,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f6690,plain,
spl0_841,
inference(avatar_split_clause,[],[f2575,f6688]) ).
fof(f6688,plain,
( spl0_841
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f2575,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f6686,plain,
spl0_840,
inference(avatar_split_clause,[],[f2574,f6684]) ).
fof(f6684,plain,
( spl0_840
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f2574,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
fof(f6682,plain,
spl0_839,
inference(avatar_split_clause,[],[f2573,f6680]) ).
fof(f6680,plain,
( spl0_839
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f2573,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
fof(f6678,plain,
spl0_838,
inference(avatar_split_clause,[],[f2572,f6676]) ).
fof(f6676,plain,
( spl0_838
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2572,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
fof(f6674,plain,
spl0_837,
inference(avatar_split_clause,[],[f2571,f6672]) ).
fof(f6672,plain,
( spl0_837
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f2571,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
fof(f6670,plain,
spl0_836,
inference(avatar_split_clause,[],[f2570,f6668]) ).
fof(f6668,plain,
( spl0_836
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2570,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f6666,plain,
spl0_835,
inference(avatar_split_clause,[],[f2569,f6664]) ).
fof(f6664,plain,
( spl0_835
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2569,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
fof(f6662,plain,
spl0_834,
inference(avatar_split_clause,[],[f2568,f6660]) ).
fof(f6660,plain,
( spl0_834
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2568,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f6658,plain,
spl0_833,
inference(avatar_split_clause,[],[f2567,f6656]) ).
fof(f6656,plain,
( spl0_833
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2567,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f6654,plain,
spl0_832,
inference(avatar_split_clause,[],[f2566,f6652]) ).
fof(f6652,plain,
( spl0_832
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2566,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f6650,plain,
spl0_831,
inference(avatar_split_clause,[],[f2565,f6648]) ).
fof(f6648,plain,
( spl0_831
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2565,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f6646,plain,
spl0_830,
inference(avatar_split_clause,[],[f2564,f6644]) ).
fof(f6644,plain,
( spl0_830
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2564,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
fof(f6642,plain,
spl0_829,
inference(avatar_split_clause,[],[f2563,f6640]) ).
fof(f6640,plain,
( spl0_829
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2563,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f6638,plain,
spl0_828,
inference(avatar_split_clause,[],[f2562,f6636]) ).
fof(f6636,plain,
( spl0_828
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2562,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f6634,plain,
spl0_827,
inference(avatar_split_clause,[],[f2561,f6632]) ).
fof(f6632,plain,
( spl0_827
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2561,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f6630,plain,
spl0_826,
inference(avatar_split_clause,[],[f2560,f6628]) ).
fof(f6628,plain,
( spl0_826
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2560,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f6626,plain,
spl0_825,
inference(avatar_split_clause,[],[f2559,f6624]) ).
fof(f6624,plain,
( spl0_825
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2559,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f6622,plain,
spl0_824,
inference(avatar_split_clause,[],[f2558,f6620]) ).
fof(f6620,plain,
( spl0_824
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2558,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f6618,plain,
spl0_823,
inference(avatar_split_clause,[],[f2557,f6616]) ).
fof(f6616,plain,
( spl0_823
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2557,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f6614,plain,
spl0_822,
inference(avatar_split_clause,[],[f2556,f6612]) ).
fof(f6612,plain,
( spl0_822
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2556,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f6610,plain,
spl0_821,
inference(avatar_split_clause,[],[f2555,f6608]) ).
fof(f6608,plain,
( spl0_821
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2555,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f6606,plain,
spl0_820,
inference(avatar_split_clause,[],[f2554,f6604]) ).
fof(f6604,plain,
( spl0_820
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2554,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f6602,plain,
spl0_819,
inference(avatar_split_clause,[],[f2553,f6600]) ).
fof(f6600,plain,
( spl0_819
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2553,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f6598,plain,
spl0_818,
inference(avatar_split_clause,[],[f2552,f6596]) ).
fof(f6596,plain,
( spl0_818
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2552,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f6594,plain,
spl0_817,
inference(avatar_split_clause,[],[f2551,f6592]) ).
fof(f6592,plain,
( spl0_817
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2551,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f6590,plain,
spl0_816,
inference(avatar_split_clause,[],[f2550,f6588]) ).
fof(f6588,plain,
( spl0_816
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2550,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f6586,plain,
spl0_815,
inference(avatar_split_clause,[],[f2549,f6584]) ).
fof(f6584,plain,
( spl0_815
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2549,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f6582,plain,
spl0_814,
inference(avatar_split_clause,[],[f2548,f6580]) ).
fof(f6580,plain,
( spl0_814
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2548,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f6578,plain,
spl0_813,
inference(avatar_split_clause,[],[f2547,f6576]) ).
fof(f6576,plain,
( spl0_813
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2547,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f6574,plain,
spl0_812,
inference(avatar_split_clause,[],[f2546,f6572]) ).
fof(f6572,plain,
( spl0_812
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2546,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f6570,plain,
spl0_811,
inference(avatar_split_clause,[],[f2545,f6568]) ).
fof(f6568,plain,
( spl0_811
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2545,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f6566,plain,
spl0_810,
inference(avatar_split_clause,[],[f2544,f6564]) ).
fof(f6564,plain,
( spl0_810
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2544,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f6562,plain,
spl0_809,
inference(avatar_split_clause,[],[f2543,f6560]) ).
fof(f6560,plain,
( spl0_809
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f2543,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f6558,plain,
spl0_808,
inference(avatar_split_clause,[],[f2542,f6556]) ).
fof(f6556,plain,
( spl0_808
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2542,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f6554,plain,
spl0_807,
inference(avatar_split_clause,[],[f2541,f6552]) ).
fof(f6552,plain,
( spl0_807
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2541,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f6550,plain,
spl0_806,
inference(avatar_split_clause,[],[f2540,f6548]) ).
fof(f6548,plain,
( spl0_806
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2540,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f6546,plain,
spl0_805,
inference(avatar_split_clause,[],[f2539,f6544]) ).
fof(f6544,plain,
( spl0_805
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2539,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f6542,plain,
spl0_804,
inference(avatar_split_clause,[],[f2538,f6540]) ).
fof(f6540,plain,
( spl0_804
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2538,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f6538,plain,
spl0_803,
inference(avatar_split_clause,[],[f2537,f6536]) ).
fof(f6536,plain,
( spl0_803
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2537,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f6534,plain,
spl0_802,
inference(avatar_split_clause,[],[f2536,f6532]) ).
fof(f6532,plain,
( spl0_802
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2536,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f6530,plain,
spl0_801,
inference(avatar_split_clause,[],[f2535,f6528]) ).
fof(f6528,plain,
( spl0_801
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2535,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f6526,plain,
spl0_800,
inference(avatar_split_clause,[],[f2534,f6524]) ).
fof(f6524,plain,
( spl0_800
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2534,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f6522,plain,
spl0_799,
inference(avatar_split_clause,[],[f2533,f6520]) ).
fof(f6520,plain,
( spl0_799
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f2533,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f6518,plain,
spl0_798,
inference(avatar_split_clause,[],[f2532,f6516]) ).
fof(f6516,plain,
( spl0_798
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2532,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f6514,plain,
spl0_797,
inference(avatar_split_clause,[],[f2531,f6512]) ).
fof(f6512,plain,
( spl0_797
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2531,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f6510,plain,
spl0_796,
inference(avatar_split_clause,[],[f2530,f6508]) ).
fof(f6508,plain,
( spl0_796
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2530,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f6506,plain,
spl0_795,
inference(avatar_split_clause,[],[f2529,f6504]) ).
fof(f6504,plain,
( spl0_795
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2529,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f6502,plain,
spl0_794,
inference(avatar_split_clause,[],[f2528,f6500]) ).
fof(f6500,plain,
( spl0_794
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2528,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
fof(f6498,plain,
spl0_793,
inference(avatar_split_clause,[],[f2527,f6496]) ).
fof(f6496,plain,
( spl0_793
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2527,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
fof(f6494,plain,
spl0_792,
inference(avatar_split_clause,[],[f2526,f6492]) ).
fof(f6492,plain,
( spl0_792
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2526,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f6490,plain,
spl0_791,
inference(avatar_split_clause,[],[f2525,f6488]) ).
fof(f6488,plain,
( spl0_791
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2525,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
fof(f6486,plain,
spl0_790,
inference(avatar_split_clause,[],[f2524,f6484]) ).
fof(f6484,plain,
( spl0_790
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2524,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f6482,plain,
spl0_789,
inference(avatar_split_clause,[],[f2523,f6480]) ).
fof(f6480,plain,
( spl0_789
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2523,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f6478,plain,
spl0_788,
inference(avatar_split_clause,[],[f2522,f6476]) ).
fof(f6476,plain,
( spl0_788
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2522,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
fof(f6474,plain,
spl0_787,
inference(avatar_split_clause,[],[f2521,f6472]) ).
fof(f6472,plain,
( spl0_787
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f2521,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f6470,plain,
spl0_786,
inference(avatar_split_clause,[],[f2520,f6468]) ).
fof(f6468,plain,
( spl0_786
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f2520,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
fof(f6466,plain,
spl0_785,
inference(avatar_split_clause,[],[f2519,f6464]) ).
fof(f6464,plain,
( spl0_785
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f2519,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
fof(f6462,plain,
spl0_784,
inference(avatar_split_clause,[],[f2518,f6460]) ).
fof(f6460,plain,
( spl0_784
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f2518,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f6458,plain,
spl0_783,
inference(avatar_split_clause,[],[f2517,f6456]) ).
fof(f6456,plain,
( spl0_783
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f2517,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f6454,plain,
spl0_782,
inference(avatar_split_clause,[],[f2516,f6452]) ).
fof(f6452,plain,
( spl0_782
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2516,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f6450,plain,
spl0_781,
inference(avatar_split_clause,[],[f2515,f6448]) ).
fof(f6448,plain,
( spl0_781
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2515,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
fof(f6446,plain,
spl0_780,
inference(avatar_split_clause,[],[f2514,f6444]) ).
fof(f6444,plain,
( spl0_780
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2514,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f6442,plain,
spl0_779,
inference(avatar_split_clause,[],[f2513,f6440]) ).
fof(f6440,plain,
( spl0_779
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2513,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f6438,plain,
spl0_778,
inference(avatar_split_clause,[],[f2512,f6436]) ).
fof(f6436,plain,
( spl0_778
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2512,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f6434,plain,
spl0_777,
inference(avatar_split_clause,[],[f2511,f6432]) ).
fof(f6432,plain,
( spl0_777
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2511,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
fof(f6430,plain,
spl0_776,
inference(avatar_split_clause,[],[f2510,f6428]) ).
fof(f6428,plain,
( spl0_776
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f2510,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
fof(f6426,plain,
spl0_775,
inference(avatar_split_clause,[],[f2509,f6424]) ).
fof(f6424,plain,
( spl0_775
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f2509,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f6422,plain,
spl0_774,
inference(avatar_split_clause,[],[f2508,f6420]) ).
fof(f6420,plain,
( spl0_774
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f2508,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f6418,plain,
spl0_773,
inference(avatar_split_clause,[],[f2507,f6416]) ).
fof(f6416,plain,
( spl0_773
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f2507,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f6414,plain,
spl0_772,
inference(avatar_split_clause,[],[f2506,f6412]) ).
fof(f6412,plain,
( spl0_772
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f2506,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f6410,plain,
spl0_771,
inference(avatar_split_clause,[],[f2505,f6408]) ).
fof(f6408,plain,
( spl0_771
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f2505,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
fof(f6406,plain,
spl0_770,
inference(avatar_split_clause,[],[f2504,f6404]) ).
fof(f6404,plain,
( spl0_770
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2504,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f6402,plain,
spl0_769,
inference(avatar_split_clause,[],[f2503,f6400]) ).
fof(f6400,plain,
( spl0_769
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f2503,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f6398,plain,
spl0_768,
inference(avatar_split_clause,[],[f2502,f6396]) ).
fof(f6396,plain,
( spl0_768
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f2502,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f6394,plain,
spl0_767,
inference(avatar_split_clause,[],[f2501,f6392]) ).
fof(f6392,plain,
( spl0_767
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f2501,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f6390,plain,
spl0_766,
inference(avatar_split_clause,[],[f2500,f6388]) ).
fof(f6388,plain,
( spl0_766
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f2500,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f6386,plain,
spl0_765,
inference(avatar_split_clause,[],[f2499,f6384]) ).
fof(f6384,plain,
( spl0_765
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f2499,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f6382,plain,
spl0_764,
inference(avatar_split_clause,[],[f2498,f6380]) ).
fof(f6380,plain,
( spl0_764
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f2498,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f6378,plain,
spl0_763,
inference(avatar_split_clause,[],[f2497,f6376]) ).
fof(f6376,plain,
( spl0_763
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f2497,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f6374,plain,
spl0_762,
inference(avatar_split_clause,[],[f2496,f6372]) ).
fof(f6372,plain,
( spl0_762
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f2496,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f6370,plain,
spl0_761,
inference(avatar_split_clause,[],[f2495,f6368]) ).
fof(f6368,plain,
( spl0_761
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f2495,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f6366,plain,
spl0_760,
inference(avatar_split_clause,[],[f2494,f6364]) ).
fof(f6364,plain,
( spl0_760
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f2494,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f6362,plain,
spl0_759,
inference(avatar_split_clause,[],[f2493,f6360]) ).
fof(f6360,plain,
( spl0_759
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f2493,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f6358,plain,
spl0_758,
inference(avatar_split_clause,[],[f2492,f6356]) ).
fof(f6356,plain,
( spl0_758
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f2492,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f6354,plain,
spl0_757,
inference(avatar_split_clause,[],[f2491,f6352]) ).
fof(f6352,plain,
( spl0_757
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f2491,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f6350,plain,
spl0_756,
inference(avatar_split_clause,[],[f2490,f6348]) ).
fof(f6348,plain,
( spl0_756
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f2490,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f6346,plain,
spl0_755,
inference(avatar_split_clause,[],[f2489,f6344]) ).
fof(f6344,plain,
( spl0_755
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f2489,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f6342,plain,
spl0_754,
inference(avatar_split_clause,[],[f2488,f6340]) ).
fof(f6340,plain,
( spl0_754
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f2488,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f6338,plain,
spl0_753,
inference(avatar_split_clause,[],[f2487,f6336]) ).
fof(f6336,plain,
( spl0_753
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f2487,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
fof(f6334,plain,
spl0_752,
inference(avatar_split_clause,[],[f2486,f6332]) ).
fof(f6332,plain,
( spl0_752
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f2486,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f6330,plain,
spl0_751,
inference(avatar_split_clause,[],[f2485,f6328]) ).
fof(f6328,plain,
( spl0_751
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2485,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f6326,plain,
spl0_750,
inference(avatar_split_clause,[],[f2484,f6324]) ).
fof(f6324,plain,
( spl0_750
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f2484,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f6322,plain,
spl0_749,
inference(avatar_split_clause,[],[f2483,f6320]) ).
fof(f6320,plain,
( spl0_749
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f2483,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f6318,plain,
spl0_748,
inference(avatar_split_clause,[],[f2482,f6316]) ).
fof(f6316,plain,
( spl0_748
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2482,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f6314,plain,
spl0_747,
inference(avatar_split_clause,[],[f2481,f6312]) ).
fof(f6312,plain,
( spl0_747
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2481,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
fof(f6310,plain,
spl0_746,
inference(avatar_split_clause,[],[f2480,f6308]) ).
fof(f6308,plain,
( spl0_746
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2480,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
fof(f6306,plain,
spl0_745,
inference(avatar_split_clause,[],[f2479,f6304]) ).
fof(f6304,plain,
( spl0_745
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f2479,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
fof(f6302,plain,
spl0_744,
inference(avatar_split_clause,[],[f2478,f6300]) ).
fof(f6300,plain,
( spl0_744
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2478,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
fof(f6298,plain,
spl0_743,
inference(avatar_split_clause,[],[f2477,f6296]) ).
fof(f6296,plain,
( spl0_743
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2477,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f6294,plain,
spl0_742,
inference(avatar_split_clause,[],[f2476,f6292]) ).
fof(f6292,plain,
( spl0_742
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2476,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f6290,plain,
spl0_741,
inference(avatar_split_clause,[],[f2475,f6288]) ).
fof(f6288,plain,
( spl0_741
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2475,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f6286,plain,
spl0_740,
inference(avatar_split_clause,[],[f2474,f6284]) ).
fof(f6284,plain,
( spl0_740
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2474,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f6282,plain,
spl0_739,
inference(avatar_split_clause,[],[f2473,f6280]) ).
fof(f6280,plain,
( spl0_739
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2473,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f6278,plain,
spl0_738,
inference(avatar_split_clause,[],[f2472,f6276]) ).
fof(f6276,plain,
( spl0_738
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2472,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f6274,plain,
spl0_737,
inference(avatar_split_clause,[],[f2471,f6272]) ).
fof(f6272,plain,
( spl0_737
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2471,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f6270,plain,
spl0_736,
inference(avatar_split_clause,[],[f2470,f6268]) ).
fof(f6268,plain,
( spl0_736
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2470,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f6266,plain,
spl0_735,
inference(avatar_split_clause,[],[f2469,f6264]) ).
fof(f6264,plain,
( spl0_735
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2469,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
fof(f6262,plain,
spl0_734,
inference(avatar_split_clause,[],[f2468,f6260]) ).
fof(f6260,plain,
( spl0_734
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2468,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f6258,plain,
spl0_733,
inference(avatar_split_clause,[],[f2467,f6256]) ).
fof(f6256,plain,
( spl0_733
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2467,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f6254,plain,
spl0_732,
inference(avatar_split_clause,[],[f2466,f6252]) ).
fof(f6252,plain,
( spl0_732
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2466,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f6250,plain,
spl0_731,
inference(avatar_split_clause,[],[f2465,f6248]) ).
fof(f6248,plain,
( spl0_731
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2465,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f6246,plain,
spl0_730,
inference(avatar_split_clause,[],[f2464,f6244]) ).
fof(f6244,plain,
( spl0_730
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2464,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f6242,plain,
spl0_729,
inference(avatar_split_clause,[],[f2463,f6240]) ).
fof(f6240,plain,
( spl0_729
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2463,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f6238,plain,
spl0_728,
inference(avatar_split_clause,[],[f2462,f6236]) ).
fof(f6236,plain,
( spl0_728
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2462,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
fof(f6234,plain,
spl0_727,
inference(avatar_split_clause,[],[f2461,f6232]) ).
fof(f6232,plain,
( spl0_727
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2461,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f6230,plain,
spl0_726,
inference(avatar_split_clause,[],[f2460,f6228]) ).
fof(f6228,plain,
( spl0_726
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2460,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f6226,plain,
spl0_725,
inference(avatar_split_clause,[],[f2459,f6224]) ).
fof(f6224,plain,
( spl0_725
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2459,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f6222,plain,
spl0_724,
inference(avatar_split_clause,[],[f2458,f6220]) ).
fof(f6220,plain,
( spl0_724
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2458,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f6218,plain,
spl0_723,
inference(avatar_split_clause,[],[f2457,f6216]) ).
fof(f6216,plain,
( spl0_723
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2457,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f6214,plain,
spl0_722,
inference(avatar_split_clause,[],[f2456,f6212]) ).
fof(f6212,plain,
( spl0_722
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2456,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f6210,plain,
spl0_721,
inference(avatar_split_clause,[],[f2455,f6208]) ).
fof(f6208,plain,
( spl0_721
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2455,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f6206,plain,
spl0_720,
inference(avatar_split_clause,[],[f2454,f6204]) ).
fof(f6204,plain,
( spl0_720
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2454,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f6202,plain,
spl0_719,
inference(avatar_split_clause,[],[f2453,f6200]) ).
fof(f6200,plain,
( spl0_719
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2453,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f6198,plain,
spl0_718,
inference(avatar_split_clause,[],[f2452,f6196]) ).
fof(f6196,plain,
( spl0_718
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f2452,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f6194,plain,
spl0_717,
inference(avatar_split_clause,[],[f2451,f6192]) ).
fof(f6192,plain,
( spl0_717
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f2451,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f6190,plain,
spl0_716,
inference(avatar_split_clause,[],[f2450,f6188]) ).
fof(f6188,plain,
( spl0_716
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2450,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f6186,plain,
spl0_715,
inference(avatar_split_clause,[],[f2449,f6184]) ).
fof(f6184,plain,
( spl0_715
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2449,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f6182,plain,
spl0_714,
inference(avatar_split_clause,[],[f2448,f6180]) ).
fof(f6180,plain,
( spl0_714
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2448,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f6178,plain,
spl0_713,
inference(avatar_split_clause,[],[f2447,f6176]) ).
fof(f6176,plain,
( spl0_713
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2447,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f6174,plain,
spl0_712,
inference(avatar_split_clause,[],[f2446,f6172]) ).
fof(f6172,plain,
( spl0_712
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f2446,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f6170,plain,
spl0_711,
inference(avatar_split_clause,[],[f2445,f6168]) ).
fof(f6168,plain,
( spl0_711
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2445,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f6166,plain,
spl0_710,
inference(avatar_split_clause,[],[f2444,f6164]) ).
fof(f6164,plain,
( spl0_710
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f2444,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f6162,plain,
spl0_709,
inference(avatar_split_clause,[],[f2443,f6160]) ).
fof(f6160,plain,
( spl0_709
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f2443,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f6158,plain,
spl0_708,
inference(avatar_split_clause,[],[f2442,f6156]) ).
fof(f6156,plain,
( spl0_708
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f2442,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f6154,plain,
spl0_707,
inference(avatar_split_clause,[],[f2441,f6152]) ).
fof(f6152,plain,
( spl0_707
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f2441,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f6150,plain,
spl0_706,
inference(avatar_split_clause,[],[f2440,f6148]) ).
fof(f6148,plain,
( spl0_706
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f2440,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f6146,plain,
spl0_705,
inference(avatar_split_clause,[],[f2439,f6144]) ).
fof(f6144,plain,
( spl0_705
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f2439,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
fof(f6142,plain,
spl0_704,
inference(avatar_split_clause,[],[f2438,f6140]) ).
fof(f6140,plain,
( spl0_704
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2438,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
fof(f6138,plain,
spl0_703,
inference(avatar_split_clause,[],[f2437,f6136]) ).
fof(f6136,plain,
( spl0_703
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f2437,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f6134,plain,
spl0_702,
inference(avatar_split_clause,[],[f2436,f6132]) ).
fof(f6132,plain,
( spl0_702
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f2436,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
fof(f6130,plain,
spl0_701,
inference(avatar_split_clause,[],[f2435,f6128]) ).
fof(f6128,plain,
( spl0_701
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f2435,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f6126,plain,
spl0_700,
inference(avatar_split_clause,[],[f2434,f6124]) ).
fof(f6124,plain,
( spl0_700
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f2434,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
fof(f6122,plain,
spl0_699,
inference(avatar_split_clause,[],[f2433,f6120]) ).
fof(f6120,plain,
( spl0_699
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f2433,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f6118,plain,
spl0_698,
inference(avatar_split_clause,[],[f2432,f6116]) ).
fof(f6116,plain,
( spl0_698
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f2432,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
fof(f6114,plain,
spl0_697,
inference(avatar_split_clause,[],[f2431,f6112]) ).
fof(f6112,plain,
( spl0_697
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2431,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f6110,plain,
spl0_696,
inference(avatar_split_clause,[],[f2430,f6108]) ).
fof(f6108,plain,
( spl0_696
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f2430,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f6106,plain,
spl0_695,
inference(avatar_split_clause,[],[f2429,f6104]) ).
fof(f6104,plain,
( spl0_695
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2429,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f6102,plain,
spl0_694,
inference(avatar_split_clause,[],[f2428,f6100]) ).
fof(f6100,plain,
( spl0_694
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2428,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f6098,plain,
spl0_693,
inference(avatar_split_clause,[],[f2427,f6096]) ).
fof(f6096,plain,
( spl0_693
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f2427,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f6094,plain,
spl0_692,
inference(avatar_split_clause,[],[f2426,f6092]) ).
fof(f6092,plain,
( spl0_692
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f2426,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f6090,plain,
spl0_691,
inference(avatar_split_clause,[],[f2425,f6088]) ).
fof(f6088,plain,
( spl0_691
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2425,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f6086,plain,
spl0_690,
inference(avatar_split_clause,[],[f2424,f6084]) ).
fof(f6084,plain,
( spl0_690
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f2424,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f6082,plain,
spl0_689,
inference(avatar_split_clause,[],[f2423,f6080]) ).
fof(f6080,plain,
( spl0_689
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f2423,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f6078,plain,
spl0_688,
inference(avatar_split_clause,[],[f2422,f6076]) ).
fof(f6076,plain,
( spl0_688
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f2422,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f6074,plain,
spl0_687,
inference(avatar_split_clause,[],[f2421,f6072]) ).
fof(f6072,plain,
( spl0_687
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f2421,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f6070,plain,
spl0_686,
inference(avatar_split_clause,[],[f2420,f6068]) ).
fof(f6068,plain,
( spl0_686
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f2420,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f6066,plain,
spl0_685,
inference(avatar_split_clause,[],[f2419,f6064]) ).
fof(f6064,plain,
( spl0_685
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f2419,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f6062,plain,
spl0_684,
inference(avatar_split_clause,[],[f2418,f6060]) ).
fof(f6060,plain,
( spl0_684
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f2418,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f6058,plain,
spl0_683,
inference(avatar_split_clause,[],[f2417,f6056]) ).
fof(f6056,plain,
( spl0_683
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f2417,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f6054,plain,
spl0_682,
inference(avatar_split_clause,[],[f2416,f6052]) ).
fof(f2416,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_9) ).
fof(f6050,plain,
spl0_681,
inference(avatar_split_clause,[],[f2415,f6048]) ).
fof(f2415,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).
fof(f6046,plain,
spl0_680,
inference(avatar_split_clause,[],[f2414,f6044]) ).
fof(f2414,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_7) ).
fof(f6042,plain,
spl0_679,
inference(avatar_split_clause,[],[f2413,f6040]) ).
fof(f2413,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).
fof(f6038,plain,
spl0_678,
inference(avatar_split_clause,[],[f2412,f6036]) ).
fof(f2412,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).
fof(f6034,plain,
spl0_677,
inference(avatar_split_clause,[],[f2411,f6032]) ).
fof(f2411,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_59) ).
fof(f6030,plain,
spl0_676,
inference(avatar_split_clause,[],[f2410,f6028]) ).
fof(f2410,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f6026,plain,
spl0_675,
inference(avatar_split_clause,[],[f2409,f6024]) ).
fof(f2409,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_57) ).
fof(f6022,plain,
spl0_674,
inference(avatar_split_clause,[],[f2408,f6020]) ).
fof(f2408,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).
fof(f6018,plain,
spl0_673,
inference(avatar_split_clause,[],[f2407,f6016]) ).
fof(f2407,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_55) ).
fof(f6014,plain,
spl0_672,
inference(avatar_split_clause,[],[f2406,f6012]) ).
fof(f2406,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).
fof(f6010,plain,
spl0_671,
inference(avatar_split_clause,[],[f2405,f6008]) ).
fof(f2405,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).
fof(f6006,plain,
spl0_670,
inference(avatar_split_clause,[],[f2404,f6004]) ).
fof(f2404,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).
fof(f6002,plain,
spl0_669,
inference(avatar_split_clause,[],[f2403,f6000]) ).
fof(f2403,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).
fof(f5998,plain,
spl0_668,
inference(avatar_split_clause,[],[f2402,f5996]) ).
fof(f2402,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).
fof(f5994,plain,
spl0_667,
inference(avatar_split_clause,[],[f2401,f5992]) ).
fof(f2401,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_5) ).
fof(f5990,plain,
spl0_666,
inference(avatar_split_clause,[],[f2400,f5988]) ).
fof(f2400,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).
fof(f5986,plain,
spl0_665,
inference(avatar_split_clause,[],[f2399,f5984]) ).
fof(f2399,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).
fof(f5982,plain,
spl0_664,
inference(avatar_split_clause,[],[f2398,f5980]) ).
fof(f2398,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f5978,plain,
spl0_663,
inference(avatar_split_clause,[],[f2397,f5976]) ).
fof(f2397,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
fof(f5974,plain,
spl0_662,
inference(avatar_split_clause,[],[f2396,f5972]) ).
fof(f2396,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).
fof(f5970,plain,
spl0_661,
inference(avatar_split_clause,[],[f2395,f5968]) ).
fof(f2395,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_44) ).
fof(f5966,plain,
spl0_660,
inference(avatar_split_clause,[],[f2394,f5964]) ).
fof(f2394,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_43) ).
fof(f5962,plain,
spl0_659,
inference(avatar_split_clause,[],[f2393,f5960]) ).
fof(f2393,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).
fof(f5958,plain,
spl0_658,
inference(avatar_split_clause,[],[f2392,f5956]) ).
fof(f2392,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_41) ).
fof(f5954,plain,
spl0_657,
inference(avatar_split_clause,[],[f2391,f5952]) ).
fof(f2391,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).
fof(f5950,plain,
spl0_656,
inference(avatar_split_clause,[],[f2390,f5948]) ).
fof(f2390,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_4) ).
fof(f5946,plain,
spl0_655,
inference(avatar_split_clause,[],[f2389,f5944]) ).
fof(f2389,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_39) ).
fof(f5942,plain,
spl0_654,
inference(avatar_split_clause,[],[f2388,f5940]) ).
fof(f2388,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).
fof(f5938,plain,
spl0_653,
inference(avatar_split_clause,[],[f2387,f5936]) ).
fof(f2387,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).
fof(f5934,plain,
spl0_652,
inference(avatar_split_clause,[],[f2386,f5932]) ).
fof(f2386,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_36) ).
fof(f5930,plain,
spl0_651,
inference(avatar_split_clause,[],[f2385,f5928]) ).
fof(f2385,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_35) ).
fof(f5926,plain,
spl0_650,
inference(avatar_split_clause,[],[f2384,f5924]) ).
fof(f2384,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oordered__idom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f5922,plain,
spl0_649,
inference(avatar_split_clause,[],[f2383,f5920]) ).
fof(f2383,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_33) ).
fof(f5918,plain,
spl0_648,
inference(avatar_split_clause,[],[f2382,f5916]) ).
fof(f2382,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_32) ).
fof(f5914,plain,
spl0_647,
inference(avatar_split_clause,[],[f2381,f5912]) ).
fof(f2381,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).
fof(f5910,plain,
spl0_646,
inference(avatar_split_clause,[],[f2380,f5908]) ).
fof(f2380,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_30) ).
fof(f5906,plain,
spl0_645,
inference(avatar_split_clause,[],[f2379,f5904]) ).
fof(f2379,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_3) ).
fof(f5902,plain,
spl0_644,
inference(avatar_split_clause,[],[f2378,f5900]) ).
fof(f2378,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_29) ).
fof(f5898,plain,
spl0_643,
inference(avatar_split_clause,[],[f2377,f5896]) ).
fof(f2377,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_28) ).
fof(f5894,plain,
spl0_642,
inference(avatar_split_clause,[],[f2376,f5892]) ).
fof(f2376,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_27) ).
fof(f5890,plain,
spl0_641,
inference(avatar_split_clause,[],[f2375,f5888]) ).
fof(f2375,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_26) ).
fof(f5886,plain,
spl0_640,
inference(avatar_split_clause,[],[f2374,f5884]) ).
fof(f2374,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_25) ).
fof(f5882,plain,
spl0_639,
inference(avatar_split_clause,[],[f2373,f5880]) ).
fof(f2373,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_24) ).
fof(f5878,plain,
spl0_638,
inference(avatar_split_clause,[],[f2372,f5876]) ).
fof(f2372,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_23) ).
fof(f5874,plain,
spl0_637,
inference(avatar_split_clause,[],[f2371,f5872]) ).
fof(f2371,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_22) ).
fof(f5870,plain,
spl0_636,
inference(avatar_split_clause,[],[f2370,f5868]) ).
fof(f2370,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).
fof(f5866,plain,
spl0_635,
inference(avatar_split_clause,[],[f2369,f5864]) ).
fof(f2369,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).
fof(f5862,plain,
spl0_634,
inference(avatar_split_clause,[],[f2368,f5860]) ).
fof(f2368,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_2) ).
fof(f5858,plain,
spl0_633,
inference(avatar_split_clause,[],[f2367,f5856]) ).
fof(f2367,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_19) ).
fof(f5854,plain,
spl0_632,
inference(avatar_split_clause,[],[f2366,f5852]) ).
fof(f2366,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_18) ).
fof(f5850,plain,
spl0_631,
inference(avatar_split_clause,[],[f2365,f5848]) ).
fof(f2365,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_17) ).
fof(f5846,plain,
spl0_630,
inference(avatar_split_clause,[],[f2364,f5844]) ).
fof(f2364,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_16) ).
fof(f5842,plain,
spl0_629,
inference(avatar_split_clause,[],[f2363,f5840]) ).
fof(f2363,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).
fof(f5838,plain,
spl0_628,
inference(avatar_split_clause,[],[f2362,f5836]) ).
fof(f2362,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).
fof(f5834,plain,
spl0_627,
inference(avatar_split_clause,[],[f2361,f5832]) ).
fof(f2361,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_13) ).
fof(f5830,plain,
spl0_626,
inference(avatar_split_clause,[],[f2360,f5828]) ).
fof(f2360,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_12) ).
fof(f5826,plain,
spl0_625,
inference(avatar_split_clause,[],[f2359,f5824]) ).
fof(f2359,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).
fof(f5822,plain,
spl0_624,
inference(avatar_split_clause,[],[f2358,f5820]) ).
fof(f2358,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_10) ).
fof(f5818,plain,
spl0_623,
inference(avatar_split_clause,[],[f2356,f5816]) ).
fof(f2356,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__field(X87)
| class_Ring__and__Field_Ofield(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f5814,plain,
spl0_622,
inference(avatar_split_clause,[],[f2355,f5812]) ).
fof(f5812,plain,
( spl0_622
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2355,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
fof(f5810,plain,
spl0_621,
inference(avatar_split_clause,[],[f2354,f5808]) ).
fof(f5808,plain,
( spl0_621
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2354,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
fof(f5806,plain,
spl0_620,
inference(avatar_split_clause,[],[f2353,f5804]) ).
fof(f5804,plain,
( spl0_620
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2353,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f5802,plain,
spl0_619,
inference(avatar_split_clause,[],[f2352,f5800]) ).
fof(f5800,plain,
( spl0_619
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2352,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
fof(f5798,plain,
spl0_618,
inference(avatar_split_clause,[],[f2351,f5796]) ).
fof(f5796,plain,
( spl0_618
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2351,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
fof(f5794,plain,
spl0_617,
inference(avatar_split_clause,[],[f2350,f5792]) ).
fof(f5792,plain,
( spl0_617
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2350,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f5790,plain,
spl0_616,
inference(avatar_split_clause,[],[f2349,f5788]) ).
fof(f5788,plain,
( spl0_616
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2349,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f5786,plain,
spl0_615,
inference(avatar_split_clause,[],[f2348,f5784]) ).
fof(f5784,plain,
( spl0_615
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2348,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f5782,plain,
spl0_614,
inference(avatar_split_clause,[],[f2347,f5780]) ).
fof(f5780,plain,
( spl0_614
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2347,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f5778,plain,
spl0_613,
inference(avatar_split_clause,[],[f2346,f5776]) ).
fof(f5776,plain,
( spl0_613
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2346,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f5774,plain,
spl0_612,
inference(avatar_split_clause,[],[f2345,f5772]) ).
fof(f5772,plain,
( spl0_612
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2345,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f5770,plain,
spl0_611,
inference(avatar_split_clause,[],[f2344,f5768]) ).
fof(f5768,plain,
( spl0_611
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2344,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f5766,plain,
spl0_610,
inference(avatar_split_clause,[],[f2343,f5764]) ).
fof(f5764,plain,
( spl0_610
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2343,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f5762,plain,
spl0_609,
inference(avatar_split_clause,[],[f2342,f5760]) ).
fof(f5760,plain,
( spl0_609
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2342,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f5758,plain,
spl0_608,
inference(avatar_split_clause,[],[f2341,f5756]) ).
fof(f5756,plain,
( spl0_608
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2341,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f5754,plain,
spl0_607,
inference(avatar_split_clause,[],[f2340,f5752]) ).
fof(f5752,plain,
( spl0_607
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2340,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f5750,plain,
spl0_606,
inference(avatar_split_clause,[],[f2339,f5748]) ).
fof(f5748,plain,
( spl0_606
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2339,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f5746,plain,
spl0_605,
inference(avatar_split_clause,[],[f2338,f5744]) ).
fof(f5744,plain,
( spl0_605
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2338,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
fof(f5742,plain,
spl0_604,
inference(avatar_split_clause,[],[f2337,f5740]) ).
fof(f5740,plain,
( spl0_604
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2337,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f5738,plain,
spl0_603,
inference(avatar_split_clause,[],[f2336,f5736]) ).
fof(f5736,plain,
( spl0_603
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2336,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f5734,plain,
spl0_602,
inference(avatar_split_clause,[],[f2335,f5732]) ).
fof(f5732,plain,
( spl0_602
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2335,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f5730,plain,
spl0_601,
inference(avatar_split_clause,[],[f2334,f5728]) ).
fof(f5728,plain,
( spl0_601
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2334,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f5726,plain,
spl0_600,
inference(avatar_split_clause,[],[f2333,f5724]) ).
fof(f5724,plain,
( spl0_600
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2333,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f5722,plain,
spl0_599,
inference(avatar_split_clause,[],[f2332,f5720]) ).
fof(f5720,plain,
( spl0_599
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2332,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f5718,plain,
spl0_598,
inference(avatar_split_clause,[],[f2331,f5716]) ).
fof(f5716,plain,
( spl0_598
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2331,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f5714,plain,
spl0_597,
inference(avatar_split_clause,[],[f2330,f5712]) ).
fof(f5712,plain,
( spl0_597
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2330,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f5710,plain,
spl0_596,
inference(avatar_split_clause,[],[f2329,f5708]) ).
fof(f5708,plain,
( spl0_596
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2329,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
fof(f5706,plain,
spl0_595,
inference(avatar_split_clause,[],[f2328,f5704]) ).
fof(f5704,plain,
( spl0_595
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2328,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
fof(f5702,plain,
spl0_594,
inference(avatar_split_clause,[],[f2327,f5700]) ).
fof(f5700,plain,
( spl0_594
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2327,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f5698,plain,
spl0_593,
inference(avatar_split_clause,[],[f2326,f5696]) ).
fof(f5696,plain,
( spl0_593
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2326,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f5694,plain,
spl0_592,
inference(avatar_split_clause,[],[f2325,f5692]) ).
fof(f5692,plain,
( spl0_592
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2325,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f5690,plain,
spl0_591,
inference(avatar_split_clause,[],[f2324,f5688]) ).
fof(f5688,plain,
( spl0_591
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2324,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f5686,plain,
spl0_590,
inference(avatar_split_clause,[],[f2323,f5684]) ).
fof(f5684,plain,
( spl0_590
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2323,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f5682,plain,
spl0_589,
inference(avatar_split_clause,[],[f2322,f5680]) ).
fof(f5680,plain,
( spl0_589
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2322,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f5678,plain,
spl0_588,
inference(avatar_split_clause,[],[f2321,f5676]) ).
fof(f5676,plain,
( spl0_588
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2321,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f5674,plain,
spl0_587,
inference(avatar_split_clause,[],[f2320,f5672]) ).
fof(f5672,plain,
( spl0_587
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2320,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
fof(f5670,plain,
spl0_586,
inference(avatar_split_clause,[],[f2319,f5668]) ).
fof(f5668,plain,
( spl0_586
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2319,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f5666,plain,
spl0_585,
inference(avatar_split_clause,[],[f2318,f5664]) ).
fof(f5664,plain,
( spl0_585
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2318,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f5662,plain,
spl0_584,
inference(avatar_split_clause,[],[f2317,f5660]) ).
fof(f5660,plain,
( spl0_584
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2317,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f5658,plain,
spl0_583,
inference(avatar_split_clause,[],[f2316,f5656]) ).
fof(f5656,plain,
( spl0_583
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2316,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f5654,plain,
spl0_582,
inference(avatar_split_clause,[],[f2315,f5652]) ).
fof(f5652,plain,
( spl0_582
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2315,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f5650,plain,
spl0_581,
inference(avatar_split_clause,[],[f2314,f5648]) ).
fof(f5648,plain,
( spl0_581
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2314,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f5646,plain,
spl0_580,
inference(avatar_split_clause,[],[f2313,f5644]) ).
fof(f5644,plain,
( spl0_580
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2313,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f5642,plain,
spl0_579,
inference(avatar_split_clause,[],[f2312,f5640]) ).
fof(f5640,plain,
( spl0_579
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2312,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f5638,plain,
spl0_578,
inference(avatar_split_clause,[],[f2311,f5636]) ).
fof(f5636,plain,
( spl0_578
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2311,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
fof(f5634,plain,
spl0_577,
inference(avatar_split_clause,[],[f2310,f5632]) ).
fof(f5632,plain,
( spl0_577
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2310,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
fof(f5630,plain,
spl0_576,
inference(avatar_split_clause,[],[f2309,f5628]) ).
fof(f5628,plain,
( spl0_576
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2309,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f5626,plain,
spl0_575,
inference(avatar_split_clause,[],[f2308,f5624]) ).
fof(f5624,plain,
( spl0_575
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2308,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
fof(f5622,plain,
spl0_574,
inference(avatar_split_clause,[],[f2307,f5620]) ).
fof(f5620,plain,
( spl0_574
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2307,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f5618,plain,
spl0_573,
inference(avatar_split_clause,[],[f2306,f5616]) ).
fof(f5616,plain,
( spl0_573
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2306,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f5614,plain,
spl0_572,
inference(avatar_split_clause,[],[f2305,f5612]) ).
fof(f5612,plain,
( spl0_572
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2305,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
fof(f5610,plain,
spl0_571,
inference(avatar_split_clause,[],[f2304,f5608]) ).
fof(f5608,plain,
( spl0_571
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2304,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f5606,plain,
spl0_570,
inference(avatar_split_clause,[],[f2303,f5604]) ).
fof(f5604,plain,
( spl0_570
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2303,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
fof(f5602,plain,
spl0_569,
inference(avatar_split_clause,[],[f2302,f5600]) ).
fof(f5600,plain,
( spl0_569
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2302,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
fof(f5598,plain,
spl0_568,
inference(avatar_split_clause,[],[f2301,f5596]) ).
fof(f5596,plain,
( spl0_568
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2301,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f5594,plain,
spl0_567,
inference(avatar_split_clause,[],[f2300,f5592]) ).
fof(f5592,plain,
( spl0_567
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2300,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f5590,plain,
spl0_566,
inference(avatar_split_clause,[],[f2299,f5588]) ).
fof(f5588,plain,
( spl0_566
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2299,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f5586,plain,
spl0_565,
inference(avatar_split_clause,[],[f2298,f5584]) ).
fof(f5584,plain,
( spl0_565
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2298,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f5582,plain,
spl0_564,
inference(avatar_split_clause,[],[f2297,f5580]) ).
fof(f5580,plain,
( spl0_564
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2297,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f5578,plain,
spl0_563,
inference(avatar_split_clause,[],[f2296,f5576]) ).
fof(f5576,plain,
( spl0_563
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2296,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f5574,plain,
spl0_562,
inference(avatar_split_clause,[],[f2295,f5572]) ).
fof(f5572,plain,
( spl0_562
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2295,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f5570,plain,
spl0_561,
inference(avatar_split_clause,[],[f2294,f5568]) ).
fof(f5568,plain,
( spl0_561
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2294,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f5566,plain,
spl0_560,
inference(avatar_split_clause,[],[f2293,f5564]) ).
fof(f5564,plain,
( spl0_560
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2293,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f5562,plain,
spl0_559,
inference(avatar_split_clause,[],[f2292,f5560]) ).
fof(f5560,plain,
( spl0_559
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2292,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f5558,plain,
spl0_558,
inference(avatar_split_clause,[],[f2291,f5556]) ).
fof(f5556,plain,
( spl0_558
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2291,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f5554,plain,
spl0_557,
inference(avatar_split_clause,[],[f2290,f5552]) ).
fof(f5552,plain,
( spl0_557
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2290,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
fof(f5550,plain,
spl0_556,
inference(avatar_split_clause,[],[f2289,f5548]) ).
fof(f5548,plain,
( spl0_556
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2289,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f5546,plain,
spl0_555,
inference(avatar_split_clause,[],[f2288,f5544]) ).
fof(f5544,plain,
( spl0_555
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2288,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
fof(f5542,plain,
spl0_554,
inference(avatar_split_clause,[],[f2287,f5540]) ).
fof(f5540,plain,
( spl0_554
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2287,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f5538,plain,
spl0_553,
inference(avatar_split_clause,[],[f2286,f5536]) ).
fof(f5536,plain,
( spl0_553
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2286,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
fof(f5534,plain,
spl0_552,
inference(avatar_split_clause,[],[f2285,f5532]) ).
fof(f5532,plain,
( spl0_552
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2285,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
fof(f5530,plain,
spl0_551,
inference(avatar_split_clause,[],[f2284,f5528]) ).
fof(f5528,plain,
( spl0_551
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2284,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f5526,plain,
spl0_550,
inference(avatar_split_clause,[],[f2283,f5524]) ).
fof(f5524,plain,
( spl0_550
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2283,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
fof(f5522,plain,
spl0_549,
inference(avatar_split_clause,[],[f2282,f5520]) ).
fof(f5520,plain,
( spl0_549
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2282,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f5518,plain,
spl0_548,
inference(avatar_split_clause,[],[f2281,f5516]) ).
fof(f5516,plain,
( spl0_548
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2281,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
fof(f5514,plain,
spl0_547,
inference(avatar_split_clause,[],[f2280,f5512]) ).
fof(f5512,plain,
( spl0_547
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2280,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f5510,plain,
spl0_546,
inference(avatar_split_clause,[],[f2279,f5508]) ).
fof(f5508,plain,
( spl0_546
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2279,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
fof(f5506,plain,
spl0_545,
inference(avatar_split_clause,[],[f2278,f5504]) ).
fof(f5504,plain,
( spl0_545
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2278,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
fof(f5502,plain,
spl0_544,
inference(avatar_split_clause,[],[f2277,f5500]) ).
fof(f5500,plain,
( spl0_544
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2277,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f5498,plain,
spl0_543,
inference(avatar_split_clause,[],[f2276,f5496]) ).
fof(f5496,plain,
( spl0_543
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2276,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f5494,plain,
spl0_542,
inference(avatar_split_clause,[],[f2275,f5492]) ).
fof(f5492,plain,
( spl0_542
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2275,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f5490,plain,
spl0_541,
inference(avatar_split_clause,[],[f2274,f5488]) ).
fof(f5488,plain,
( spl0_541
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2274,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f5486,plain,
spl0_540,
inference(avatar_split_clause,[],[f2273,f5484]) ).
fof(f5484,plain,
( spl0_540
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2273,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
fof(f5482,plain,
spl0_539,
inference(avatar_split_clause,[],[f2272,f5480]) ).
fof(f5480,plain,
( spl0_539
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2272,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f5478,plain,
spl0_538,
inference(avatar_split_clause,[],[f2271,f5476]) ).
fof(f5476,plain,
( spl0_538
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2271,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f5474,plain,
spl0_537,
inference(avatar_split_clause,[],[f2270,f5472]) ).
fof(f5472,plain,
( spl0_537
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2270,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f5470,plain,
spl0_536,
inference(avatar_split_clause,[],[f2269,f5468]) ).
fof(f5468,plain,
( spl0_536
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2269,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f5466,plain,
spl0_535,
inference(avatar_split_clause,[],[f2268,f5464]) ).
fof(f5464,plain,
( spl0_535
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2268,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f5462,plain,
spl0_534,
inference(avatar_split_clause,[],[f2267,f5460]) ).
fof(f5460,plain,
( spl0_534
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2267,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f5458,plain,
spl0_533,
inference(avatar_split_clause,[],[f2266,f5456]) ).
fof(f5456,plain,
( spl0_533
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2266,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f5454,plain,
spl0_532,
inference(avatar_split_clause,[],[f2265,f5452]) ).
fof(f5452,plain,
( spl0_532
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2265,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f5450,plain,
spl0_531,
inference(avatar_split_clause,[],[f2264,f5448]) ).
fof(f5448,plain,
( spl0_531
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2264,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f5446,plain,
spl0_530,
inference(avatar_split_clause,[],[f2263,f5444]) ).
fof(f5444,plain,
( spl0_530
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2263,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_9) ).
fof(f5442,plain,
spl0_529,
inference(avatar_split_clause,[],[f2262,f5440]) ).
fof(f5440,plain,
( spl0_529
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2262,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
fof(f5438,plain,
spl0_528,
inference(avatar_split_clause,[],[f2261,f5436]) ).
fof(f5436,plain,
( spl0_528
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2261,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_7) ).
fof(f5434,plain,
spl0_527,
inference(avatar_split_clause,[],[f2260,f5432]) ).
fof(f5432,plain,
( spl0_527
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2260,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_6) ).
fof(f5430,plain,
spl0_526,
inference(avatar_split_clause,[],[f2259,f5428]) ).
fof(f5428,plain,
( spl0_526
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2259,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
fof(f5426,plain,
spl0_525,
inference(avatar_split_clause,[],[f2258,f5424]) ).
fof(f5424,plain,
( spl0_525
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2258,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_4) ).
fof(f5422,plain,
spl0_524,
inference(avatar_split_clause,[],[f2257,f5420]) ).
fof(f5420,plain,
( spl0_524
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2257,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
fof(f5418,plain,
spl0_523,
inference(avatar_split_clause,[],[f2256,f5416]) ).
fof(f5416,plain,
( spl0_523
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2256,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_31) ).
fof(f5414,plain,
spl0_522,
inference(avatar_split_clause,[],[f2254,f5412]) ).
fof(f5412,plain,
( spl0_522
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2254,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_3) ).
fof(f5410,plain,
spl0_521,
inference(avatar_split_clause,[],[f2253,f5408]) ).
fof(f5408,plain,
( spl0_521
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2253,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_29) ).
fof(f5406,plain,
spl0_520,
inference(avatar_split_clause,[],[f2252,f5404]) ).
fof(f5404,plain,
( spl0_520
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2252,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_28) ).
fof(f5402,plain,
spl0_519,
inference(avatar_split_clause,[],[f2251,f5400]) ).
fof(f5400,plain,
( spl0_519
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2251,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_27) ).
fof(f5398,plain,
spl0_518,
inference(avatar_split_clause,[],[f2250,f5396]) ).
fof(f5396,plain,
( spl0_518
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2250,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_26) ).
fof(f5394,plain,
spl0_517,
inference(avatar_split_clause,[],[f2249,f5392]) ).
fof(f5392,plain,
( spl0_517
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2249,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_25) ).
fof(f5390,plain,
spl0_516,
inference(avatar_split_clause,[],[f2248,f5388]) ).
fof(f5388,plain,
( spl0_516
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2248,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_24) ).
fof(f5386,plain,
spl0_515,
inference(avatar_split_clause,[],[f2247,f5384]) ).
fof(f5384,plain,
( spl0_515
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2247,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_23) ).
fof(f5382,plain,
spl0_514,
inference(avatar_split_clause,[],[f2246,f5380]) ).
fof(f5380,plain,
( spl0_514
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2246,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_22) ).
fof(f5378,plain,
spl0_513,
inference(avatar_split_clause,[],[f2245,f5376]) ).
fof(f5376,plain,
( spl0_513
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2245,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f5374,plain,
spl0_512,
inference(avatar_split_clause,[],[f2244,f5372]) ).
fof(f5372,plain,
( spl0_512
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2244,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_20) ).
fof(f5370,plain,
spl0_511,
inference(avatar_split_clause,[],[f2243,f5368]) ).
fof(f5368,plain,
( spl0_511
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2243,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_2) ).
fof(f5366,plain,
spl0_510,
inference(avatar_split_clause,[],[f2242,f5364]) ).
fof(f5364,plain,
( spl0_510
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2242,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_19) ).
fof(f5362,plain,
spl0_509,
inference(avatar_split_clause,[],[f2241,f5360]) ).
fof(f5360,plain,
( spl0_509
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2241,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
fof(f5358,plain,
spl0_508,
inference(avatar_split_clause,[],[f2240,f5356]) ).
fof(f5356,plain,
( spl0_508
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2240,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
fof(f5354,plain,
spl0_507,
inference(avatar_split_clause,[],[f2239,f5352]) ).
fof(f5352,plain,
( spl0_507
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2239,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_16) ).
fof(f5350,plain,
spl0_506,
inference(avatar_split_clause,[],[f2238,f5348]) ).
fof(f5348,plain,
( spl0_506
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2238,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_15) ).
fof(f5346,plain,
spl0_505,
inference(avatar_split_clause,[],[f2237,f5344]) ).
fof(f5344,plain,
( spl0_505
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2237,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_14) ).
fof(f5342,plain,
spl0_504,
inference(avatar_split_clause,[],[f2236,f5340]) ).
fof(f5340,plain,
( spl0_504
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2236,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_13) ).
fof(f5338,plain,
spl0_503,
inference(avatar_split_clause,[],[f2235,f5336]) ).
fof(f5336,plain,
( spl0_503
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2235,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
fof(f5334,plain,
spl0_502,
inference(avatar_split_clause,[],[f2234,f5332]) ).
fof(f5332,plain,
( spl0_502
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2234,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
fof(f5330,plain,
spl0_501,
inference(avatar_split_clause,[],[f2233,f5328]) ).
fof(f5328,plain,
( spl0_501
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2233,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_10) ).
fof(f5326,plain,
spl0_500,
inference(avatar_split_clause,[],[f2232,f5324]) ).
fof(f5324,plain,
( spl0_500
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2232,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_1) ).
fof(f5322,plain,
spl0_499,
inference(avatar_split_clause,[],[f2231,f5320]) ).
fof(f5320,plain,
( spl0_499
<=> ! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2231,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ofield(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_0) ).
fof(f5318,plain,
spl0_498,
inference(avatar_split_clause,[],[f2228,f5316]) ).
fof(f5316,plain,
( spl0_498
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2228,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f5314,plain,
spl0_497,
inference(avatar_split_clause,[],[f2227,f5312]) ).
fof(f5312,plain,
( spl0_497
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2227,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f5310,plain,
spl0_496,
inference(avatar_split_clause,[],[f2226,f5308]) ).
fof(f5308,plain,
( spl0_496
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2226,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f5306,plain,
spl0_495,
inference(avatar_split_clause,[],[f2225,f5304]) ).
fof(f5304,plain,
( spl0_495
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2225,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f5302,plain,
spl0_494,
inference(avatar_split_clause,[],[f2224,f5300]) ).
fof(f5300,plain,
( spl0_494
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2224,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f5298,plain,
spl0_493,
inference(avatar_split_clause,[],[f2223,f5296]) ).
fof(f5296,plain,
( spl0_493
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2223,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
fof(f5294,plain,
spl0_492,
inference(avatar_split_clause,[],[f2222,f5292]) ).
fof(f5292,plain,
( spl0_492
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2222,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f5290,plain,
spl0_491,
inference(avatar_split_clause,[],[f2221,f5288]) ).
fof(f5288,plain,
( spl0_491
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2221,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f5286,plain,
spl0_490,
inference(avatar_split_clause,[],[f2220,f5284]) ).
fof(f5284,plain,
( spl0_490
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2220,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f5282,plain,
spl0_489,
inference(avatar_split_clause,[],[f2219,f5280]) ).
fof(f5280,plain,
( spl0_489
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2219,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f5278,plain,
spl0_488,
inference(avatar_split_clause,[],[f2218,f5276]) ).
fof(f5276,plain,
( spl0_488
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2218,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f5274,plain,
spl0_487,
inference(avatar_split_clause,[],[f2217,f5272]) ).
fof(f5272,plain,
( spl0_487
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2217,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f5270,plain,
spl0_486,
inference(avatar_split_clause,[],[f2216,f5268]) ).
fof(f5268,plain,
( spl0_486
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2216,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f5266,plain,
spl0_485,
inference(avatar_split_clause,[],[f2215,f5264]) ).
fof(f5264,plain,
( spl0_485
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2215,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
fof(f5262,plain,
spl0_484,
inference(avatar_split_clause,[],[f2214,f5260]) ).
fof(f5260,plain,
( spl0_484
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2214,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
fof(f5258,plain,
spl0_483,
inference(avatar_split_clause,[],[f2213,f5256]) ).
fof(f5256,plain,
( spl0_483
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2213,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f5254,plain,
spl0_482,
inference(avatar_split_clause,[],[f2212,f5252]) ).
fof(f5252,plain,
( spl0_482
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2212,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f5250,plain,
spl0_481,
inference(avatar_split_clause,[],[f2211,f5248]) ).
fof(f5248,plain,
( spl0_481
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2211,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
fof(f5246,plain,
spl0_480,
inference(avatar_split_clause,[],[f2210,f5244]) ).
fof(f5244,plain,
( spl0_480
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2210,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
fof(f5242,plain,
spl0_479,
inference(avatar_split_clause,[],[f2209,f5240]) ).
fof(f5240,plain,
( spl0_479
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2209,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
fof(f5238,plain,
spl0_478,
inference(avatar_split_clause,[],[f2208,f5236]) ).
fof(f5236,plain,
( spl0_478
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2208,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
fof(f5234,plain,
spl0_477,
inference(avatar_split_clause,[],[f2207,f5232]) ).
fof(f5232,plain,
( spl0_477
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2207,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f5230,plain,
spl0_476,
inference(avatar_split_clause,[],[f2206,f5228]) ).
fof(f5228,plain,
( spl0_476
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2206,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f5226,plain,
spl0_475,
inference(avatar_split_clause,[],[f2205,f5224]) ).
fof(f5224,plain,
( spl0_475
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2205,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
fof(f5222,plain,
spl0_474,
inference(avatar_split_clause,[],[f2204,f5220]) ).
fof(f5220,plain,
( spl0_474
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2204,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
fof(f5218,plain,
spl0_473,
inference(avatar_split_clause,[],[f2203,f5216]) ).
fof(f5216,plain,
( spl0_473
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2203,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f5214,plain,
spl0_472,
inference(avatar_split_clause,[],[f2202,f5212]) ).
fof(f5212,plain,
( spl0_472
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2202,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f5210,plain,
spl0_471,
inference(avatar_split_clause,[],[f2201,f5208]) ).
fof(f5208,plain,
( spl0_471
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2201,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
fof(f5206,plain,
spl0_470,
inference(avatar_split_clause,[],[f2200,f5204]) ).
fof(f5204,plain,
( spl0_470
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2200,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f5202,plain,
spl0_469,
inference(avatar_split_clause,[],[f2199,f5200]) ).
fof(f5200,plain,
( spl0_469
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2199,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f5198,plain,
spl0_468,
inference(avatar_split_clause,[],[f2198,f5196]) ).
fof(f5196,plain,
( spl0_468
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2198,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f5194,plain,
spl0_467,
inference(avatar_split_clause,[],[f2197,f5192]) ).
fof(f5192,plain,
( spl0_467
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2197,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f5190,plain,
spl0_466,
inference(avatar_split_clause,[],[f2196,f5188]) ).
fof(f5188,plain,
( spl0_466
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2196,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f5186,plain,
spl0_465,
inference(avatar_split_clause,[],[f2195,f5184]) ).
fof(f5184,plain,
( spl0_465
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2195,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f5182,plain,
spl0_464,
inference(avatar_split_clause,[],[f2194,f5180]) ).
fof(f5180,plain,
( spl0_464
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2194,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
fof(f5178,plain,
spl0_463,
inference(avatar_split_clause,[],[f2193,f5176]) ).
fof(f5176,plain,
( spl0_463
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2193,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
fof(f5174,plain,
spl0_462,
inference(avatar_split_clause,[],[f2192,f5172]) ).
fof(f5172,plain,
( spl0_462
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2192,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
fof(f5170,plain,
spl0_461,
inference(avatar_split_clause,[],[f2191,f5168]) ).
fof(f5168,plain,
( spl0_461
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2191,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f5166,plain,
spl0_460,
inference(avatar_split_clause,[],[f2190,f5164]) ).
fof(f5164,plain,
( spl0_460
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2190,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
fof(f5162,plain,
spl0_459,
inference(avatar_split_clause,[],[f2189,f5160]) ).
fof(f5160,plain,
( spl0_459
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2189,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f5158,plain,
spl0_458,
inference(avatar_split_clause,[],[f2188,f5156]) ).
fof(f5156,plain,
( spl0_458
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2188,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
fof(f5154,plain,
spl0_457,
inference(avatar_split_clause,[],[f2187,f5152]) ).
fof(f5152,plain,
( spl0_457
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2187,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
fof(f5150,plain,
spl0_456,
inference(avatar_split_clause,[],[f2186,f5148]) ).
fof(f5148,plain,
( spl0_456
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2186,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f5146,plain,
spl0_455,
inference(avatar_split_clause,[],[f2185,f5144]) ).
fof(f5144,plain,
( spl0_455
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2185,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
fof(f5142,plain,
spl0_454,
inference(avatar_split_clause,[],[f2184,f5140]) ).
fof(f5140,plain,
( spl0_454
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2184,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
fof(f5138,plain,
spl0_453,
inference(avatar_split_clause,[],[f2183,f5136]) ).
fof(f5136,plain,
( spl0_453
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2183,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f5134,plain,
spl0_452,
inference(avatar_split_clause,[],[f2182,f5132]) ).
fof(f5132,plain,
( spl0_452
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2182,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f5130,plain,
spl0_451,
inference(avatar_split_clause,[],[f2181,f5128]) ).
fof(f5128,plain,
( spl0_451
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2181,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
fof(f5126,plain,
spl0_450,
inference(avatar_split_clause,[],[f2180,f5124]) ).
fof(f5124,plain,
( spl0_450
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2180,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f5122,plain,
spl0_449,
inference(avatar_split_clause,[],[f2179,f5120]) ).
fof(f5120,plain,
( spl0_449
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2179,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f5118,plain,
spl0_448,
inference(avatar_split_clause,[],[f2178,f5116]) ).
fof(f5116,plain,
( spl0_448
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2178,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f5114,plain,
spl0_447,
inference(avatar_split_clause,[],[f2177,f5112]) ).
fof(f5112,plain,
( spl0_447
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2177,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
fof(f5110,plain,
spl0_446,
inference(avatar_split_clause,[],[f2176,f5108]) ).
fof(f5108,plain,
( spl0_446
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2176,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
fof(f5106,plain,
spl0_445,
inference(avatar_split_clause,[],[f2175,f5104]) ).
fof(f5104,plain,
( spl0_445
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2175,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f5102,plain,
spl0_444,
inference(avatar_split_clause,[],[f2174,f5100]) ).
fof(f5100,plain,
( spl0_444
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2174,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f5098,plain,
spl0_443,
inference(avatar_split_clause,[],[f2173,f5096]) ).
fof(f5096,plain,
( spl0_443
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2173,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
fof(f5094,plain,
spl0_442,
inference(avatar_split_clause,[],[f2172,f5092]) ).
fof(f5092,plain,
( spl0_442
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2172,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f5090,plain,
spl0_441,
inference(avatar_split_clause,[],[f2171,f5088]) ).
fof(f5088,plain,
( spl0_441
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2171,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
fof(f5086,plain,
spl0_440,
inference(avatar_split_clause,[],[f2170,f5084]) ).
fof(f5084,plain,
( spl0_440
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2170,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
fof(f5082,plain,
spl0_439,
inference(avatar_split_clause,[],[f2169,f5080]) ).
fof(f5080,plain,
( spl0_439
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2169,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
fof(f5078,plain,
spl0_438,
inference(avatar_split_clause,[],[f2168,f5076]) ).
fof(f5076,plain,
( spl0_438
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2168,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
fof(f5074,plain,
spl0_437,
inference(avatar_split_clause,[],[f2167,f5072]) ).
fof(f5072,plain,
( spl0_437
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2167,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
fof(f5070,plain,
spl0_436,
inference(avatar_split_clause,[],[f2166,f5068]) ).
fof(f5068,plain,
( spl0_436
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2166,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f5066,plain,
spl0_435,
inference(avatar_split_clause,[],[f2165,f5064]) ).
fof(f5064,plain,
( spl0_435
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2165,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f5062,plain,
spl0_434,
inference(avatar_split_clause,[],[f2164,f5060]) ).
fof(f5060,plain,
( spl0_434
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2164,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
fof(f5058,plain,
spl0_433,
inference(avatar_split_clause,[],[f2163,f5056]) ).
fof(f5056,plain,
( spl0_433
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2163,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f5054,plain,
spl0_432,
inference(avatar_split_clause,[],[f2162,f5052]) ).
fof(f5052,plain,
( spl0_432
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2162,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f5050,plain,
spl0_431,
inference(avatar_split_clause,[],[f2161,f5048]) ).
fof(f5048,plain,
( spl0_431
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2161,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
fof(f5046,plain,
spl0_430,
inference(avatar_split_clause,[],[f2160,f5044]) ).
fof(f5044,plain,
( spl0_430
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2160,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
fof(f5042,plain,
spl0_429,
inference(avatar_split_clause,[],[f2159,f5040]) ).
fof(f5040,plain,
( spl0_429
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2159,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
fof(f5038,plain,
spl0_428,
inference(avatar_split_clause,[],[f2158,f5036]) ).
fof(f5036,plain,
( spl0_428
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2158,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
fof(f5034,plain,
spl0_427,
inference(avatar_split_clause,[],[f2157,f5032]) ).
fof(f5032,plain,
( spl0_427
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2157,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
fof(f5030,plain,
spl0_426,
inference(avatar_split_clause,[],[f2156,f5028]) ).
fof(f5028,plain,
( spl0_426
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2156,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
fof(f5026,plain,
spl0_425,
inference(avatar_split_clause,[],[f2155,f5024]) ).
fof(f5024,plain,
( spl0_425
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2155,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f5022,plain,
spl0_424,
inference(avatar_split_clause,[],[f2154,f5020]) ).
fof(f5020,plain,
( spl0_424
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2154,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f5018,plain,
spl0_423,
inference(avatar_split_clause,[],[f2153,f5016]) ).
fof(f5016,plain,
( spl0_423
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2153,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
fof(f5014,plain,
spl0_422,
inference(avatar_split_clause,[],[f2152,f5012]) ).
fof(f5012,plain,
( spl0_422
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2152,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f5010,plain,
spl0_421,
inference(avatar_split_clause,[],[f2151,f5008]) ).
fof(f5008,plain,
( spl0_421
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2151,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f5006,plain,
spl0_420,
inference(avatar_split_clause,[],[f2150,f5004]) ).
fof(f5004,plain,
( spl0_420
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2150,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f5002,plain,
spl0_419,
inference(avatar_split_clause,[],[f2149,f5000]) ).
fof(f5000,plain,
( spl0_419
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2149,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
fof(f4998,plain,
spl0_418,
inference(avatar_split_clause,[],[f2148,f4996]) ).
fof(f4996,plain,
( spl0_418
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2148,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4994,plain,
spl0_417,
inference(avatar_split_clause,[],[f2147,f4992]) ).
fof(f4992,plain,
( spl0_417
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2147,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4990,plain,
spl0_416,
inference(avatar_split_clause,[],[f2146,f4988]) ).
fof(f4988,plain,
( spl0_416
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2146,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4986,plain,
spl0_415,
inference(avatar_split_clause,[],[f2145,f4984]) ).
fof(f4984,plain,
( spl0_415
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2145,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4982,plain,
spl0_414,
inference(avatar_split_clause,[],[f2144,f4980]) ).
fof(f4980,plain,
( spl0_414
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2144,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4978,plain,
spl0_413,
inference(avatar_split_clause,[],[f2143,f4976]) ).
fof(f4976,plain,
( spl0_413
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2143,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4974,plain,
spl0_412,
inference(avatar_split_clause,[],[f2142,f4972]) ).
fof(f4972,plain,
( spl0_412
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2142,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4970,plain,
spl0_411,
inference(avatar_split_clause,[],[f2141,f4968]) ).
fof(f4968,plain,
( spl0_411
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2141,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4966,plain,
spl0_410,
inference(avatar_split_clause,[],[f2140,f4964]) ).
fof(f4964,plain,
( spl0_410
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2140,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4962,plain,
spl0_409,
inference(avatar_split_clause,[],[f2139,f4960]) ).
fof(f4960,plain,
( spl0_409
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2139,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4958,plain,
spl0_408,
inference(avatar_split_clause,[],[f2138,f4956]) ).
fof(f4956,plain,
( spl0_408
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2138,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
fof(f4954,plain,
spl0_407,
inference(avatar_split_clause,[],[f2137,f4952]) ).
fof(f4952,plain,
( spl0_407
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2137,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
fof(f4950,plain,
spl0_406,
inference(avatar_split_clause,[],[f2136,f4948]) ).
fof(f4948,plain,
( spl0_406
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2136,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4946,plain,
spl0_405,
inference(avatar_split_clause,[],[f2135,f4944]) ).
fof(f4944,plain,
( spl0_405
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2135,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
fof(f4942,plain,
spl0_404,
inference(avatar_split_clause,[],[f2134,f4940]) ).
fof(f4940,plain,
( spl0_404
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2134,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4938,plain,
spl0_403,
inference(avatar_split_clause,[],[f2133,f4936]) ).
fof(f4936,plain,
( spl0_403
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2133,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
fof(f4934,plain,
spl0_402,
inference(avatar_split_clause,[],[f2132,f4932]) ).
fof(f4932,plain,
( spl0_402
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2132,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4930,plain,
spl0_401,
inference(avatar_split_clause,[],[f2131,f4928]) ).
fof(f4928,plain,
( spl0_401
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2131,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
fof(f4926,plain,
spl0_400,
inference(avatar_split_clause,[],[f2130,f4924]) ).
fof(f4924,plain,
( spl0_400
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2130,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
fof(f4922,plain,
spl0_399,
inference(avatar_split_clause,[],[f2129,f4920]) ).
fof(f4920,plain,
( spl0_399
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2129,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4918,plain,
spl0_398,
inference(avatar_split_clause,[],[f2128,f4916]) ).
fof(f4916,plain,
( spl0_398
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2128,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4914,plain,
spl0_397,
inference(avatar_split_clause,[],[f2127,f4912]) ).
fof(f4912,plain,
( spl0_397
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2127,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4910,plain,
spl0_396,
inference(avatar_split_clause,[],[f2126,f4908]) ).
fof(f4908,plain,
( spl0_396
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2126,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
fof(f4906,plain,
spl0_395,
inference(avatar_split_clause,[],[f2125,f4904]) ).
fof(f4904,plain,
( spl0_395
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2125,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
fof(f4902,plain,
spl0_394,
inference(avatar_split_clause,[],[f2124,f4900]) ).
fof(f4900,plain,
( spl0_394
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2124,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4898,plain,
spl0_393,
inference(avatar_split_clause,[],[f2123,f4896]) ).
fof(f4896,plain,
( spl0_393
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2123,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
fof(f4894,plain,
spl0_392,
inference(avatar_split_clause,[],[f2122,f4892]) ).
fof(f4892,plain,
( spl0_392
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2122,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
fof(f4890,plain,
spl0_391,
inference(avatar_split_clause,[],[f2121,f4888]) ).
fof(f4888,plain,
( spl0_391
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2121,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4886,plain,
spl0_390,
inference(avatar_split_clause,[],[f2120,f4884]) ).
fof(f4884,plain,
( spl0_390
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2120,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4882,plain,
spl0_389,
inference(avatar_split_clause,[],[f2119,f4880]) ).
fof(f4880,plain,
( spl0_389
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2119,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
fof(f4878,plain,
spl0_388,
inference(avatar_split_clause,[],[f2118,f4876]) ).
fof(f4876,plain,
( spl0_388
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2118,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4874,plain,
spl0_387,
inference(avatar_split_clause,[],[f2117,f4872]) ).
fof(f4872,plain,
( spl0_387
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2117,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4870,plain,
spl0_386,
inference(avatar_split_clause,[],[f2116,f4868]) ).
fof(f4868,plain,
( spl0_386
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2116,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4866,plain,
spl0_385,
inference(avatar_split_clause,[],[f2115,f4864]) ).
fof(f4864,plain,
( spl0_385
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2115,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4862,plain,
spl0_384,
inference(avatar_split_clause,[],[f2114,f4860]) ).
fof(f4860,plain,
( spl0_384
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2114,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4858,plain,
spl0_383,
inference(avatar_split_clause,[],[f2113,f4856]) ).
fof(f4856,plain,
( spl0_383
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2113,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
fof(f4854,plain,
spl0_382,
inference(avatar_split_clause,[],[f2112,f4852]) ).
fof(f4852,plain,
( spl0_382
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2112,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4850,plain,
spl0_381,
inference(avatar_split_clause,[],[f2111,f4848]) ).
fof(f4848,plain,
( spl0_381
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2111,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
fof(f4846,plain,
spl0_380,
inference(avatar_split_clause,[],[f2110,f4844]) ).
fof(f4844,plain,
( spl0_380
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2110,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
fof(f4842,plain,
spl0_379,
inference(avatar_split_clause,[],[f2109,f4840]) ).
fof(f4840,plain,
( spl0_379
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2109,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4838,plain,
spl0_378,
inference(avatar_split_clause,[],[f2108,f4836]) ).
fof(f4836,plain,
( spl0_378
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2108,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4834,plain,
spl0_377,
inference(avatar_split_clause,[],[f2107,f4832]) ).
fof(f4832,plain,
( spl0_377
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2107,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
fof(f4830,plain,
spl0_376,
inference(avatar_split_clause,[],[f2106,f4828]) ).
fof(f4828,plain,
( spl0_376
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2106,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
fof(f4826,plain,
spl0_375,
inference(avatar_split_clause,[],[f2105,f4824]) ).
fof(f4824,plain,
( spl0_375
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2105,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
fof(f4822,plain,
spl0_374,
inference(avatar_split_clause,[],[f2104,f4820]) ).
fof(f4820,plain,
( spl0_374
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2104,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4818,plain,
spl0_373,
inference(avatar_split_clause,[],[f2103,f4816]) ).
fof(f4816,plain,
( spl0_373
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2103,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
fof(f4814,plain,
spl0_372,
inference(avatar_split_clause,[],[f2102,f4812]) ).
fof(f4812,plain,
( spl0_372
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2102,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4810,plain,
spl0_371,
inference(avatar_split_clause,[],[f2101,f4808]) ).
fof(f4808,plain,
( spl0_371
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2101,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
fof(f4806,plain,
spl0_370,
inference(avatar_split_clause,[],[f2100,f4804]) ).
fof(f4804,plain,
( spl0_370
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2100,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
fof(f4802,plain,
spl0_369,
inference(avatar_split_clause,[],[f2099,f4800]) ).
fof(f4800,plain,
( spl0_369
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2099,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
fof(f4798,plain,
spl0_368,
inference(avatar_split_clause,[],[f2098,f4796]) ).
fof(f4796,plain,
( spl0_368
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2098,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
fof(f4794,plain,
spl0_367,
inference(avatar_split_clause,[],[f2097,f4792]) ).
fof(f4792,plain,
( spl0_367
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2097,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
fof(f4790,plain,
spl0_366,
inference(avatar_split_clause,[],[f2096,f4788]) ).
fof(f4788,plain,
( spl0_366
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2096,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
fof(f4786,plain,
spl0_365,
inference(avatar_split_clause,[],[f2095,f4784]) ).
fof(f4784,plain,
( spl0_365
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2095,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
fof(f4782,plain,
spl0_364,
inference(avatar_split_clause,[],[f2094,f4780]) ).
fof(f4780,plain,
( spl0_364
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2094,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4778,plain,
spl0_363,
inference(avatar_split_clause,[],[f2093,f4776]) ).
fof(f4776,plain,
( spl0_363
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2093,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4774,plain,
spl0_362,
inference(avatar_split_clause,[],[f2092,f4772]) ).
fof(f4772,plain,
( spl0_362
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2092,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4770,plain,
spl0_361,
inference(avatar_split_clause,[],[f2091,f4768]) ).
fof(f4768,plain,
( spl0_361
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2091,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4766,plain,
spl0_360,
inference(avatar_split_clause,[],[f2090,f4764]) ).
fof(f4764,plain,
( spl0_360
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2090,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4762,plain,
spl0_359,
inference(avatar_split_clause,[],[f2089,f4760]) ).
fof(f4760,plain,
( spl0_359
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2089,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4758,plain,
spl0_358,
inference(avatar_split_clause,[],[f2088,f4756]) ).
fof(f4756,plain,
( spl0_358
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2088,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4754,plain,
spl0_357,
inference(avatar_split_clause,[],[f2087,f4752]) ).
fof(f4752,plain,
( spl0_357
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2087,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4750,plain,
spl0_356,
inference(avatar_split_clause,[],[f2086,f4748]) ).
fof(f4748,plain,
( spl0_356
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2086,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4746,plain,
spl0_355,
inference(avatar_split_clause,[],[f2085,f4744]) ).
fof(f4744,plain,
( spl0_355
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2085,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4742,plain,
spl0_354,
inference(avatar_split_clause,[],[f2084,f4740]) ).
fof(f4740,plain,
( spl0_354
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2084,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4738,plain,
spl0_353,
inference(avatar_split_clause,[],[f2083,f4736]) ).
fof(f4736,plain,
( spl0_353
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2083,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4734,plain,
spl0_352,
inference(avatar_split_clause,[],[f2082,f4732]) ).
fof(f4732,plain,
( spl0_352
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2082,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4730,plain,
spl0_351,
inference(avatar_split_clause,[],[f2081,f4728]) ).
fof(f4728,plain,
( spl0_351
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2081,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4726,plain,
spl0_350,
inference(avatar_split_clause,[],[f2080,f4724]) ).
fof(f4724,plain,
( spl0_350
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2080,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4722,plain,
spl0_349,
inference(avatar_split_clause,[],[f2079,f4720]) ).
fof(f4720,plain,
( spl0_349
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2079,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4718,plain,
spl0_348,
inference(avatar_split_clause,[],[f2078,f4716]) ).
fof(f4716,plain,
( spl0_348
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2078,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4714,plain,
spl0_347,
inference(avatar_split_clause,[],[f2077,f4712]) ).
fof(f4712,plain,
( spl0_347
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2077,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
fof(f4710,plain,
spl0_346,
inference(avatar_split_clause,[],[f2075,f4708]) ).
fof(f4708,plain,
( spl0_346
<=> ! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2075,axiom,
! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4706,plain,
spl0_345,
inference(avatar_split_clause,[],[f2074,f4704]) ).
fof(f4704,plain,
( spl0_345
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2074,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4702,plain,
spl0_344,
inference(avatar_split_clause,[],[f2073,f4700]) ).
fof(f4700,plain,
( spl0_344
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2073,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4698,plain,
spl0_343,
inference(avatar_split_clause,[],[f2072,f4696]) ).
fof(f4696,plain,
( spl0_343
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2072,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4694,plain,
spl0_342,
inference(avatar_split_clause,[],[f2071,f4692]) ).
fof(f4692,plain,
( spl0_342
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2071,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4690,plain,
spl0_341,
inference(avatar_split_clause,[],[f2070,f4688]) ).
fof(f4688,plain,
( spl0_341
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2070,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4686,plain,
spl0_340,
inference(avatar_split_clause,[],[f2069,f4684]) ).
fof(f4684,plain,
( spl0_340
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2069,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
fof(f4682,plain,
spl0_339,
inference(avatar_split_clause,[],[f2068,f4680]) ).
fof(f4680,plain,
( spl0_339
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2068,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
fof(f4678,plain,
spl0_338,
inference(avatar_split_clause,[],[f2067,f4676]) ).
fof(f4676,plain,
( spl0_338
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2067,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4674,plain,
spl0_337,
inference(avatar_split_clause,[],[f2066,f4672]) ).
fof(f4672,plain,
( spl0_337
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2066,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4670,plain,
spl0_336,
inference(avatar_split_clause,[],[f2065,f4668]) ).
fof(f4668,plain,
( spl0_336
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2065,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
fof(f4666,plain,
spl0_335,
inference(avatar_split_clause,[],[f2064,f4664]) ).
fof(f4664,plain,
( spl0_335
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2064,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
fof(f4662,plain,
spl0_334,
inference(avatar_split_clause,[],[f2063,f4660]) ).
fof(f4660,plain,
( spl0_334
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2063,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
fof(f4658,plain,
spl0_333,
inference(avatar_split_clause,[],[f2062,f4656]) ).
fof(f4656,plain,
( spl0_333
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2062,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4654,plain,
spl0_332,
inference(avatar_split_clause,[],[f2061,f4652]) ).
fof(f4652,plain,
( spl0_332
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2061,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4650,plain,
spl0_331,
inference(avatar_split_clause,[],[f2060,f4648]) ).
fof(f4648,plain,
( spl0_331
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2060,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4646,plain,
spl0_330,
inference(avatar_split_clause,[],[f2059,f4644]) ).
fof(f4644,plain,
( spl0_330
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2059,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
fof(f4642,plain,
spl0_329,
inference(avatar_split_clause,[],[f2058,f4640]) ).
fof(f4640,plain,
( spl0_329
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2058,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
fof(f4638,plain,
spl0_328,
inference(avatar_split_clause,[],[f2057,f4636]) ).
fof(f4636,plain,
( spl0_328
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2057,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4634,plain,
spl0_327,
inference(avatar_split_clause,[],[f2056,f4632]) ).
fof(f4632,plain,
( spl0_327
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2056,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
fof(f4630,plain,
spl0_326,
inference(avatar_split_clause,[],[f2055,f4628]) ).
fof(f4628,plain,
( spl0_326
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2055,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4626,plain,
spl0_325,
inference(avatar_split_clause,[],[f2054,f4624]) ).
fof(f4624,plain,
( spl0_325
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2054,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4622,plain,
spl0_324,
inference(avatar_split_clause,[],[f2053,f4620]) ).
fof(f4620,plain,
( spl0_324
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2053,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4618,plain,
spl0_323,
inference(avatar_split_clause,[],[f2052,f4616]) ).
fof(f4616,plain,
( spl0_323
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2052,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4614,plain,
spl0_322,
inference(avatar_split_clause,[],[f2051,f4612]) ).
fof(f4612,plain,
( spl0_322
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2051,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4610,plain,
spl0_321,
inference(avatar_split_clause,[],[f2050,f4608]) ).
fof(f4608,plain,
( spl0_321
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2050,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
fof(f4606,plain,
spl0_320,
inference(avatar_split_clause,[],[f2049,f4604]) ).
fof(f4604,plain,
( spl0_320
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2049,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
fof(f4602,plain,
spl0_319,
inference(avatar_split_clause,[],[f2048,f4600]) ).
fof(f4600,plain,
( spl0_319
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2048,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
fof(f4598,plain,
spl0_318,
inference(avatar_split_clause,[],[f2047,f4596]) ).
fof(f4596,plain,
( spl0_318
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2047,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4594,plain,
spl0_317,
inference(avatar_split_clause,[],[f2046,f4592]) ).
fof(f4592,plain,
( spl0_317
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2046,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4590,plain,
spl0_316,
inference(avatar_split_clause,[],[f2045,f4588]) ).
fof(f4588,plain,
( spl0_316
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2045,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4586,plain,
spl0_315,
inference(avatar_split_clause,[],[f2044,f4584]) ).
fof(f4584,plain,
( spl0_315
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2044,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
fof(f4582,plain,
spl0_314,
inference(avatar_split_clause,[],[f2043,f4580]) ).
fof(f4580,plain,
( spl0_314
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2043,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
fof(f4578,plain,
spl0_313,
inference(avatar_split_clause,[],[f2042,f4576]) ).
fof(f4576,plain,
( spl0_313
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2042,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4574,plain,
spl0_312,
inference(avatar_split_clause,[],[f2041,f4572]) ).
fof(f4572,plain,
( spl0_312
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2041,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
fof(f4570,plain,
spl0_311,
inference(avatar_split_clause,[],[f2040,f4568]) ).
fof(f4568,plain,
( spl0_311
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2040,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4566,plain,
spl0_310,
inference(avatar_split_clause,[],[f2039,f4564]) ).
fof(f4564,plain,
( spl0_310
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2039,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
fof(f4562,plain,
spl0_309,
inference(avatar_split_clause,[],[f2038,f4560]) ).
fof(f4560,plain,
( spl0_309
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2038,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4558,plain,
spl0_308,
inference(avatar_split_clause,[],[f2037,f4556]) ).
fof(f4556,plain,
( spl0_308
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2037,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4554,plain,
spl0_307,
inference(avatar_split_clause,[],[f2036,f4552]) ).
fof(f4552,plain,
( spl0_307
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2036,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4550,plain,
spl0_306,
inference(avatar_split_clause,[],[f2035,f4548]) ).
fof(f4548,plain,
( spl0_306
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2035,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4546,plain,
spl0_305,
inference(avatar_split_clause,[],[f2034,f4544]) ).
fof(f4544,plain,
( spl0_305
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2034,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4542,plain,
spl0_304,
inference(avatar_split_clause,[],[f2033,f4540]) ).
fof(f4540,plain,
( spl0_304
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2033,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
fof(f4538,plain,
spl0_303,
inference(avatar_split_clause,[],[f2032,f4536]) ).
fof(f4536,plain,
( spl0_303
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2032,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4534,plain,
spl0_302,
inference(avatar_split_clause,[],[f2031,f4532]) ).
fof(f4532,plain,
( spl0_302
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2031,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4530,plain,
spl0_301,
inference(avatar_split_clause,[],[f2030,f4528]) ).
fof(f4528,plain,
( spl0_301
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2030,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
fof(f4526,plain,
spl0_300,
inference(avatar_split_clause,[],[f2029,f4524]) ).
fof(f4524,plain,
( spl0_300
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2029,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
fof(f4522,plain,
spl0_299,
inference(avatar_split_clause,[],[f2028,f4520]) ).
fof(f4520,plain,
( spl0_299
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2028,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4518,plain,
spl0_298,
inference(avatar_split_clause,[],[f2027,f4516]) ).
fof(f4516,plain,
( spl0_298
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2027,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
fof(f4514,plain,
spl0_297,
inference(avatar_split_clause,[],[f2026,f4512]) ).
fof(f4512,plain,
( spl0_297
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2026,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4510,plain,
spl0_296,
inference(avatar_split_clause,[],[f2025,f4508]) ).
fof(f4508,plain,
( spl0_296
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2025,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4506,plain,
spl0_295,
inference(avatar_split_clause,[],[f2024,f4504]) ).
fof(f4504,plain,
( spl0_295
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2024,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4502,plain,
spl0_294,
inference(avatar_split_clause,[],[f2023,f4500]) ).
fof(f4500,plain,
( spl0_294
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2023,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4498,plain,
spl0_293,
inference(avatar_split_clause,[],[f2022,f4496]) ).
fof(f4496,plain,
( spl0_293
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2022,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4494,plain,
spl0_292,
inference(avatar_split_clause,[],[f2021,f4492]) ).
fof(f4492,plain,
( spl0_292
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2021,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4490,plain,
spl0_291,
inference(avatar_split_clause,[],[f2020,f4488]) ).
fof(f4488,plain,
( spl0_291
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2020,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4486,plain,
spl0_290,
inference(avatar_split_clause,[],[f2019,f4484]) ).
fof(f4484,plain,
( spl0_290
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2019,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4482,plain,
spl0_289,
inference(avatar_split_clause,[],[f2018,f4480]) ).
fof(f4480,plain,
( spl0_289
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2018,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4478,plain,
spl0_288,
inference(avatar_split_clause,[],[f2017,f4476]) ).
fof(f4476,plain,
( spl0_288
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2017,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
fof(f4474,plain,
spl0_287,
inference(avatar_split_clause,[],[f2016,f4472]) ).
fof(f4472,plain,
( spl0_287
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2016,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
fof(f4470,plain,
spl0_286,
inference(avatar_split_clause,[],[f2015,f4468]) ).
fof(f4468,plain,
( spl0_286
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2015,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4466,plain,
spl0_285,
inference(avatar_split_clause,[],[f2014,f4464]) ).
fof(f4464,plain,
( spl0_285
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2014,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4462,plain,
spl0_284,
inference(avatar_split_clause,[],[f2013,f4460]) ).
fof(f4460,plain,
( spl0_284
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2013,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4458,plain,
spl0_283,
inference(avatar_split_clause,[],[f2012,f4456]) ).
fof(f4456,plain,
( spl0_283
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2012,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4454,plain,
spl0_282,
inference(avatar_split_clause,[],[f2011,f4452]) ).
fof(f4452,plain,
( spl0_282
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2011,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4450,plain,
spl0_281,
inference(avatar_split_clause,[],[f2010,f4448]) ).
fof(f4448,plain,
( spl0_281
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2010,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4446,plain,
spl0_280,
inference(avatar_split_clause,[],[f2009,f4444]) ).
fof(f4444,plain,
( spl0_280
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2009,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
fof(f4442,plain,
spl0_279,
inference(avatar_split_clause,[],[f2008,f4440]) ).
fof(f4440,plain,
( spl0_279
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2008,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4438,plain,
spl0_278,
inference(avatar_split_clause,[],[f2007,f4436]) ).
fof(f4436,plain,
( spl0_278
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2007,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
fof(f4434,plain,
spl0_277,
inference(avatar_split_clause,[],[f2006,f4432]) ).
fof(f4432,plain,
( spl0_277
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2006,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4430,plain,
spl0_276,
inference(avatar_split_clause,[],[f2005,f4428]) ).
fof(f4428,plain,
( spl0_276
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2005,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4426,plain,
spl0_275,
inference(avatar_split_clause,[],[f2004,f4424]) ).
fof(f4424,plain,
( spl0_275
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2004,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4422,plain,
spl0_274,
inference(avatar_split_clause,[],[f2003,f4420]) ).
fof(f4420,plain,
( spl0_274
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2003,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4418,plain,
spl0_273,
inference(avatar_split_clause,[],[f2002,f4416]) ).
fof(f4416,plain,
( spl0_273
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2002,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
fof(f4414,plain,
spl0_272,
inference(avatar_split_clause,[],[f2001,f4412]) ).
fof(f4412,plain,
( spl0_272
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2001,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
fof(f4410,plain,
spl0_271,
inference(avatar_split_clause,[],[f2000,f4408]) ).
fof(f4408,plain,
( spl0_271
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2000,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4406,plain,
spl0_270,
inference(avatar_split_clause,[],[f1999,f4404]) ).
fof(f4404,plain,
( spl0_270
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1999,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
fof(f4402,plain,
spl0_269,
inference(avatar_split_clause,[],[f1998,f4400]) ).
fof(f4400,plain,
( spl0_269
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1998,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4398,plain,
spl0_268,
inference(avatar_split_clause,[],[f1997,f4396]) ).
fof(f4396,plain,
( spl0_268
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1997,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4394,plain,
spl0_267,
inference(avatar_split_clause,[],[f1996,f4392]) ).
fof(f4392,plain,
( spl0_267
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1996,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4390,plain,
spl0_266,
inference(avatar_split_clause,[],[f1995,f4388]) ).
fof(f4388,plain,
( spl0_266
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1995,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4386,plain,
spl0_265,
inference(avatar_split_clause,[],[f1994,f4384]) ).
fof(f4384,plain,
( spl0_265
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1994,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4382,plain,
spl0_264,
inference(avatar_split_clause,[],[f1993,f4380]) ).
fof(f4380,plain,
( spl0_264
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1993,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4378,plain,
spl0_263,
inference(avatar_split_clause,[],[f1992,f4376]) ).
fof(f4376,plain,
( spl0_263
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1992,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4374,plain,
spl0_262,
inference(avatar_split_clause,[],[f1991,f4372]) ).
fof(f4372,plain,
( spl0_262
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1991,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4370,plain,
spl0_261,
inference(avatar_split_clause,[],[f1990,f4368]) ).
fof(f4368,plain,
( spl0_261
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1990,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
fof(f4366,plain,
spl0_260,
inference(avatar_split_clause,[],[f1989,f4364]) ).
fof(f4364,plain,
( spl0_260
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1989,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4362,plain,
spl0_259,
inference(avatar_split_clause,[],[f1988,f4360]) ).
fof(f4360,plain,
( spl0_259
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1988,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
fof(f4358,plain,
spl0_258,
inference(avatar_split_clause,[],[f1987,f4356]) ).
fof(f4356,plain,
( spl0_258
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1987,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4354,plain,
spl0_257,
inference(avatar_split_clause,[],[f1986,f4352]) ).
fof(f4352,plain,
( spl0_257
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1986,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4350,plain,
spl0_256,
inference(avatar_split_clause,[],[f1985,f4348]) ).
fof(f4348,plain,
( spl0_256
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1985,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4346,plain,
spl0_255,
inference(avatar_split_clause,[],[f1984,f4344]) ).
fof(f4344,plain,
( spl0_255
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1984,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4342,plain,
spl0_254,
inference(avatar_split_clause,[],[f1983,f4340]) ).
fof(f4340,plain,
( spl0_254
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1983,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
fof(f4338,plain,
spl0_253,
inference(avatar_split_clause,[],[f1982,f4336]) ).
fof(f4336,plain,
( spl0_253
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1982,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
fof(f4334,plain,
spl0_252,
inference(avatar_split_clause,[],[f1981,f4332]) ).
fof(f4332,plain,
( spl0_252
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1981,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4330,plain,
spl0_251,
inference(avatar_split_clause,[],[f1980,f4328]) ).
fof(f4328,plain,
( spl0_251
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1980,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
fof(f4326,plain,
spl0_250,
inference(avatar_split_clause,[],[f1979,f4324]) ).
fof(f4324,plain,
( spl0_250
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1979,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4322,plain,
spl0_249,
inference(avatar_split_clause,[],[f1978,f4320]) ).
fof(f4320,plain,
( spl0_249
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1978,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4318,plain,
spl0_248,
inference(avatar_split_clause,[],[f1977,f4316]) ).
fof(f4316,plain,
( spl0_248
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1977,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4314,plain,
spl0_247,
inference(avatar_split_clause,[],[f1976,f4312]) ).
fof(f4312,plain,
( spl0_247
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1976,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4310,plain,
spl0_246,
inference(avatar_split_clause,[],[f1975,f4308]) ).
fof(f4308,plain,
( spl0_246
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1975,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4306,plain,
spl0_245,
inference(avatar_split_clause,[],[f1974,f4304]) ).
fof(f4304,plain,
( spl0_245
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1974,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4302,plain,
spl0_244,
inference(avatar_split_clause,[],[f1973,f4300]) ).
fof(f4300,plain,
( spl0_244
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1973,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4298,plain,
spl0_243,
inference(avatar_split_clause,[],[f1972,f4296]) ).
fof(f4296,plain,
( spl0_243
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1972,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
fof(f4294,plain,
spl0_242,
inference(avatar_split_clause,[],[f1971,f4292]) ).
fof(f4292,plain,
( spl0_242
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1971,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4290,plain,
spl0_241,
inference(avatar_split_clause,[],[f1970,f4288]) ).
fof(f4288,plain,
( spl0_241
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1970,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
fof(f4286,plain,
spl0_240,
inference(avatar_split_clause,[],[f1969,f4284]) ).
fof(f4284,plain,
( spl0_240
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1969,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4282,plain,
spl0_239,
inference(avatar_split_clause,[],[f1968,f4280]) ).
fof(f4280,plain,
( spl0_239
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1968,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4278,plain,
spl0_238,
inference(avatar_split_clause,[],[f1967,f4276]) ).
fof(f4276,plain,
( spl0_238
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1967,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4274,plain,
spl0_237,
inference(avatar_split_clause,[],[f1966,f4272]) ).
fof(f4272,plain,
( spl0_237
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1966,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4270,plain,
spl0_236,
inference(avatar_split_clause,[],[f1965,f4268]) ).
fof(f4268,plain,
( spl0_236
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1965,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4266,plain,
spl0_235,
inference(avatar_split_clause,[],[f1964,f4264]) ).
fof(f4264,plain,
( spl0_235
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1964,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4262,plain,
spl0_234,
inference(avatar_split_clause,[],[f1963,f4260]) ).
fof(f4260,plain,
( spl0_234
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1963,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
fof(f4258,plain,
spl0_233,
inference(avatar_split_clause,[],[f1962,f4256]) ).
fof(f4256,plain,
( spl0_233
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1962,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
fof(f4254,plain,
spl0_232,
inference(avatar_split_clause,[],[f1961,f4252]) ).
fof(f4252,plain,
( spl0_232
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1961,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4250,plain,
spl0_231,
inference(avatar_split_clause,[],[f1960,f4248]) ).
fof(f4248,plain,
( spl0_231
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1960,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
fof(f4246,plain,
spl0_230,
inference(avatar_split_clause,[],[f1959,f4244]) ).
fof(f4244,plain,
( spl0_230
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1959,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4242,plain,
spl0_229,
inference(avatar_split_clause,[],[f1958,f4240]) ).
fof(f4240,plain,
( spl0_229
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1958,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4238,plain,
spl0_228,
inference(avatar_split_clause,[],[f1957,f4236]) ).
fof(f4236,plain,
( spl0_228
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1957,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4234,plain,
spl0_227,
inference(avatar_split_clause,[],[f1956,f4232]) ).
fof(f4232,plain,
( spl0_227
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1956,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4230,plain,
spl0_226,
inference(avatar_split_clause,[],[f1955,f4228]) ).
fof(f4228,plain,
( spl0_226
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1955,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f4226,plain,
spl0_225,
inference(avatar_split_clause,[],[f1954,f4224]) ).
fof(f4224,plain,
( spl0_225
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1954,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f4222,plain,
spl0_224,
inference(avatar_split_clause,[],[f1953,f4220]) ).
fof(f4220,plain,
( spl0_224
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1953,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f4218,plain,
spl0_223,
inference(avatar_split_clause,[],[f1952,f4216]) ).
fof(f4216,plain,
( spl0_223
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1952,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
fof(f4214,plain,
spl0_222,
inference(avatar_split_clause,[],[f1951,f4212]) ).
fof(f4212,plain,
( spl0_222
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1951,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f4210,plain,
spl0_221,
inference(avatar_split_clause,[],[f1950,f4208]) ).
fof(f4208,plain,
( spl0_221
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1950,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
fof(f4206,plain,
spl0_220,
inference(avatar_split_clause,[],[f1949,f4204]) ).
fof(f4204,plain,
( spl0_220
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1949,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f4202,plain,
spl0_219,
inference(avatar_split_clause,[],[f1948,f4200]) ).
fof(f4200,plain,
( spl0_219
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1948,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f4198,plain,
spl0_218,
inference(avatar_split_clause,[],[f1947,f4196]) ).
fof(f4196,plain,
( spl0_218
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1947,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f4194,plain,
spl0_217,
inference(avatar_split_clause,[],[f1946,f4192]) ).
fof(f4192,plain,
( spl0_217
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1946,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
fof(f4190,plain,
spl0_216,
inference(avatar_split_clause,[],[f1945,f4188]) ).
fof(f4188,plain,
( spl0_216
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1945,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
fof(f4186,plain,
spl0_215,
inference(avatar_split_clause,[],[f1944,f4184]) ).
fof(f4184,plain,
( spl0_215
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1944,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f4182,plain,
spl0_214,
inference(avatar_split_clause,[],[f1943,f4180]) ).
fof(f4180,plain,
( spl0_214
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1943,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
fof(f4178,plain,
spl0_213,
inference(avatar_split_clause,[],[f1942,f4176]) ).
fof(f4176,plain,
( spl0_213
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1942,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f4174,plain,
spl0_212,
inference(avatar_split_clause,[],[f1941,f4172]) ).
fof(f4172,plain,
( spl0_212
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1941,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f4170,plain,
spl0_211,
inference(avatar_split_clause,[],[f1940,f4168]) ).
fof(f4168,plain,
( spl0_211
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1940,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f4166,plain,
spl0_210,
inference(avatar_split_clause,[],[f1939,f4164]) ).
fof(f4164,plain,
( spl0_210
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1939,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f4162,plain,
spl0_209,
inference(avatar_split_clause,[],[f1938,f4160]) ).
fof(f4160,plain,
( spl0_209
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1938,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
fof(f4158,plain,
spl0_208,
inference(avatar_split_clause,[],[f1937,f4156]) ).
fof(f4156,plain,
( spl0_208
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1937,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
fof(f4154,plain,
spl0_207,
inference(avatar_split_clause,[],[f1936,f4152]) ).
fof(f4152,plain,
( spl0_207
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1936,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
fof(f4150,plain,
spl0_206,
inference(avatar_split_clause,[],[f1935,f4148]) ).
fof(f4148,plain,
( spl0_206
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1935,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f4146,plain,
spl0_205,
inference(avatar_split_clause,[],[f1934,f4144]) ).
fof(f4144,plain,
( spl0_205
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1934,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
fof(f4142,plain,
spl0_204,
inference(avatar_split_clause,[],[f1933,f4140]) ).
fof(f4140,plain,
( spl0_204
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1933,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
fof(f4138,plain,
spl0_203,
inference(avatar_split_clause,[],[f1932,f4136]) ).
fof(f4136,plain,
( spl0_203
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1932,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
fof(f4134,plain,
spl0_202,
inference(avatar_split_clause,[],[f1931,f4132]) ).
fof(f4132,plain,
( spl0_202
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1931,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
fof(f4130,plain,
spl0_201,
inference(avatar_split_clause,[],[f1930,f4128]) ).
fof(f4128,plain,
( spl0_201
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1930,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
fof(f4126,plain,
spl0_200,
inference(avatar_split_clause,[],[f1929,f4124]) ).
fof(f4124,plain,
( spl0_200
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1929,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
fof(f4122,plain,
spl0_199,
inference(avatar_split_clause,[],[f1928,f4120]) ).
fof(f4120,plain,
( spl0_199
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1928,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f4118,plain,
spl0_198,
inference(avatar_split_clause,[],[f1927,f4116]) ).
fof(f4116,plain,
( spl0_198
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1927,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
fof(f4114,plain,
spl0_197,
inference(avatar_split_clause,[],[f1926,f4112]) ).
fof(f4112,plain,
( spl0_197
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1926,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
fof(f4110,plain,
spl0_196,
inference(avatar_split_clause,[],[f1925,f4108]) ).
fof(f4108,plain,
( spl0_196
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1925,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
fof(f4106,plain,
spl0_195,
inference(avatar_split_clause,[],[f1924,f4104]) ).
fof(f4104,plain,
( spl0_195
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1924,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
fof(f4102,plain,
spl0_194,
inference(avatar_split_clause,[],[f1923,f4100]) ).
fof(f4100,plain,
( spl0_194
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1923,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
fof(f4098,plain,
spl0_193,
inference(avatar_split_clause,[],[f1922,f4096]) ).
fof(f4096,plain,
( spl0_193
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1922,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
fof(f4094,plain,
spl0_192,
inference(avatar_split_clause,[],[f1921,f4092]) ).
fof(f4092,plain,
( spl0_192
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1921,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
fof(f4090,plain,
spl0_191,
inference(avatar_split_clause,[],[f1920,f4088]) ).
fof(f4088,plain,
( spl0_191
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1920,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f4086,plain,
spl0_190,
inference(avatar_split_clause,[],[f1919,f4084]) ).
fof(f4084,plain,
( spl0_190
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1919,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f4082,plain,
spl0_189,
inference(avatar_split_clause,[],[f1918,f4080]) ).
fof(f4080,plain,
( spl0_189
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1918,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
fof(f4078,plain,
spl0_188,
inference(avatar_split_clause,[],[f1917,f4076]) ).
fof(f4076,plain,
( spl0_188
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1917,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
fof(f4074,plain,
spl0_187,
inference(avatar_split_clause,[],[f1916,f4072]) ).
fof(f4072,plain,
( spl0_187
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1916,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
fof(f4070,plain,
spl0_186,
inference(avatar_split_clause,[],[f1915,f4068]) ).
fof(f4068,plain,
( spl0_186
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1915,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
fof(f4066,plain,
spl0_185,
inference(avatar_split_clause,[],[f1914,f4064]) ).
fof(f4064,plain,
( spl0_185
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1914,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f4062,plain,
spl0_184,
inference(avatar_split_clause,[],[f1913,f4060]) ).
fof(f4060,plain,
( spl0_184
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1913,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
fof(f4058,plain,
spl0_183,
inference(avatar_split_clause,[],[f1912,f4056]) ).
fof(f4056,plain,
( spl0_183
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1912,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f4054,plain,
spl0_182,
inference(avatar_split_clause,[],[f1911,f4052]) ).
fof(f4052,plain,
( spl0_182
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1911,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).
fof(f4050,plain,
spl0_181,
inference(avatar_split_clause,[],[f1910,f4048]) ).
fof(f4048,plain,
( spl0_181
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1910,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f4046,plain,
spl0_180,
inference(avatar_split_clause,[],[f1909,f4044]) ).
fof(f4044,plain,
( spl0_180
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1909,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f4042,plain,
spl0_179,
inference(avatar_split_clause,[],[f1908,f4040]) ).
fof(f4040,plain,
( spl0_179
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1908,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
fof(f4038,plain,
spl0_178,
inference(avatar_split_clause,[],[f1907,f4036]) ).
fof(f4036,plain,
( spl0_178
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1907,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).
fof(f4034,plain,
spl0_177,
inference(avatar_split_clause,[],[f1906,f4032]) ).
fof(f4032,plain,
( spl0_177
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1906,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f4030,plain,
spl0_176,
inference(avatar_split_clause,[],[f1905,f4028]) ).
fof(f4028,plain,
( spl0_176
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1905,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).
fof(f4026,plain,
spl0_175,
inference(avatar_split_clause,[],[f1904,f4024]) ).
fof(f4024,plain,
( spl0_175
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1904,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f4022,plain,
spl0_174,
inference(avatar_split_clause,[],[f1903,f4020]) ).
fof(f4020,plain,
( spl0_174
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1903,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f4018,plain,
spl0_173,
inference(avatar_split_clause,[],[f1902,f4016]) ).
fof(f4016,plain,
( spl0_173
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1902,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f4014,plain,
spl0_172,
inference(avatar_split_clause,[],[f1901,f4012]) ).
fof(f4012,plain,
( spl0_172
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1901,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f4010,plain,
spl0_171,
inference(avatar_split_clause,[],[f1900,f4008]) ).
fof(f4008,plain,
( spl0_171
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1900,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f4006,plain,
spl0_170,
inference(avatar_split_clause,[],[f1899,f4004]) ).
fof(f4004,plain,
( spl0_170
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1899,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f4002,plain,
spl0_169,
inference(avatar_split_clause,[],[f1898,f4000]) ).
fof(f4000,plain,
( spl0_169
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1898,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3998,plain,
spl0_168,
inference(avatar_split_clause,[],[f1897,f3996]) ).
fof(f3996,plain,
( spl0_168
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1897,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3994,plain,
spl0_167,
inference(avatar_split_clause,[],[f1896,f3992]) ).
fof(f3992,plain,
( spl0_167
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1896,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3990,plain,
spl0_166,
inference(avatar_split_clause,[],[f1895,f3988]) ).
fof(f3988,plain,
( spl0_166
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1895,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3986,plain,
spl0_165,
inference(avatar_split_clause,[],[f1894,f3984]) ).
fof(f3984,plain,
( spl0_165
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1894,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).
fof(f3982,plain,
spl0_164,
inference(avatar_split_clause,[],[f1893,f3980]) ).
fof(f3980,plain,
( spl0_164
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1893,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3978,plain,
spl0_163,
inference(avatar_split_clause,[],[f1892,f3976]) ).
fof(f3976,plain,
( spl0_163
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1892,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3974,plain,
spl0_162,
inference(avatar_split_clause,[],[f1891,f3972]) ).
fof(f3972,plain,
( spl0_162
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1891,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3970,plain,
spl0_161,
inference(avatar_split_clause,[],[f1890,f3968]) ).
fof(f3968,plain,
( spl0_161
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1890,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3966,plain,
spl0_160,
inference(avatar_split_clause,[],[f1889,f3964]) ).
fof(f3964,plain,
( spl0_160
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1889,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3962,plain,
spl0_159,
inference(avatar_split_clause,[],[f1888,f3960]) ).
fof(f3960,plain,
( spl0_159
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1888,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3958,plain,
spl0_158,
inference(avatar_split_clause,[],[f1887,f3956]) ).
fof(f3956,plain,
( spl0_158
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1887,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3954,plain,
spl0_157,
inference(avatar_split_clause,[],[f1886,f3952]) ).
fof(f3952,plain,
( spl0_157
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1886,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
fof(f3950,plain,
spl0_156,
inference(avatar_split_clause,[],[f1885,f3948]) ).
fof(f3948,plain,
( spl0_156
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1885,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3946,plain,
spl0_155,
inference(avatar_split_clause,[],[f1884,f3944]) ).
fof(f3944,plain,
( spl0_155
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1884,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3942,plain,
spl0_154,
inference(avatar_split_clause,[],[f1883,f3940]) ).
fof(f3940,plain,
( spl0_154
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1883,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).
fof(f3938,plain,
spl0_153,
inference(avatar_split_clause,[],[f1882,f3936]) ).
fof(f3936,plain,
( spl0_153
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1882,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).
fof(f3934,plain,
spl0_152,
inference(avatar_split_clause,[],[f1881,f3932]) ).
fof(f3932,plain,
( spl0_152
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1881,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3930,plain,
spl0_151,
inference(avatar_split_clause,[],[f1880,f3928]) ).
fof(f3928,plain,
( spl0_151
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1880,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3926,plain,
spl0_150,
inference(avatar_split_clause,[],[f1879,f3924]) ).
fof(f3924,plain,
( spl0_150
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1879,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3922,plain,
spl0_149,
inference(avatar_split_clause,[],[f1878,f3920]) ).
fof(f3920,plain,
( spl0_149
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1878,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3918,plain,
spl0_148,
inference(avatar_split_clause,[],[f1877,f3916]) ).
fof(f3916,plain,
( spl0_148
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1877,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3914,plain,
spl0_147,
inference(avatar_split_clause,[],[f1876,f3912]) ).
fof(f3912,plain,
( spl0_147
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1876,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3910,plain,
spl0_146,
inference(avatar_split_clause,[],[f1875,f3908]) ).
fof(f3908,plain,
( spl0_146
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1875,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3906,plain,
spl0_145,
inference(avatar_split_clause,[],[f1874,f3904]) ).
fof(f3904,plain,
( spl0_145
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1874,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3902,plain,
spl0_144,
inference(avatar_split_clause,[],[f1719,f3900]) ).
fof(f3900,plain,
( spl0_144
<=> ! [X0,X12] : c_in(X12,c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1719,axiom,
! [X0,X12] : c_in(X12,c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3898,plain,
spl0_143,
inference(avatar_split_clause,[],[f1687,f3896]) ).
fof(f3896,plain,
( spl0_143
<=> ! [X11] : ~ c_less(X11,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1687,axiom,
! [X11] : ~ c_less(X11,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3894,plain,
spl0_142,
inference(avatar_split_clause,[],[f1685,f3892]) ).
fof(f3892,plain,
( spl0_142
<=> ! [X11] : c_lessequals(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1685,axiom,
! [X11] : c_lessequals(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3890,plain,
spl0_141,
inference(avatar_split_clause,[],[f1661,f3888]) ).
fof(f3888,plain,
( spl0_141
<=> ! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1661,axiom,
! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3886,plain,
spl0_140,
inference(avatar_split_clause,[],[f1660,f3884]) ).
fof(f3884,plain,
( spl0_140
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1660,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3882,plain,
spl0_139,
inference(avatar_split_clause,[],[f1644,f3880]) ).
fof(f3880,plain,
( spl0_139
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1644,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3878,plain,
spl0_138,
inference(avatar_split_clause,[],[f1566,f3876]) ).
fof(f3876,plain,
( spl0_138
<=> ! [X25,X0] : ~ c_in(X25,c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1566,axiom,
! [X0,X25] : ~ c_in(X25,c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3874,plain,
spl0_137,
inference(avatar_split_clause,[],[f1049,f3871]) ).
fof(f3871,plain,
( spl0_137
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1049,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(f3869,plain,
spl0_136,
inference(avatar_split_clause,[],[f985,f3867]) ).
fof(f3867,plain,
( spl0_136
<=> ! [X11] : ~ c_less(X11,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f985,axiom,
! [X11] : ~ c_less(X11,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3865,plain,
spl0_135,
inference(avatar_split_clause,[],[f943,f3862]) ).
fof(f3862,plain,
( spl0_135
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f943,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3860,plain,
spl0_134,
inference(avatar_split_clause,[],[f603,f3858]) ).
fof(f3858,plain,
( spl0_134
<=> ! [X12,X14] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f603,axiom,
! [X14,X12] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3856,plain,
spl0_133,
inference(avatar_split_clause,[],[f376,f3854]) ).
fof(f3854,plain,
( spl0_133
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f376,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3852,plain,
spl0_132,
inference(avatar_split_clause,[],[f287,f3850]) ).
fof(f287,axiom,
! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3848,plain,
spl0_131,
inference(avatar_split_clause,[],[f280,f3845]) ).
fof(f3845,plain,
( spl0_131
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f280,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3843,plain,
spl0_130,
inference(avatar_split_clause,[],[f268,f3840]) ).
fof(f3838,plain,
spl0_129,
inference(avatar_split_clause,[],[f265,f3835]) ).
fof(f265,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3833,plain,
spl0_128,
inference(avatar_split_clause,[],[f123,f3831]) ).
fof(f3831,plain,
( spl0_128
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f123,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3829,plain,
spl0_127,
inference(avatar_split_clause,[],[f1870,f3827]) ).
fof(f3827,plain,
( spl0_127
<=> ! [X8] : class_Orderings_Oorder(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1870,axiom,
! [X8] : class_Orderings_Oorder(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3825,plain,
spl0_126,
inference(avatar_split_clause,[],[f1869,f3823]) ).
fof(f3823,plain,
( spl0_126
<=> ! [X8] : class_Orderings_Oord(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1869,axiom,
! [X8] : class_Orderings_Oord(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3821,plain,
spl0_125,
inference(avatar_split_clause,[],[f1868,f3819]) ).
fof(f3819,plain,
( spl0_125
<=> ! [X8] : class_HOL_Ominus(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1868,axiom,
! [X8] : class_HOL_Ominus(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
fof(f3817,plain,
spl0_124,
inference(avatar_split_clause,[],[f1747,f3814]) ).
fof(f3814,plain,
( spl0_124
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1747,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(f3812,plain,
spl0_123,
inference(avatar_split_clause,[],[f1745,f3809]) ).
fof(f3809,plain,
( spl0_123
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1745,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(f3807,plain,
spl0_122,
inference(avatar_split_clause,[],[f1744,f3805]) ).
fof(f3805,plain,
( spl0_122
<=> ! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1744,axiom,
! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3803,plain,
~ spl0_121,
inference(avatar_split_clause,[],[f1523,f3800]) ).
fof(f3800,plain,
( spl0_121
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1523,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3798,plain,
~ spl0_120,
inference(avatar_split_clause,[],[f1204,f3795]) ).
fof(f3795,plain,
( spl0_120
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1204,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3793,plain,
spl0_119,
inference(avatar_split_clause,[],[f1197,f3790]) ).
fof(f3790,plain,
( spl0_119
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1197,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3788,plain,
spl0_118,
inference(avatar_split_clause,[],[f1184,f3785]) ).
fof(f3785,plain,
( spl0_118
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1184,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3783,plain,
~ spl0_117,
inference(avatar_split_clause,[],[f1054,f3780]) ).
fof(f3780,plain,
( spl0_117
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1054,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
fof(f3778,plain,
spl0_116,
inference(avatar_split_clause,[],[f600,f3776]) ).
fof(f3776,plain,
( spl0_116
<=> ! [X14] : c_List_Onull(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f600,axiom,
! [X14] : c_List_Onull(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3774,plain,
spl0_115,
inference(avatar_split_clause,[],[f445,f3772]) ).
fof(f3772,plain,
( spl0_115
<=> ! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f445,axiom,
! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3770,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f264,f3767]) ).
fof(f264,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3765,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f144,f3762]) ).
fof(f3762,plain,
( spl0_113
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f144,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3760,plain,
spl0_112,
inference(avatar_split_clause,[],[f2785,f3758]) ).
fof(f2785,axiom,
! [X29] : ~ c_lessequals(c_1,c_times(X29,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3756,plain,
spl0_111,
inference(avatar_split_clause,[],[f1866,f3753]) ).
fof(f3753,plain,
( spl0_111
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1866,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
fof(f3751,plain,
spl0_110,
inference(avatar_split_clause,[],[f1865,f3748]) ).
fof(f3748,plain,
( spl0_110
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1865,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3746,plain,
spl0_109,
inference(avatar_split_clause,[],[f1864,f3743]) ).
fof(f3743,plain,
( spl0_109
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1864,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3741,plain,
spl0_108,
inference(avatar_split_clause,[],[f1863,f3738]) ).
fof(f3738,plain,
( spl0_108
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1863,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3736,plain,
spl0_107,
inference(avatar_split_clause,[],[f1862,f3733]) ).
fof(f3733,plain,
( spl0_107
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1862,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3731,plain,
spl0_106,
inference(avatar_split_clause,[],[f1860,f3728]) ).
fof(f3728,plain,
( spl0_106
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1860,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3726,plain,
spl0_105,
inference(avatar_split_clause,[],[f1859,f3723]) ).
fof(f3723,plain,
( spl0_105
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1859,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3721,plain,
spl0_104,
inference(avatar_split_clause,[],[f1857,f3718]) ).
fof(f3718,plain,
( spl0_104
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1857,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3716,plain,
spl0_103,
inference(avatar_split_clause,[],[f1856,f3713]) ).
fof(f3713,plain,
( spl0_103
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1856,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3711,plain,
spl0_102,
inference(avatar_split_clause,[],[f1855,f3708]) ).
fof(f3708,plain,
( spl0_102
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1855,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3706,plain,
spl0_101,
inference(avatar_split_clause,[],[f1854,f3703]) ).
fof(f3703,plain,
( spl0_101
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1854,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3701,plain,
spl0_100,
inference(avatar_split_clause,[],[f1853,f3698]) ).
fof(f3698,plain,
( spl0_100
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1853,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3696,plain,
spl0_99,
inference(avatar_split_clause,[],[f1852,f3693]) ).
fof(f3693,plain,
( spl0_99
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1852,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3691,plain,
spl0_98,
inference(avatar_split_clause,[],[f1851,f3688]) ).
fof(f3688,plain,
( spl0_98
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1851,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3686,plain,
spl0_97,
inference(avatar_split_clause,[],[f1850,f3683]) ).
fof(f3683,plain,
( spl0_97
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1850,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3681,plain,
spl0_96,
inference(avatar_split_clause,[],[f1849,f3678]) ).
fof(f3678,plain,
( spl0_96
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1849,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3676,plain,
spl0_95,
inference(avatar_split_clause,[],[f1848,f3673]) ).
fof(f3673,plain,
( spl0_95
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1848,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3671,plain,
spl0_94,
inference(avatar_split_clause,[],[f1847,f3668]) ).
fof(f3668,plain,
( spl0_94
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1847,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3666,plain,
spl0_93,
inference(avatar_split_clause,[],[f1846,f3663]) ).
fof(f3663,plain,
( spl0_93
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1846,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3661,plain,
spl0_92,
inference(avatar_split_clause,[],[f1845,f3658]) ).
fof(f3658,plain,
( spl0_92
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1845,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3656,plain,
spl0_91,
inference(avatar_split_clause,[],[f1844,f3653]) ).
fof(f3653,plain,
( spl0_91
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1844,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3651,plain,
spl0_90,
inference(avatar_split_clause,[],[f1843,f3648]) ).
fof(f3648,plain,
( spl0_90
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1843,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3646,plain,
spl0_89,
inference(avatar_split_clause,[],[f1842,f3643]) ).
fof(f3643,plain,
( spl0_89
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1842,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3641,plain,
spl0_88,
inference(avatar_split_clause,[],[f1841,f3638]) ).
fof(f3638,plain,
( spl0_88
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1841,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3636,plain,
spl0_87,
inference(avatar_split_clause,[],[f1840,f3633]) ).
fof(f3633,plain,
( spl0_87
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1840,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3631,plain,
spl0_86,
inference(avatar_split_clause,[],[f1839,f3628]) ).
fof(f3628,plain,
( spl0_86
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1839,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3626,plain,
spl0_85,
inference(avatar_split_clause,[],[f1838,f3623]) ).
fof(f3623,plain,
( spl0_85
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1838,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3621,plain,
spl0_84,
inference(avatar_split_clause,[],[f1837,f3618]) ).
fof(f3618,plain,
( spl0_84
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1837,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3616,plain,
spl0_83,
inference(avatar_split_clause,[],[f1836,f3613]) ).
fof(f3613,plain,
( spl0_83
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1836,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3611,plain,
spl0_82,
inference(avatar_split_clause,[],[f1835,f3608]) ).
fof(f3608,plain,
( spl0_82
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1835,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3606,plain,
spl0_81,
inference(avatar_split_clause,[],[f1834,f3603]) ).
fof(f3603,plain,
( spl0_81
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1834,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3601,plain,
spl0_80,
inference(avatar_split_clause,[],[f1833,f3598]) ).
fof(f3598,plain,
( spl0_80
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1833,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3596,plain,
spl0_79,
inference(avatar_split_clause,[],[f1832,f3593]) ).
fof(f3593,plain,
( spl0_79
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1832,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3591,plain,
spl0_78,
inference(avatar_split_clause,[],[f1831,f3588]) ).
fof(f3588,plain,
( spl0_78
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1831,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3586,plain,
spl0_77,
inference(avatar_split_clause,[],[f1830,f3583]) ).
fof(f3583,plain,
( spl0_77
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1830,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3581,plain,
spl0_76,
inference(avatar_split_clause,[],[f1829,f3578]) ).
fof(f3578,plain,
( spl0_76
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1829,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3576,plain,
spl0_75,
inference(avatar_split_clause,[],[f1828,f3573]) ).
fof(f3573,plain,
( spl0_75
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1828,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
fof(f3571,plain,
spl0_74,
inference(avatar_split_clause,[],[f1827,f3568]) ).
fof(f3568,plain,
( spl0_74
<=> class_OrderedGroup_Osemigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1827,axiom,
class_OrderedGroup_Osemigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).
fof(f3566,plain,
spl0_73,
inference(avatar_split_clause,[],[f1826,f3563]) ).
fof(f3563,plain,
( spl0_73
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1826,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).
fof(f3561,plain,
spl0_72,
inference(avatar_split_clause,[],[f1825,f3558]) ).
fof(f3558,plain,
( spl0_72
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1825,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).
fof(f3556,plain,
spl0_71,
inference(avatar_split_clause,[],[f1824,f3553]) ).
fof(f3553,plain,
( spl0_71
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1824,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3551,plain,
spl0_70,
inference(avatar_split_clause,[],[f1822,f3548]) ).
fof(f3548,plain,
( spl0_70
<=> class_HOL_Otimes(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1822,axiom,
class_HOL_Otimes(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).
fof(f3546,plain,
spl0_69,
inference(avatar_split_clause,[],[f1821,f3543]) ).
fof(f3543,plain,
( spl0_69
<=> class_HOL_Oplus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1821,axiom,
class_HOL_Oplus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).
fof(f3541,plain,
spl0_68,
inference(avatar_split_clause,[],[f1820,f3538]) ).
fof(f3538,plain,
( spl0_68
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1820,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).
fof(f3536,plain,
spl0_67,
inference(avatar_split_clause,[],[f1819,f3533]) ).
fof(f3533,plain,
( spl0_67
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1819,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3531,plain,
spl0_66,
inference(avatar_split_clause,[],[f1816,f3528]) ).
fof(f3528,plain,
( spl0_66
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1816,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3526,plain,
spl0_65,
inference(avatar_split_clause,[],[f1815,f3523]) ).
fof(f3523,plain,
( spl0_65
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1815,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3521,plain,
spl0_64,
inference(avatar_split_clause,[],[f1814,f3518]) ).
fof(f3518,plain,
( spl0_64
<=> class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1814,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
fof(f3516,plain,
spl0_63,
inference(avatar_split_clause,[],[f1813,f3513]) ).
fof(f3513,plain,
( spl0_63
<=> class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1813,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
fof(f3511,plain,
spl0_62,
inference(avatar_split_clause,[],[f1812,f3508]) ).
fof(f3508,plain,
( spl0_62
<=> class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1812,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
fof(f3506,plain,
spl0_61,
inference(avatar_split_clause,[],[f1810,f3503]) ).
fof(f3503,plain,
( spl0_61
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1810,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3501,plain,
spl0_60,
inference(avatar_split_clause,[],[f1807,f3498]) ).
fof(f1807,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3496,plain,
spl0_59,
inference(avatar_split_clause,[],[f1806,f3493]) ).
fof(f3493,plain,
( spl0_59
<=> class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1806,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
fof(f3491,plain,
spl0_58,
inference(avatar_split_clause,[],[f1805,f3488]) ).
fof(f3488,plain,
( spl0_58
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1805,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3486,plain,
spl0_57,
inference(avatar_split_clause,[],[f1804,f3483]) ).
fof(f3483,plain,
( spl0_57
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1804,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3481,plain,
spl0_56,
inference(avatar_split_clause,[],[f1803,f3478]) ).
fof(f3478,plain,
( spl0_56
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1803,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3476,plain,
spl0_55,
inference(avatar_split_clause,[],[f1802,f3473]) ).
fof(f3473,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1802,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3471,plain,
spl0_54,
inference(avatar_split_clause,[],[f1801,f3468]) ).
fof(f3468,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1801,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3466,plain,
spl0_53,
inference(avatar_split_clause,[],[f1800,f3463]) ).
fof(f3463,plain,
( spl0_53
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
fof(f3461,plain,
spl0_52,
inference(avatar_split_clause,[],[f1799,f3458]) ).
fof(f3458,plain,
( spl0_52
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3456,plain,
spl0_51,
inference(avatar_split_clause,[],[f1798,f3453]) ).
fof(f3453,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1798,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3451,plain,
spl0_50,
inference(avatar_split_clause,[],[f1797,f3448]) ).
fof(f3448,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1797,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3446,plain,
spl0_49,
inference(avatar_split_clause,[],[f1796,f3443]) ).
fof(f3443,plain,
( spl0_49
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1796,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3441,plain,
spl0_48,
inference(avatar_split_clause,[],[f1795,f3438]) ).
fof(f3438,plain,
( spl0_48
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1795,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3436,plain,
spl0_47,
inference(avatar_split_clause,[],[f1794,f3433]) ).
fof(f3433,plain,
( spl0_47
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1794,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3431,plain,
spl0_46,
inference(avatar_split_clause,[],[f1793,f3428]) ).
fof(f1793,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3426,plain,
spl0_45,
inference(avatar_split_clause,[],[f1792,f3423]) ).
fof(f3423,plain,
( spl0_45
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1792,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3421,plain,
spl0_44,
inference(avatar_split_clause,[],[f1791,f3418]) ).
fof(f3418,plain,
( spl0_44
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1791,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3416,plain,
spl0_43,
inference(avatar_split_clause,[],[f1790,f3413]) ).
fof(f3413,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3411,plain,
spl0_42,
inference(avatar_split_clause,[],[f1789,f3408]) ).
fof(f3408,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1789,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3406,plain,
spl0_41,
inference(avatar_split_clause,[],[f1788,f3403]) ).
fof(f3403,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1788,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3401,plain,
spl0_40,
inference(avatar_split_clause,[],[f1787,f3398]) ).
fof(f3398,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1787,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3396,plain,
spl0_39,
inference(avatar_split_clause,[],[f1786,f3393]) ).
fof(f3393,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1786,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3391,plain,
spl0_38,
inference(avatar_split_clause,[],[f1785,f3388]) ).
fof(f3388,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3386,plain,
spl0_37,
inference(avatar_split_clause,[],[f1784,f3383]) ).
fof(f3383,plain,
( spl0_37
<=> class_HOL_Ozero(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1784,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
fof(f3381,plain,
spl0_36,
inference(avatar_split_clause,[],[f1783,f3378]) ).
fof(f3378,plain,
( spl0_36
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1783,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3376,plain,
spl0_35,
inference(avatar_split_clause,[],[f1782,f3373]) ).
fof(f3373,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1782,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3371,plain,
spl0_34,
inference(avatar_split_clause,[],[f1781,f3368]) ).
fof(f3368,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1781,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3366,plain,
spl0_33,
inference(avatar_split_clause,[],[f1780,f3363]) ).
fof(f3363,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1780,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3361,plain,
spl0_32,
inference(avatar_split_clause,[],[f1779,f3358]) ).
fof(f1779,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3356,plain,
spl0_31,
inference(avatar_split_clause,[],[f1778,f3353]) ).
fof(f3353,plain,
( spl0_31
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1778,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3351,plain,
spl0_30,
inference(avatar_split_clause,[],[f1777,f3348]) ).
fof(f3348,plain,
( spl0_30
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1777,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3346,plain,
spl0_29,
inference(avatar_split_clause,[],[f1776,f3343]) ).
fof(f3343,plain,
( spl0_29
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1776,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3341,plain,
spl0_28,
inference(avatar_split_clause,[],[f1775,f3338]) ).
fof(f3338,plain,
( spl0_28
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1775,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3336,plain,
spl0_27,
inference(avatar_split_clause,[],[f1774,f3333]) ).
fof(f3333,plain,
( spl0_27
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1774,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3331,plain,
spl0_26,
inference(avatar_split_clause,[],[f1773,f3328]) ).
fof(f3328,plain,
( spl0_26
<=> class_HOL_Otimes(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1773,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
fof(f3326,plain,
spl0_25,
inference(avatar_split_clause,[],[f1772,f3323]) ).
fof(f3323,plain,
( spl0_25
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1772,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3321,plain,
spl0_24,
inference(avatar_split_clause,[],[f1771,f3318]) ).
fof(f3318,plain,
( spl0_24
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1771,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3316,plain,
spl0_23,
inference(avatar_split_clause,[],[f1770,f3313]) ).
fof(f3313,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1770,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3311,plain,
spl0_22,
inference(avatar_split_clause,[],[f1769,f3308]) ).
fof(f3308,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1769,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3306,plain,
spl0_21,
inference(avatar_split_clause,[],[f1768,f3303]) ).
fof(f3303,plain,
( spl0_21
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1768,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3301,plain,
spl0_20,
inference(avatar_split_clause,[],[f1767,f3298]) ).
fof(f3298,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1767,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3296,plain,
spl0_19,
inference(avatar_split_clause,[],[f1766,f3293]) ).
fof(f3293,plain,
( spl0_19
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1766,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3291,plain,
spl0_18,
inference(avatar_split_clause,[],[f1765,f3288]) ).
fof(f3288,plain,
( spl0_18
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1765,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3286,plain,
spl0_17,
inference(avatar_split_clause,[],[f1764,f3283]) ).
fof(f3283,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1764,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3281,plain,
spl0_16,
inference(avatar_split_clause,[],[f1763,f3278]) ).
fof(f3278,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1763,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3276,plain,
spl0_15,
inference(avatar_split_clause,[],[f1762,f3273]) ).
fof(f3273,plain,
( spl0_15
<=> class_HOL_Oplus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1762,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
fof(f3271,plain,
spl0_14,
inference(avatar_split_clause,[],[f1761,f3268]) ).
fof(f3268,plain,
( spl0_14
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1761,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3266,plain,
spl0_13,
inference(avatar_split_clause,[],[f1760,f3263]) ).
fof(f3263,plain,
( spl0_13
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1760,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3261,plain,
spl0_12,
inference(avatar_split_clause,[],[f1759,f3258]) ).
fof(f3258,plain,
( spl0_12
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1759,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3256,plain,
spl0_11,
inference(avatar_split_clause,[],[f1758,f3253]) ).
fof(f3253,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1758,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3251,plain,
spl0_10,
inference(avatar_split_clause,[],[f1757,f3248]) ).
fof(f3248,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1757,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3246,plain,
spl0_9,
inference(avatar_split_clause,[],[f1756,f3243]) ).
fof(f3243,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1756,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3241,plain,
spl0_8,
inference(avatar_split_clause,[],[f1755,f3238]) ).
fof(f3238,plain,
( spl0_8
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1755,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3236,plain,
spl0_7,
inference(avatar_split_clause,[],[f1754,f3233]) ).
fof(f3233,plain,
( spl0_7
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1754,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3231,plain,
spl0_6,
inference(avatar_split_clause,[],[f1753,f3228]) ).
fof(f3228,plain,
( spl0_6
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1753,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3226,plain,
spl0_5,
inference(avatar_split_clause,[],[f1752,f3223]) ).
fof(f3223,plain,
( spl0_5
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1752,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3221,plain,
spl0_4,
inference(avatar_split_clause,[],[f1751,f3218]) ).
fof(f3218,plain,
( spl0_4
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1751,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3216,plain,
spl0_3,
inference(avatar_split_clause,[],[f1750,f3213]) ).
fof(f3213,plain,
( spl0_3
<=> class_HOL_Ominus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1750,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
fof(f3211,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f2784,f3208]) ).
fof(f2784,axiom,
c_0 != v_c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3206,plain,
spl0_1,
inference(avatar_split_clause,[],[f2786,f3203]) ).
fof(f2786,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ANA012-1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 15:30:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (24418)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.47 % (24421)WARNING: value z3 for option sas not known
% 0.22/0.47 % (24419)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.47 % (24420)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.47 % (24422)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.47 % (24421)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)
% 0.22/0.47 % (24424)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)
% 0.22/0.47 % (24423)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)
% 0.22/0.47 % (24425)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.81/0.70 TRYING [1]
% 4.94/1.14 TRYING [2]
% 6.56/1.38 % (24423)First to succeed.
% 6.56/1.38 TRYING [1]
% 7.06/1.44 % (24423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24418"
% 7.06/1.44 % (24423)Refutation found. Thanks to Tanya!
% 7.06/1.44 % SZS status Unsatisfiable for theBenchmark
% 7.06/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 7.17/1.48 % (24423)------------------------------
% 7.17/1.48 % (24423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.17/1.48 % (24423)Termination reason: Refutation
% 7.17/1.48
% 7.17/1.48 % (24423)Memory used [KB]: 18086
% 7.17/1.48 % (24423)Time elapsed: 0.955 s
% 7.17/1.48 % (24423)Instructions burned: 2257 (million)
% 7.17/1.48 % (24418)Success in time 1.102 s
%------------------------------------------------------------------------------